KABB: Knowledge-Aware Bayesian Bandits for Dynamic Expert Coordination in Multi-Agent Systems
Authors: Jusheng Zhang
Zimeng Huang
Yijia Fan
Ningyuan Liu
Mingyan Li
Zhuojie Yang
Jiawei Yao
Jian Wang
Keze Wang
Venue: ICML 2025 poster (2025)
Keywords: LLM
Agent
Primary area: deep_learning->large_language_models
TL;DR: LLM,Agent

Abstract: As scaling large language models faces prohibitive costs, multi-agent systems emerge as a promising alternative, though challenged by static knowledge assumptions and coordination inefficiencies. We introduce Knowledge-Aware Bayesian Bandits (KABB), a novel framework that enhances multi-agent system coordination through semantic understanding and dynamic adaptation. The framework features three key innovations: a customized knowledge distance model for deep semantic understanding, a dual-adaptation mechanism for continuous expert optimization, and a knowledge-aware Thompson Sampling strategy for efficient expert selection. Extensive evaluation demonstrates KABB achieves an optimal cost-performance balance, maintaining high performance while keeping computational demands relatively low in multi-agent coordination.

KABB: Knowledge-Aware Bayesian Bandits for Dynamic Expert Coordination in Multi-Agent Systems
Jusheng Zhang"! 1 Zimeng Huang" 11
Yijia Fan
Ningyuan Liu'
Mingyan Li Zhuojie Yang' Jiawei Yao?
Jian Wang? Keze Wang 145
Abstract
is prohibitively expensive and often requires retraining on datasets comprising trillions of tokens.
As scaling large language models faces pro- hibitive costs, multi-agent systems emerge promising alternative, though challenged by static knowledge assumptions and coordination inefficiencies. We introduce Knowledge-Awan Bayesian Bandits (KABB), a novel framework that enhances multi-agent system coordination through semantic understanding and dynamic adaptation. The framework features three key innovations: customized knowledge distance model for deep semantic understanding, a dual- adaptation mechanism for continuous expert optimization, and a knowledge-aware Thomp- son Sampling strategy for efficient expert selec- tion. Extensive evaluation demonstrates KABB achieves an optimal cost-performance balance, maintaining high performance while keeping com- putational demands relatively low in multi-agent coordination.
Multi-Agent Systems (MAS) (Guo et al., 2024) offer promising alternative by coordinating multiple specialized agents to achieve superior performance compared to individ- ual systems while maintaining manageable computational costs and budgets. Recent advances in MAS have led to the development of several frameworks. For example, the Mixture of Agents (MoA) (Wang et al., 2025) employs mul- tiple LLMs as proposers iteratively refine responses, with central aggregator delivering the final output. Although MoA has demonstrated robustness and scalability in deploy- ment, its computational cost scales linearly with the number of agents, and significant redundancy and noise become a problem. For example, on datasets like MATH (Hendrycks et al., 2021), weaker models in the ensemble often interfere with the aggregator's decisions, leading to incorrect results (see Figure 1).
Alternatively, Mixture of Experts (MoE) frameworks (Gong et al., 2024; Zhang et al., 2024; Wang et al., 2024a; Tang et al., 2024), in the context of multi-agent systems, focus on fostering collaboration among domain-specific experts, enabling the integration of diverse responses across fields. This approach reduces redundancy and noise, but is often limited to predefined tasks. A fundamental limitation of both frameworks lies in their reliance on static knowledge assumptions, making them ill-suited to address dynamic changes in expert capabilities or the emergence of novel concepts. These limitations highlight deeper challenges in MAS, particularly in areas such as knowledge understand- ing, response integration, and dynamic adaptability.
1. Introduction
With the rapid advancement of large language models (LLMss, their applications have expanded to complex tasks such as cross-domain knowledge integration and multistep decision-making. Although many LLMS (Achiam et al., 2023; Liu et al., 2024; Adams et al., 2024; Team et al., 2024; Bai et al., 2023) demonstrate impressive versatility in vari- ous tasks through techniques such as in-context learning and instruction-uuning, their performance remains constrained by factors such as model size and the limitations of train- ing data (Jiang et al., 2023; Lu et al., 2024a; Zhang et al., 2025). Scaling these models further to improve performance
The increasing complexity of real-world scenarios re- quires systems that can adaptively select relevant knowl- edge domains and identify the optimal combination of ex- perts. Multi-Armed Bandit (MAB) algorithms (Mahajan & Teneketzis, 2008) have emerged as a powerful tool for tackling such dynamic decision problems. By striking a bal- ance between "exploration" (discovering new expert com- binations) and "exploitation" (leveraging known successful strategies). MAB can continuously optimize system perfor-
Equal contribution 'Sun Yat-sen University University of Washington "Snap Inc. "Peng Cheng Laboratory Guangdong Key Laboratory of Big Data Analysis and Processing, Guangzhou. Correspondence to: Keze Wang <kezewangee @ gomi..com>>
Proceedings of the 4nnd International Conference Machine Learning. Vancouver, Canada. PMLR 267, 2025. Copyright 2025 by the author(s).

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
integrating concept overlap, dependency path optimization, and dynamic historical performance evaluation. Specifically, expert capabilities and task requirements are represented as vectors, with concept overlap calculated using enhanced co- sine similarity, dependency path lengths optimized through hierarchical knowledge relationships, and historical feed- back dynamically adjusted via an adaptive time-decay factor. These components are unified into a comprehensive distance metric, further refined with deep learning techniques op- timize the weight parameters.
_ 90 3 1
What is greatest integer less than or equal
User
MoA
WessUM y Boza
Let's thaie stop byskey The arowee is
Propurrs
Oecar Talkut
lere than
eoprosution willl
The greneet trzeger less of equatio
Second, we develop dual adaptation mechanism to support continuous expert optimization and knowledge evolution. This mechanism employs Bayesian parameter updates with exponential time decay to mitigate the influence of outdated data while dynamically adjusting key metries within the knowledge graph, such as concept overlap and historical performance. This ensures that expert capabilities remain adaptive to the evolving demands of tasks in real-time.
The proteed Intggr lese thanor eg
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KArrsOurs)
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Finally, we design a knowledge aware Thompson sampling strategy to improve computational efficiency in expert se- lection. By incorporating the knowledge distance metric into the Beta distribution sampling process, our strategy enables efficient identification of the top-k experts for dy- namic decision decision-making This approach demonstrated signif- icant improvements in performance and cost efficiency on leading datasets like AlpacaFvall 2.0 (Dubois et al., 2024). Additionally, a two-stage knowledge graph graph-guided response integration process ensures logical consistency by detecting semantic conflicts and enhancing contextual coherence, thus substantially reducing contradictory output.
Math Solaties Eqpart
Jassec Sa.
Figure 1. Comparison of MoA and KABB (Ours) on solving mathematical problem: MoA's aggregator is misled by conflicting weaker proposals, resulting in an incorrect answer, while KABB employs knowledge-aware approach to drive related experts and arrive at the correct solution.
mance. However, traditional MAB approaches rely solely on historical feedback(Diao et al., 2025), often overlooking the semantic relationships between tasks and experts.
Together, our innovations enable the KABB framework to effectively address the challenges of dynamic expert co- ordination, offering a scalable, adaptive, and semantically informed solution for multi-agent systems in complex real- world scenarios.
To bridge this gap, knowledge graphs (Ge et al., 2024) pro- vide compelling framework for representing and leverag- ing these semantic connections. By structuring expert capa- bilities and task requirements as interconnected knowledge networks, knowledge graphs enable: (1) precise modeling of dependencies across knowledge domains, (2) dynamic tracking of expert capabilities over time, and (3) identifi- cation of knowledge gaps in task-solving pathways. This structured representation not only enhances the accuracy of expert selection but also provides semantic-level guid- ance for response integration. Together, these advancements pave the way for more adaptive, efficient, and semantically informed multi-agent collaboration systems.
2. Related Work
2. Large Language Model Ensemble
The ensemble of large language models (LLMs) has emerged as an effective strategy to leverage the complemen- tary strengths of different models and improve performance across diverse tasks. Early approaches primarily focused on combining outputs from multiple models through tech- niques like reranking probability distribution averaging. For instance, Jiang al. (2023) proposed PAIRRANKER for pairwise output comparisons and GENFUSER for gen- erating improved responses by synthesizing multiple candi- dates. Similarly, Huang et al. (2024) explored output fusion by averaging probability distributions, while FrugalGPT (Chen et al., 2023) introduced cost-efficient cascading mechanism that allocates tasks dynamically across LLMs
In this work, we propose the Knowledge- Awwre Bayesian Bandits (KABB) framework to significantly enhance the co- ordination capabilities of multi-agent systems through three core innovations. First, we introduce a customized knowl- edge distance model grounded in deep semantic understand- ing, which surpasses traditional keyword-baad -aase methods by
2

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
reduce computational overhead. These methods highlight the potential of ensembling to amplify individual model capabilities while addressing computational constraints.
cent advances in KG representation address challenges like entity and relation heterogeneity using multisource hierar- chical neural networks (Jiang et al., 2024). KG embed- dings have been explored with models like M2GNN and DGS using mixed-curvature spaces to capture hierarchical and cyclic patterns (Wang et al., 2021; Iyer et al., 2022). Yang et al. (2023) proposed a contextualized KG embed- ding method combining neighbor semantics and meta-paths to improve explainability in talent training course recom- mendations. Temporal aspects of KGs have been addressed through Large Language Models-guided Dynamic Adapta- tion (LLM-DA), which combines LLMs' temporal reason- ing capabilities with dynamic rule adaptation (Wang et al., 2024b).
Beyond simple output aggregation, recent research has shifted toward more dynamic and adaptive frameworks for LLM collaboration. bixture-of-Agente (MoA) (Wang et al., 2025) exemplifies this trend by introducing iterative refine- ment processes where multiple LLMs serve distinct roles, such as generating and refining responses through multi- layered agent interactions. This approach emphasizes the importance of both diversity and performance in model se- lection, demonstrating that combining heterogeneous mod- els often yields superior results compared to homogeneous ensembles. Additionally, routing-basse methods, such as those proposed by Wang et al. (2024a) and Shnitzer al. (2023), optimize efficiency by dynamically selecting the most suitable model for given input, while ZOOTER (Lu et al., 2024b) further refines this concept by distilling model expertise without requiring full inference for all candidates. These advancements highlight the progress in LLM ensem- ble techniques, focusing on efficiency and quality. Building on this, we propose a framework that integrates knowledge- aware mechanisms to improve adaptability and semantic coherence in multi-agent systems.
3. Method
This chapter presents the Knowledge-Aware Bayesian Multi- Armed Bandits (KABB) framework for solving the ex- pert selection problem in multi-agent collaborative systems. Our dual adaptation mechanism combines (1) Bayesian Parameter Adaptation uuing exponential time decay to weight recent interactions for setting the Beta distribution parameters- and (2) Knowledge Graph whohution-which continuously updates concept relationships and team syn- ergy based on task outcomes.
2.2. Multi-Armed Bandit for Decision Optimization
We begin by defining the problem space and identifying key gaps in classical approaches with respect to knowledge representation and dynamic adaptability. Building upon this foundation, we propose dynamic Bayesian optimiza- tion strategy that incorporates knowledge-driven decision mechanisms, synergy-based distance metrics, and robust theoretical guarantees. Through detailed analysis and illus- trative examples, we demonstrate that the KABB framework achieves both improved exploration efficiency and stronger convergence properties, thereby providing a new paradigm for multi-agent collaboration and expert team formation.
The
Bandit (MAB) framework balances explo- ration and exploitation in sequential decision- making under uncertainty. Classical algorithms like UCB and Thompson Sampling excel in recommendation and resource alloca- tion, while Contextual Bandits and adaptive methods refine decision decision-making in dynamic settings (Li et al., 2010), Re- cent advances integrate Large Language Models (LLMs) to reduce learning regret and enhance decision-making by leveraging pre-trained knowledge (Alamdari et al., 2024).
Bandit- based reinforcement learning frameworks further aid retrieval in knowledge-intene intensive tasks (Tang et al., 2025). In- novations in clustering and transfer learning have improved MAB efficiency across applications like clinical trials and recommendation systems (Qi et al., 2025; Sharma & Sug- gala, 2025). These developments highlight the importance of semantic understanding and adaptation, aligning with the Knowledge-Aware Bayesian Bandits (KABB) framework introduced in this paper.
3.1. System Architecture
The overall decision-making process of the KABB system (see Figure 2) consists of several key steps:
1. Task Reception and Concept Extraction: The sys- tem receives a user-input task T and employs natural language processing techniques to parse the task into a concept requirement vector d' E RR]! where C is predefined set of concepts.
2.3. Knowledge Representation and Graph-based Learning
Research in knowledge representation and graph-based learning has centered on knowledge graphs (KGs) as a foundational framework. KGs serve as powerful structures for encoding complex, muchine-readable relationships be- tween entities (Wang et al., 2017; Hogan et al., 2021). Re-
Expert Capability Mapping: Each expert (i.e., dif- ferent LLMs) is represented by an ability vector V. R reflecting its expertise across various concepts. Multiple LLMs are thus mapped into an expert set E {e1, Ee1,e2....,e.
3

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
User Prompt
Semantic Matching
Task Difficulty
000 COO
Rogeetss
Concepts
Expert
Dependency Relation
Capability
Final Output
Knowledge Distance
000 .eo
Expert
Concepts
Export
Aggrogator
Complementarity
Mapping
o0O
Concepts
Expert
Historical Effectiveness
Dynamic Bayesian MAB
1000
Expertici
Performance
Conceptal
Experbb.
Feedback
Beta Distribution
Token
Allocation Layer
Concept Layer
Expert Layer
Aggregation Layer
Figure KABB framework combines knowledge graph embeddings, team synergy metrics, dynamic Bayesian MAB algorithms to enable efficient expert team selection and adaptation. In this example, the user prompt is mapped to the top-2 concepts from the set C, the top-4 relevant experts are selected to respond. An aggregator then synthesizes their outputs to generate the final response.
3. Expert Subset Selection: The optimal expert sub- set S, S is identified through a knowledge-aware Thompson sampling process that leverages both the task requirement vector d' and expert capability vec- tors Ve. This process integrates dynamic Bayesian MAB algorithm with the knowledge distance metric Dist(S, t) to maximize task success probability. Se- lected experts in S, independently process task T", after which an aggregator synthesizes their responses through semantic conflict detection and weighted in- formation fusion generate the final output.
3.2. Knowledge Distance and Complementarity Multi-Agent Teams
better characterize the collaborative properties of multi- agent teams (expert subset), we extend the knowledge dis- tance metric from individual experts to expert subsets, in- troducing the concepts of team synergy and conflict. The knowledge distance metric Dist(S, t) serves core com- ponent of the KABB model, integrating five key dimensions of information: task difficulty, semantic matching, depen- dency relations, team complementarity. and historical effec- tiveness. These dimensions are balanced through learnable weights. The formal definition is given as follows:
4. Performance Feedback and Model Update: The sys- tem collects performance metries (c.g.. success rates and user ratings) for each task completion. These feed- back signals are used to update the Bayesian model parameters and 8, enhancing the accuracy and adapt- ability of future decisions.
Definition 3.1 (Knowledge Distance Function). The knowl- edge distance metric Dist(S, t) integrating five dimensions is formally defined as:
|Rap (Rap(S,)) (S,t)
(Sst(S, log(1 de) difically scaing
Povetua (S, +w2
K
somontic mestorch
depondaac
Through this pipeline, the KABB system achieves a closed- loop process from task parsing to expert selection and an- swer aggregation, ensuring precise alignment between task requirements and expert capabilities while continuously im- proving decision-ne makiing efficiency and effectiveness.
(1 (1- (1-Bs(()) twos (1 Synergy(S)
Hidtrical effertitnn
sorn cow.rpeeeennttty
(4)
where de the task difficulty coefficient based on knowl- edge graph topology depth, w = [W) W2 W33 wa] are

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
learnable weight parameters satisfying Σi= W/ 1, Povertu((S - [Ca is the Jaccard similarity between the expert subset S and task t, [Ras((,))] is the number of dependency edges between expert subset and task in knowledge graph, K = |&] is total expert count, Hs(() is average historical success rate of expert subset, and Synergy(S) E [0, 1] quantifies team complementarity where higher values indicate stronger collaboration and less conflict within the team.
mance while identifying the best-matched expert teams for incoming tasks.
[cs.C,,
Dynamic Beta Distribution Modeling and Parameter Evolution. We model the success probability of an expert subset S at time step t using a time-varying Beta distribu- tion:
Beta as ,,5'
where the parameters are updated dynamically according to the following equations:
The following theorem ensures the consisteney and ratio- nality of knowledge distance when measuring multi-agent team collaboration, thereby enhancing the reliability and effectiveness of the model in expert selection and task allo- cation.
(1+1) 0g
KM(S,)) 6
knondadge mucterg rewad
(5)
g(++1)
6 KM(S()) ())
Theorem 3.2 (Pseudo-Metric Properties of Knowledge Dis- tance). The knowledge distance function Disi(S,,) t) satisfies the following pseudo-metric properties:
semantic matching
Here (M(S,t)
Synergy (S) is composite
Poverlap
synergy gain
knowledge matching index, , = e e- (k > 0) is expo- nential time decay factor, and á represents prior distribution correction strength per unit knowledge matching.
Non-negativity: For any expert subset S and task t, Di O.
Conditional Symmetry: If the dependency graph G is undirected and Povertap (S1, f) = Pooverup (S2, t), and if S₁ and S2 are symmetric in terms of knowledge and dependencies. then St, Dist( (0,t(S,,tt t).
Joint Knowledge- Mewwledge-iim--eanee Time-Team Sampling Strategy. To guide the expert subset selection, define comprehen- sive confidence function 0 which incorporates historical performance, knowledge distance, time decay, and team synergy:
Approximate Triangle Inequality: There exists a con- stant e 2 such that
Dist(S1, 1) S c(Dist(S1, 82) + Disi(S2,,) 0)
lawwlii dianne Disti
coneag diten Syneegyrisy
[eta]
exp
By incorporating team complementarity, the knowledge distance measures not only external team-task matching but also internal team synergy, enabling multi-dimensional adaptability assessment.
exp (-x korl de) [ ennde
(Dnuer Contenre) 18108-
where B(0 is the Beta distribution expecta- tion, reflecting the team's historical performance, exp (->- log(1 + de) Ei W,V,,
3.3. Dynamic Bayesian Multi-Armed Bandit (MAB) Algorithm Derivation for Multi-Agent Systems
the knowl- edge distance penalty, V are the four sub-indicators defined in Equation (4), and Synergy(S)
To effectively select the most suitable expert subset for specific tasks in expert systems remains a key challenge. Traditional MAB algorithms (e.g., UCB (Behari et al., 2024; Guo & Yang. 2021), Thompson Sampling) rely solely historical feedback for Docision-making However, these methods face two significant limitations in practice: (1) they fail to account for the dynamic nature of expert performance over time, and (2) they overlook the critical alignment be- tween task requirements and the knowledge structure of expert teams. To address these issues, we propose a Dy- namic Bayesian MAB framework that integrates knowledge distance metrics, team complementarity, and temporal de- cay mechanisms into Bayesian inference. This framework establishes a joint optimization objective, enabling dynamic adjustment of expert subset selection strategies. As a result, the system can rapidly adapt to changes in expert perfor-
[ Eerezes C)y((;;, is the synergy effect quantifying team collaboration via the synergy gain coefficient Cayn.
Convergence Analysis of Dynamic Selection Strategy
Theorem 3.3 (e-Approximate Optimal Convergence). For any E > 0, there exists parameter configuration (X",n", ,,") such that algorithm's 's cumulative regret within T steps satis- fies:
T = Σ t=1
R(T)
(1) (00
5-
[
S ET +0 (VTlogT) (7)
5

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
4. Experiments
uration. It noteworthy that KABB selects only experts to respond instruction, while MoA requires 6 proposers, which shows the cost efficiency of KABB. Although KABB does not surpass Deepseek-RI (80.1%), this is expected, as not all responses the system involve Deepseek contribu- tions. Importanll, KABB w/o Deepseek outperforms both the open-source models inside the system and proprietary models including GPT-4 Omni. Similarly, KABB-Single- LLaMa3 surpasses LLaMa-3-70B-Imm collaboration and specialization in KABB enhance over- all performance. These results confirm that its ability to dynamically route queries to specialized experts and aggre- gate their responses effectively contributes to this strong alignment.
In this section, we detail the experimental setup, present the main results, and provide an in-depth analysis of KABB.
4.1. Experimental Setup
Models. To construct the default configuration of KABB, we use 6 open-source models' including Qwen2-72B- Instruct (Bai et al.. 2023), LLaMa-3--0B-IInsruuc (Adams al., 2024), Mt-2arLLM-2-8x222 (Xu al., 2024), Gemma- 2-27B (Team al., 2024), Deepseek-V? V3 (Liu et al., 2024), and Deepseek-Rl R1 (Guo et al., 2025). Twelve knowledge con- cepts and 24 experts are defined, and the models are evenly distributed across these experts using tailored prompts to specialize their expertise, resulting in a straightforward yet effective multi-agent system. By default, the system dynam- ically routes queries to top-3 experts from top-2 knowledge concepts. Following the insights from MoA (Wang et al., 2025), we designated Qwen2-72B Innstrruutt as the aggrega- tor. Two variants are also developed: KABB w/o Deepseek, which excludes the Deepseek- V3 and Deepseek-RI models from the system, and AABB-Single-LLaMal which em- ploys only LLaMa-3-70B-Instree the aggregator.
illustrating that
MT--enchh KABB achieves state-of-the-art average score of 9.60, maintaining top-tier performance in multi-turn dia- logue. KABB w/o Deepseek (9.47) exceeds GPT-4 Turbo (9.31). While individual models already perform exception- ally well on this benchmark, KABB's 's collaborative design with dynamic expert routing secures a leadership position, reinforcing robustness multi-turn interactions.
FLASK-Hard. KABB demonstrates strong performance in twelve skill-specific metrics (see Figure 3), surpassing or matching MoA and GPT-4 in two-thirds of the categories, particularly robustness, correctness, common sense, insight, metacognition, and readability. Notably, KABB outper- forms MoA in metacognition, reflecting its ability to reason and adapt effectively. However, KABB lags slightly in con- ciseness, producing more detailed outputs. This trade-off highlights KABB's emphasis thoroughness over brevity.
both the experts and
Benchmarks. The evaluation mainly uses AlpacaEval 2.0 (Dubois et al., 2024) with 805 instructions that reflect real- world cases. The model outputs are directly compared to those of the GPT-4 Preview (11/06), with a GPT-4-based evaluator determining the preference probabilities. The length-controlles (LC) win rate is adopted to eliminate po- tential length biases?. We also assess performance MT- Bench (Zheng et al., 2023) and FLASK-Hard (Ye et al., 2024). FLASK-Hard, the 89 most difficult instances in FLASK, provides a detailed evaluation of twelve skill- specific categories. For reasoning and problem-solving tasks, the results on Arena-Hard, MATH, and BBH are reported in Appendix D.
robustness
harmlessness
correctness
conciseness
efficiency
4.2. Main Results
readability
factuality
We analyze the performance of KABB and its variants across AlpacaEval 2.0, MT-Bench, and FLAS- Hard. de- tailed comparison with baseline models and their ablations provides insights into its effectiveness and robustness.
metacognition
commonsense
AlpacaEval 2.0 focuses on measuring alignment with hu- man preferences. The results, as shown in Table 1, highlight that KABB achieves a leading LC win rate of 77.9%, mark- ing a 9.8% improvement over MoA under the same config-
completeness
comprehension
insightfulness
Qwen2-72B-Instruuct
GPT-4
MoA KABB
"Inference was conducted using the Together Inference End- point:
Figure 3. Results on FLASK-Hard where use the default KABB setup with 6 models and Owen2-70B-Instruue as the aggregator. We include the results of GPT-4, (rem2-72B-Instrucce and MoA with the same 6 proposers and aggregator for comparison.
"This metric closely approximates human judgment, boasting a Spearman correlation of 0.98 when compared to actual human evaluations (Dubois et al., 2024).
6

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
AlpacaEval 2.0
MT-Bench
Model
LC win. (%)
win. (%)
Avg.
1st turn
2nd turn
KABB
77.9
72.3
9.65
9.85
9.45
MoA
68.1
65.4
9.41
9.53
9.29
KABB w/o Deepseek
62.4
66.7
9.47
9.58
9.35
GPT-4 Omni (05/13)
57.5
51.3
9.19
9.31
9.07
JPT-4Tuuhh (04/09)
55.0
46.1
9.31
9.35
9.28
GPT-4 Preview (11/06)
50.0
50.0
9.20
9.38
9.03
GPT-4 (03/14)
35.3
36.1
8.84
9.08
8.61
Qwen2-72B-Instruet
38.1
29.9
9.15
9.25
9.05
Gemma-2-27B
44.9
33.2
9.09
9.23
8.95
Wiza:dLMM-2-8x2BB
51.3
62.3
8.78
8.96
8.61
KABB-Singie-LLaMa
34.7
36.2
9.16
9.10
9.23
LLaMa-3-70B-Instruut
34.4
33.2
8.94
9.20
8.68
Deepseek-V2
67.2
69.3
9.51
9.59
9.42
Deepseek-RI
80.1
75.4
9.30
9.40
9.20
Table 1. Comparison of different models on AlpacaEval 2.0 and MT-Bench. MoA (with 2 layers) shares the same model configuration with KABB, where different proposers are in the first layer and aggregator the second. For AlpacaEval 2.0, the performance of GPT-4 variants, LLaMa-3-70BB Instruct,, and Dwwen--72B-Instenn
AlpacaEval 2.0 are sourced from public leaderboards; WizardLM-2-8x220 Gemma-2-275 AlpacaEval
results come from (Wang et al., 2025). We reproduced results Deepseek- V3, Deepseek-RI, MT-Bench, we conducted evaluations to obtain turn-based scores, except for the results of GPT-4 variants, ----------nstttucc, and WizardI M-2-8x22B, which are from (Wang al., 2025).
4.3. WHAT MAKES KABB EFFECTIVE?
Method
LC win.
RAS
PWRS
We analyze KABB's effectiveness by comparing different routing strategies.
KA (MAB) (Ours)
62.4
94.16
60.19
CL (MAB)
60.9
92.92
57.34
KA (A2C)
60.2
91.61
54.38
We replaced our Knowledge-Aware (KA) routing mecha- nism with a classifier- routing (CL) approach. To be specific, We replaced our Knowledge-Aware (KA) routing mechanism with classifier-based routing (CL) approach. The CL mechanism uses Sentence-BERR to encode both the instruction and the expert's knowledge concept into vec- tor representations. Cosine similarity then calculated between these vectors, and the expert with the highest simi- larity score is selected.
KA (PPO)
57.3
90.43
56.07
KA (MCTS)
54.8
87.95
51.74
Table 2. Comparison of different methods on LC win rate of Al- pvcaEval 2.0, RAS, PWRS metrics. experiments were conducted AlpacaEval 2.0. The system dynamically routes queries the top-3 experts derived from top-2 knowledge concepts. All model configurations align with the KABB w/o Deepseek (see Section 4.1).
Several optimization algorithms including PPO (Schulman et al., 2017), MCTS (Šwiechowski et al., 2022), and A2C (Mnih et al., 2016) are also compared with our MAB algo- rithms.
pendix A. As shown in Table 2, the KA mechanism with MAB achieves best overall performance, demonstrat- ing strong alignment with human preferences and expert output quality. Among optimization methods, MAB con- sistently outperforms PPO, MCTS, and A2C, underscoring its effectiveness in balancing exploration and exploitation. KA with MAB also outperforms CL by notable margin. This demonstrates that incorporating knowledge-awarent is critical for achieving optimal alignment with human pref- erences and expert output quality.
For more nuanced evaluation that considers both the hu- man preference for routing decisions and the relative per- formance advantage of the chosen experts, we introduce two metrics: Routing Alignment Score (RAS) for hu- Weighted Rout- ing Score (PWRS) incorporating output quality with hu- man preference. Detailed definitions are provided in Ap-
man annotation consistency and Preference-Weighted

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
4.4. Budget and Consumption Analysis
Num Swietes Exnerts
Vode Tyre GPT Sories
DeepSeee
KABB
Singlo Model
Hydel Series
$0
DespS smb-t1
win A Apacativll 2.0
70-
KABB
DeapSeet-V3
Single Model
Wi Rate on Aip aepaeEve 2.0 1%0
of Selected Experts
60
DeesSeok-V3
Mot
Grsto
GPF-40
Gemma-2-270
M:2222
6PT-6-11.0 previww
40-
22mmm-222m
Lamb 3-708-3miinu
450
Avg. TELOPS AlpacaEval
Uama 3:00 instruct
GPI4
0.000
8.002
0004
0.005
0.008
0.010
0.012
0.014
Figure 5. The trade-off between performance and computational cost (average TFLOPS, also used as proxy for latency). The ac- tual tslops of GPT-4 are unknown, so we use the rumored size from the community of an 8x220B architecture. The precise TFLOPS for GPT-4 remains undisclosed; therefore, we estimate it based on community speculation suggesting 8x220B architecture.
Cost per Instruction on Alpaca Eval 2.0
Figure 4. Performance trade-off versus cost. Our experiments use default configurations to evaluate KABB's average cost per instruc- tion on AlpacaEval 2.0, calculated from expert routing statistics and public API pricing". By routing instructions specific experts rather than all models, KABB effectively lowers costs. For in- stance, even with expensive models like DeepSeek-R1, unsuitable instructions are directed to cheaper experts, optimizing both cost and performance.
Tilops Consumption. Figure 5 shows that KABB excels at maintaining high performance while keeping computa- tional demands relatively low, even as the model scales with more experts or larger architectures. Unlike MoA models, which encounter diminishing scalability due to increased TFLOPS, KABB demonstrates efficient resource utilization. This highlights the scalability and costteffectiveness of our approach relative to alternative architectures. Additionally, by using TFLOPS as an approximate indicator of latency, we highlight the efficiency of our approach. While inference endpoint latency isn't 't solely determined by TFLOPS fac- tors like batching strategies and server load also play a role we leverage TFLOPS as a reasonable proxy for gauging the inherent computational burden of each model. pro- vides a valuable, albeit theoretical, measure of the resources model demands, allowing for relative comparison of computational intensity between different architectures.
Cost Effectiveness. In Figure 4, we plot the LCC Win Rate of KABB and several baseline models on AlpacaEval 2.0 against their inference costs. The chart shows the trade-off between cost and performance across models. Our plots depict a Pareto frontier that optimally balances performance and cost. We demonstrate that the KABB systems are po- sitioned along or close to this frontier. Our experiment illustrates that KABB, by dynamically adjusting the number of experts, is significantly more cost-effective than other models. Compared to GPT-4o, GPT-4 Turbo, and GPT-4 (11/06) Preview, KABB achieves higher LC Win Rates at lower costs. With 3, 5, or experts, KABB performs sim- ilarly DeepSeek-R1, and with experts, achieves the highest LCC Win Rate the lowest cost in that tier. For cost-sensitive scenarios, KABB with fewer experts offers better quality than GPT-4o at lower prices. With just one expert, KABB improves LC Win Rate by about approxi- mately 10% over GPT-40 at half the cost. Compared to the previous MoA model, KABB provides a much better cost-pett pest-performance balance, requiring only 1/7 of the cost to achieve a similar LC Win Rate.
5. Conclusion
This work introduces Knowledge- Bayesian Bandits (KABB), a novel framework that significantly advances multi-agent system coordination through three key innova- tions: customized knowledge distance model, dual adap- tation mechanism, and knowledge-aware Thompson sam- pling strategy. Extensive evaluations demonstrate KABB's superior performance across multiple benchmarks. Ablation experiments validate the effectiveness the Knowledge- Aware mechanism and our MAB strategy. It is also verified
'For open source models, the price information is from https:/wwww.oogchhrrripiiigcgg for GPT-4 models, we use https://openai.ce http://poenaiicom//a/ap/pccceoee as price details. API prices are obtained on January 20, 2025.
8

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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
that KABB is capable of addressing the challenges of dy- namic expert coordination while maintaining computational efficiency, requiring fewer experts than baseline approaches. Our framework provides promising direction for develop- ing more adaptive and semantically-inornee multi-agent systems, though future work could focus on optimizing output conciseness while maintaining response quality.
Methods in Natural Language Processing, EMNLP 2024, Miami, FL,, USA, November 12-16, 2024, pp. 19821-19833, Association for Computational Linguis- tics, 2024. URL https:/ https///aaaaattotoooooo . 2024. emn commlp-maiii 1..main.111. 1107..
Bai, J., Bai, S., Chu, Y., Cui, Z., Dang, K., Deng, X., Fan, Y., Ge, W., Han, Y., Huang, F., et al. Qwen technical report. arXiv preprint ar arvi:22309. 16609, 2023.
Discussion. The KABB framework advances interpretable and trustworthy AI systems through three transparent com- ponents: knowledge distance metric for expert selection rationale, a graph-guided response integration process for reasoning paths, and a dual adaptation mechanism for leamn ing evolution. These transparent features are crucial for re- sponsible AI development as systems become increasingly complex and widely deployed.
Behari, N., Zhang, E., Zhao, Y. Taneja, A., Nagaraj, D., and Tambe, M. A decision decision-language model (DLM) for dy- namic restless multi-armed bandit tasks in public health, In Globersons, A., Mackey, L., Belgrave, D.,, Fan, A., Pa- quet, U., Tomezak, J. M., and Zhang, C. (eds.), Advances in Neural Information Processing Systems 38: Annual Conference on Neural Information Processing Systems 2024, NeurIPS 2024, Vancouver, BC, Canada, December 10 15, 2024, 2024.
Acknowledgments
This work was supported in part by the National Natural Sci- ence Foundation of China (NSFC) under Grant 62276283, in part by the China Meteorological Administration's ' Science and Technology Project under Grant CMAJBGS202517, in part by Guangdong Basic and Applied Basic Research Foundation under Grant 0023A1515012995 in part by Guangdong- Kong-Macas Greater Bay Area Mete- orological Technology Collaborative Research Project un- der Grant GHMA2024704, and in part by Fundamental Research Funds for the Central Universities, Sun Yat-sen University under Grant 23hytd006.
Chen, L., Zaharia, M., and Zou, Frugalgpt: How to use large language models while reducing cost and improving performance. arXiv preprint arXiv:2305.05/76, 2023.
Diao, X., Zhang, C.,, Wu, W., Ouyang, Z., Qing, P., Cheng, M., Vosoughi, S., and Gui, J. Temporal working memory: Query-guided segment refinement for enhanced multi- modal understanding. In Findings of the Association for Computational Linguistics: NAACL 2025, 2025.
Dubois, Y., Galambosi, B., Liang, P., and Hashimoto, T. B. Length-controlled alpacaeval: A simple way to debias automatic evaluators. arXiv preprint arXiv:2404.0m 04455, 2024.
Impact Statement
This paper presents work whose goal is to advance the field of Machine Learning. There are many potential societal consequences of our work, none of which we feel must be specifically highlighted here.
Ge, X., Wang, Y. C.,, Wang, B., Kuo, C.-C. J., et al. Knowl- edge graph embedding: An overview. APSIPA Transac- tions Signal and Information Processing, 13(1), 2024.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
A. Details of Method Comparison
In this section, we provide detailed explanations the configurations used in our experiments for comparison, including the routing mechanisms, optimization algorithms, and evaluation metrics.
A.1. Routing Mechanisms and Optimization Algorithms
Classifier-Based (CL) Routing: We replaced our Knowledge-Aware (KA) routing mechanism with a classifier- based routing (CL) approach. The CL mechanism uses Sentence- BERT encode both the instruction and the expert's 's knowledge concept into vector representations. Cosine similarity then calculated between these vectors, and the expert with the highest similarity score is selected.
Proximal Policy Optimization (PPO): A reinforcement learning algorithm that updates policies in stable and efficient manner. It was applied to optimize expert selection by training policy network to maximize routing performance.
Monte Carlo Tree Search (MCTS): MCTS is employed to explore potential expert selections by simulating multiple decision paths and backpropagating scores from the outcomes. This algorithm particularly useful for decision-making in environments with large search spaces.
Advantage Actor-Critic (A2C): A2C combines the actor-critic framework with an advantage function to improve policy updates. The actor selects experts, while the critic evaluates the quality of these decisions, enabling more efficient learning.
A.2. Metries to Evaluate Routing Quality
We provide detailed definitions and formulations for the two metries used to evaluate the performance of the routing strategies: Routing Alignment Score (RAS) and Sileerence-Weightee Routing Score (PWRS).
1. ROUTING ALIGNMENT SCORE (RAS)
The Routing Alignment Score (RAS) measures the degree to which the router's ' expert selection aligns with human expert annotations. quantifies the consistency between the router's decisions and the ground truth labels provided by human annotators.
C N
RAS
where C' denotes the number of routed experts that align with human preferences and N denotes the total number of routed experts (in this case: 805 x 2).
To establish reliable ground truth labels, we engaged a panel of 7 domain experts with 3+ years of experience in Al system evaluation. Each expert independently annotated 1,610 routing instances (805 instruction-expert pairs 2 routing paths) through a two-phase process:
Human Evaluation Protocol
Calibration Phase: Experts jointly reviewed 200 samples to establish annotation guidelines and resolve edge cases.
Final Annotation: The remaining 1,410 instances were randomly distributed (200 instances per expert) with 10% overlap for inter-anootaoor agreement calculation.
We achieved substantial agreement with Fleiss' x = 0.78, calculated on the overlapping samples. Final labels were determined through majority voting.
The RAS provides basic measure of alignment between the router's decisions and the ground truth, reflecting the accuracy of the routing mechanism in selecting the most appropriate experts.
A.2.2. PREFERENCE- TREFFRENCE-WEIIHTERR WEIGHTED ROUTING SCORE (PWRS)
The Preference- Werereence-Weightedd Routing Score (PWRS) extends traditional routing accuracy metrics by incorporating human preference scores derived from the AlpacaEval 2.0 evaluation framework. This metric weights routing decisions based on the quality of the expert outputs as judged by human evaluators. The PWRS is defined as follows:
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
PWRS Σi (pi-c)) ci)
where represents the preference score from AlpacaBval 2.0 for the routed expert's output, C; is the numher of routed experts that align with human preferences, and N denotes the total number of routed experts.
Preference Score Integration The AlpacaEval 2.0 scores were obtained from a separate group of 15 crowdworkers following the standardized evaluation protocol. Each output was rated by 3 distinct evaluators using a 7-point Likert scale across three dimensions: helpfulness (actionable solutions). accuracy (factual grounding), and coherence (logical flow). Discrepancies exceeding 2 points triggered expert review, with final scores normalized using Bradley-Terry pairwise comparison models. These preference scores enable the PWRS transcend binary routing accuracy by weighting decisions according the relative quality of expert outputs, where higher weights correspond to outputs demonstrating stronger alignment with human-judged quality dimensions.
The PWRS thus provides dual-aspect evaluation: it preserves the fundamental routing correctness measurement through expert selection alignment, while simultaneously quantifying the performance advantage gained through preference-aware routing decisions.
B. Supplementary Experimental Validation and Analysis
B.1. Performance Evaluation
In order to perform comprchensive and controlled performance evaluation, selected two representative tasks from the BIG-bench Hard (BBH) dataset: commonsense reasoning (550 samples) and logical reasoning (600 samples). The reasons for choosing these two tasks are: (1) they effectively validate the core capabilities of the model; (2) they have clear evaluation criteria; (3) the sample size is moderate, which facilitates sufficient multi-round cross-validation. this experiment, we compare KABB with MoA and its lightweight version MoA-lite. Three key metrics were used for evaluation: (1) Knowledge matching F1 score, computed using BERT calculate the semantic similarity between expert capabilities and knowledge graph concepts (threshold of 0.75); (2) Path prediction accuracy, based on standard knowledge dependency paths, with a perfect match scoring full points, a path length difference of < 1 and key node matches scoring 0.5 points; (3) Historical performance prediction accuracy, using the dynamic weight a/ + 33) (where and 3 represent the number of successful and failed tasks, respectively), with a prediction error < 0.1 considered correct. The experimental results are shown in Table 3:
The performance of the three models on key metrics as follows:
Evaluation Metric
KABB
MoA
MoA-lite
MoA
lite
Knowledge Matching Fl (%)
86.5
71.2
46.8
+15.3%
+39.7%
Path Prediction Accuracy (%)
84.9
69.5
44.2
+15,4%
+40.7%
Historical Performance Prediction (%)
85.2
70.1
45.5
+15.1 1%
+39.7%
The experimental results show that KABB significantly outperforms the baseline models on all key metrics. Compared to the standard MoA, KABB shows an average improvement 15.3% across all indicators; compared the lightweight MoA-lite, the improvement reaches 40%. This performance enhancement primarily attributed to the knowledge-aware attention mechanism and dynamic path prediction strategy that we proposed. Notably, KABB exhibits stronger generalization ability in the commonsense reasoning task, validating the effectiveness of our knowledge-enhanced approach.
B.2. Parameter Sensitivity Analysis
This section explores the impact of three key parameters in the KABB framework- fannework-kkowledgee distance threshold, time decay factor, and efficiency metric-on system performance. The experiment uses the BBH dataset (commonsense reasoning 580 samples, logical reasoning 570 samples), with standard MoA and MoA-lite as baselines, and evaluates parameter sensitivity using a controlled variable approach. The evaluation metrics used are: knowledge matching F1 score, reasoning accuracy, and response efficiency. The experiment tests different values for the knowledge distance threshold [0.55-0.95] and time decay factor [0.2-1.0].
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
B.2.1. KNOWLEDGE DISTANCE THRESHOLD
Parameter Value
Knowledge Matching FI (%)
Reasoning Accuracy (%)
Efficiency Metric (%)
0.55
72.3
74.8
68.2
0.65
83.8
85,4
79.5
0.75
94,9
94.9
92.8
0.85
87.5
88.2
84.3
0.95
78.7
82.7
73.6
Analysis: When the threshold is set to 0.75, the system achieves the highest values in knowledge matching FI score, reasoning accuracy, and efficiency metric, reaching 94.9%, 94.9%, and 92.8%, respectively. A lower threshold (e.g., 0.55) introduces too many irrelevant experts, leading decline in knowledge matching and reasoning accuracy, while a higher threshold (e.g., 0.95) makes the expert selection too strict, reducing system coverage and efficiency.
B.2.2. TIME DECAY FACTOR
Parameter Value
Knowledge Matching F1 (%)
Reasoning Accuracy (%)
Efficiency Metric (%)
0.2
75.1
78.3
71.4
0.4
85.4
87.2
82.6
0.6
94,9
94,9
92.8
0.8
88.2
90.3
85.7
1.0
82.7
86.5
78.9
Analysis: When the time decay factor is set to 0.6, the system performs optimally across all metrics, indicating good balance between utilizing historical experience and dynamic adaptability. smaller factor (e.g.. 0.2) makes the system overly dependent short-term fluctuations, reducing stability, while larger factor (e.g., 1.0) suppresses adaptability to recent performance.
C. Effect of the Number of Selected Concepts and Experts.
Our empirical analysis KABB's architectural configurations reveals the critical interplay between the number of selected concepts and experts (see Figure 6). The results demonstrate that performance varies substantially across different configurations, with win rates ranging from 56% 81%. Notably, configuration of 2 concepts with experts achieves optimal performance under constrained computational resources, while expanding to 3 concepts with 6 experts yields the highest observed win rate of 81%.
Our findings indicate that configurations utilizing or more experts, combined with a moderate-to-large concept space, consistently outperform alternatives. This suggests that both the expert capacity and the conceptual representation space play crucial roles determining system effectiveness. Interestingly, the relationship between expert count and performance exhibits non-linear characteristics configurations with moderate numbers of experts (3-6) already achieve robust perfor- mance levels, suggesting efficient utilization of multi-expert collaboration. This observation has important implications for pesource-performance optimization in practical deployments.
D. Evaluations on Reasoning and Problem-Solving Tasks
D.I. Benchmarks
For reasoning and problem-solving tasks, We evaluate using three benchmarks: BBH (Suzgun et al., 2023), MATH (Hendrycks al., 2021), and Arena-Hard (Zheng et al., 2023).
BBH (Big-Bench Hard) is challenging subset of the BIG-Bench benchmark that tests advanced reasoning capabilities. Includes diverse tasks in mathematical reasoning, logical deduction, and commonsense inference, evaluating models' generalization and complex problem-solving abilities.
MATH is a specialized assessment for AI mathematical capabilities. Features competition-level problems across algebra, number theory, combinatorics, and geometry. Includes detailed solutions for comprchensive evaluation of reasoning depth and computational accuracy.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
85
80
LC win rate on Alpaca Evall 2.0
75
65
60
Selected Cancepts
55
Selected Concepts
Selected Concepts
Selected Concepts
50
GPT-4 Preview (11/06)
GPT-4 Omni (05/13)
1
2
Num of Selected Experts
Figure 6. Relationship between the number of selected experts and selected concepts, and the AlpacaEval 2.0 LC Win Rate.
Arena-Hard is a collection of 500 challenging problems from public leaderboards and research papers, covering program- ming, mathematics, and logical reasoning.
D.2. Experiment Setup
For BBH and MATH, we designated -LLMa-3-70B-Insttue and Srren2-72B-Instruun as the experts and Qwen2-72B-Insn Innssructt as the aggregator to construct simple but effective multi-agent system, with one concept and one expect selected for instruction.
For karda-Hard, we evaluate KABB w/o Deepseek and KABB-Single-LLaMMa All models are evaluated under controlled environment with fixed hyperparameters to ensure fairness.
the default configuration of KABB with the six open-source models (see Section 4.1). Additionally,
D.3. Results and Analysis
Model
BBH
MATH
KABB
84.2
59.8
MoA
81.8
57.3
Qwen2-72B- 12B-IIntruutt
82.4
51.1
81.0
42.5
Table 3, Performance comparison on BBH and MATH benchmarks.
Table 3 presents the performance of KABB and baseline models on the BBH and MATH benchmarks. KABB achieves the highest performance on both benchmarks, surpassing MoA by +2.4% on BBH and +2.5% on MATH. The significant gain on MATH highlights the effectiveness of structured multi-agent approach in handling complex mathematical reasoning tasks.
Table 4 reports model performance on the Arena-Hard benchmark. KABB demonstrates competitive performance (74.8%) but falls behind GPT-4 models in this benchmark. The Deepseck-RI model achieves the highest score (92.3%), indicating its strong generalization capabilities. The KABB-Single- 1aB--inngee-LLMaa3 outperforms Single LLaMa---70B-Instte Instruutt by 4.8%. Removing Deepseek models (KABB w/o Deepseck) significantly reduces performance (-12.0%), confirming their critical role the system.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Model
Arena-Hard win. (%)
KABB
74.8
MoA
74.3
KABB w/o Deepseek
62.8
GPT-4 Omni (05/13)
79.2
GPT-4 Turbo (04/09)
82.0
GPT-4 Preview (1//
GPT-4 (03/14)
50,0
Qwen2-72B-Instee Instruct
46,9
Gemma-2-201
57.5
WizardLM-2-8x22B
71.3
SABB-SSngle-LLLaaa
51.4
I.aaMa-3-7BB-Inttuu
46.6
Deepseek-V3 V3
85.5
Deepseek-RI
92.3
Table Arena-Hard benchmark results for different models. Performance data for GPT series, LLaMA, and WizardL comes from (Wang et al., 2025), DeepSeek models from their technical reports (Guo et al., 2025; Liu et al., 2024), and other models from public leaderboards.
It is noteworthy that MoA achieved similar performance to ours. In the context of well-defined problem-solving tasks (such programming and mathematical problem-solving! empirical evidence suggests that multi-agent architectures may encounter specific limitations. The integration of multiple agents can potentially introduce operational redundancies and decisional interference, which may adversely impact the system's 's capacity to converge on correct solutions or generate opti- mal outputs. This presents a notable challenge in domains where problem spaces are closed and solutions are deterministic. Appendix E includes a case when some models produce low-quality answers on Arena-Hard.
E. Case Study
We present case study in this section to analyze how are the different experts and models are selected, and how different experts and models generate responses. For clarity of comparison, we use KABB w/o Deepseek and set the number of selected experts as four. We report the score of their intermediate outputs as well as the final response. Due to the length of the responses, we have selected key fragments for clarity and brevity. To illustrate how the aggregator synthesizes the final output, we highlight similar expressions between the proposed responses and the aggregated response using underlined text in different colors.
Table 5 showcases the responses generated by four selected experts, along with the final aggregated response provided by the aggregator model, Qwen2-72B 1-2B-Instuct Two of the experts' responses got high preference score over 0.99, which demonstrates that MABB succeeded in selecting qualified experts. The aggregated response achieves the highest preference score, reflecting a well-balanced synthesis of key elements from all proposers. The aggregated output successfully combines the most relevant and salient points from all proposed responses, demonstrating the aggregator's 's ability to synthesize diverse perspectives into cohesive and comprehensive answer. This process highlights the collaborative nature of the models and their collective contribution generating high-quality answers.
To be specific, the selected experts- Interaciion Analyst, Dialogue Specialist, Humanities Scholar, and Cultural Inter- preter-bring distinctive perspectives and areas of specialization, which collectively contribute to the richness and depth of the final aggregated output. The Interaction Analyst ensures factual accuracy and provides foundational details, while the Dialogue Specialist focuses on clarity and narrative flow, making the response accessible to broad audience. The Humanities Scholar adds historical and cultural context, enriching the response with connections to societal trends, and the Cultural Interpreter offers reflective insights, emphasizing the sociocultural dynamics behind Superman's 's creation. By combining these complementary perspectives, the aggregator produces response that balances factual precision, narrative coherence, cultural depth, and interpretive richness. This selection of experts ensures multidimensional and high-quality final response.
Table 6 highlights a challenge in incorporating multiple experts for response generation: although diverse perspectives can broaden the scope of the output, they risk diluting the core information with excessive and redundant details. In this case, the inclusion of too many experts led loss of focus and reduced the practicality of the final response, despite offering more
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
expansive view of the topic. The selected experts each contributed their specialized perspectives. However, this diversity introduced significant overlap and irrelevant details. As result, the aggregated response, though comprehensive, lacked the specificity and clarity needed for practical implementation. This case underscores the importance of carefully curating expert involvement based on the specific requirements of the task. For highly technical prompts, prioritizing experts with deep implementation knowledge and minimizing the number of experts is essential to ensure clarity, focus, and actionable results.
Addtionally, our enror analysis for the query "What type of soil is suitable for cactus" (see Table and Table 8) revealed two key failure cases:
Inappropriate Domain Expert Selection: KABB initially selected a team without the necessary botanical expertise (e.g.. Humanities Scholar and Cultural Interpreter), leading to very low scores.
Partial Recovery Through Team Expansion: By including an Analysis Expert with broader scientific knowledge, the aggregator effectively weighted this high-quality input (preference score 0.89), improving the final response score 0.91. This demonstrates our system's ability to leverage better contributions even if the initial selection is suboptimal.
We focus on overall system performance because a slight increase in expert numbers can largely mitigate the impact of single misselection.
F. Additional Experimental Settings
Resources. All experiments on KABB are conducted on servers with one NVIDIA GeForce RTX 3090.
F.1. Prompts for Experts and the Aggregator
In this section, we provide some cases of prompts for different experts and the aggregator to show an example of the system configuration.
Analysis Expert
You are an expert in problem analysis and logical reasoning, skilled in applying analytical frameworks and systematic thinking approaches.
Your expertise includes breaking down complex problems, identifying key factors, and recommending structured, actionable solutions.
You are familiar with various problem-solving methods such root cause analysis, decision matrices, and scenario evaluation, and adapt your approach based on the unique context of each task.
Consider how your skills in critical thinking, structured reasoning, and analytical mooblem-solving might provide valuable insights or strategies for addressing the task at hand.
Strategy Expert
You are a business strategy expert with a deep understanding of markets, business models, competitive landscapes, and strategic planning.
Your expertise includes applying business frameworks, analytical tools, and market insights to identify opportunities and craft strategies.
While capable of providing comprehensive strategic analysis, you adapt your input to focus what is most valuable, practical, and relevant for the situation.
Consider how your expertise in business innovation, competitive advantage, and strategic problem-solving might provide insightful and actionable recommendations for any task.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Aggregator
You are the Wise Integrator in a multi-agent system tasked with delivering accurate, coherent, and actionable responses to user queries.
Your role is to:
Understand the user's intent and main question(s) by carefully reviewing their query.
Evaluate expert inputs, preserving their quality opinions while ensuring relevance, accuracy, and alignment with the user's s needs.
Resolve any contradictions or gaps logically, combining expert insights into a single, unified response.
Synthesize the most appropriate information into a clear, actionable, and user-friendly answer.
Add your own insight if needed to enhance the final output.
Your response must prioritize clarity, accuracy, and usefulness, ensuring it directly addresses the user's needs while retaining the value of expert contributions.
Avoid referencing the integration process individual experts.
G. Supplementary Proofs and Theoretical Analysis
To better illustrate the theoretical derivations and implementation details regarding the Knowledge-Aware Bayesian Bandit (KABB) model in Section 3, we provide the following supplementary proofs and theoretical analysis.
G.1. Proof of Pseudo-Metric Properties of Knowledge Distance Theorem
We provide proof' of Pseudo-Metric Properties of Knowledge Distance Theorem Theorem 3.2 which enhances the reliability and effectiveness of the model in expert selection and task allocation.
Proof. This follows directly from the non-negativity of log(1 + d,) and all other terms in the definition of Dist(S, t). Each term (e.g.. 1 Poverlap dependency complexity, etc.) is non-negative by construction.
Proof of Conditional Symmetry: If the dependency graph is undirected and Poverlup (S,,t) = Povertap t), and S and S2 are symmetric in terms of knowledge and dependencies, then all terms in the distance function (e.g., Reepp. H.s and weights) are equal for S and Sz. Thus, Dist(S,, t) Dist(S,, t).
Proof of Approximate Triangle Inequality: Using the properties of the knowledge graph a metric space, the subadditivity of the graph metric ensures that the dependency-based terms satisfy a triangle inequality. Similarly, the Jaccard similarity used in Lemma G.2. Combining these with the weight terms, the inequality holds with a relaxation factor e 2 determined by the extrema of the weights.
G.2. Proof Sketch of Convergence Analysis for the Dynamic Selection Strategy
The proof of convergence is outlined as follows:
1. Stability of Beta Distribution Parameters: Analyze the stability of the Beta distribution parameter evolution by leveraging KL divergence to quantify changes over time.
2. Lyapunov Function Construction: Construct Lyapunov function
v(t) Σ [[a 0)) + -
and use to demonstrate the convergence of the parameters.
3. Cumulative Regret Analysis: Establish an upper bound for cumulative regret by applying UCB (Upper Confidence Bound) principles.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
G.3. The Strict Proof of the Approximate Triangle Inequality for Theorem 2 Step 1: Decomposition of Knowledge Distance Function and Subterm Analysis For any expert teams Si, S2, S3 and task t, there exists constant
0, such that the knowledge distance function satisfies:
Si t) = log(1 + de)
V
where V, corresponds to the four subterms that key the multi-dimennionall distance measurement between the expert team and the task:
V/1 Povertap (S,
(semantic mismatch term)
2/2 Rdop (So t)]
(dependency complexity term)
K
1/ 1 H((()
(historical performance term)
4 Synergy(S) (team complementarity term)
The proof demonstrates that by establishing the approximate sub-additivity of the subterms and combining the logarithmic term properties, the knowledge distance function satisfies the approximate triangle inequality within the error bound e max ε1, E2, E3, 64, providing theoretical guarantee for algorithm design.
Step 2: Sub-additivity Analysis of Semantic Mismatch Term (Based Jaccard Similarity)
Definition G.1 (Jaccard Similarity). For any sets St, S2 and task concept set Ct, define:
CS Cc
Poverlap (Stt)
CCs C.]
Lemma G.2 (Jaccard Sub-additivity). For any St, S2 C E, there exists a constant e₁ 2 1 such that:
1 Poverlap (S, ei [[1 Poverlop
(S1, (overlop(S1,1)) + (1 Poverlap (S2, t))
Proof. By the properties of set operations:
ICs,us, nC, 2 |Cs, nC2l + [Cs, CC [Cs, nCs, ncl
ISsus UC, < CCs, UC + CCs, UC,
Let A = Cs, nC,, = =C, Cc, we get:
[ + |B| IAn B Cs. UC,, + Cs. U.,
Povertap (81 US2,()
By relaxing the denominator to 2 max UCs,, U.I,), we get = 2.
Corollary G.3. (S, U t) (S,, + V (S t)]
This conclusion allows us to effectively estimate and control the semantic differences between expert teams using a simple additive form.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Step 3: Sub-additivity of Dependency Complexity Term in Graph Metries
Definition (Dependency Edge Path Length): The number of dependency edges (Rdep(S, in the knowledge graph satisfies the triangle inequality in graph metries:
RReep (S1, t) S (Reep (S1, + (Rdep t)
where RRoo (S1, S2)l is the number of shortest path edges connecting S1 and S2-
Lemma G.4 (Existence of Relaxation Factor). For any acyclic graph, there exists a constant C2 2 1 such that:
(Reep() S <2 (R S2) + (Rdep ()]
Proof. By graph diameter constraints, set = diam (G) (the diameter of the graph), which is the longest path in terms of edges between any two nodes. The dependency complexity term establishes sub-additivity through the following reasoning: based on graph metric properties, path lengths satisfy the triangle incquality; by the graph's 's diameter constraints, we obtain an upper bound for the relaxation factor; and by normalization, the boundedness of dependency complexity is guaranteed. This property provides a quantifiable theoretical foundation for evaluating team knowledge structures.
Step 4: Approximate Linearity of Team Complementarity Term Definition (Complementarity Decomposition): The team complementarity Synergy(S) satisfies:
Synergy U S2)= 2 Synergy(Si) + Synergy (S2) - Overlap(S1,
where Overlap is the complementarity loss due to knowledge overlap between teams.
Lemma G.5 (Upper Bound of Relaxation). There exists constant c3 2 1 such that:
1 SSn U2) S [(1 Synergy(Si)) + (1 Synergy(S:)))
Proof. Let Overlap(S{,.S.) < min(Synergy(SS) Synergy(S2)) (yypergy(S)),Syneryy(s5)) set C3 = 2.
The construction of the global constant for the knowledge distance: The overall approximate sub-additivity of the subterms in
the knowledge distance function is determined by the set of relaxation factors: semantic mismatch term c₁ = 2. dependency
complexity term = diam(G) G'), team complementarity term C3 = 2, and historical performance term C4 = 1. By using these local relaxation factors, combined with the weights and the logarithmic term of task difficulty, global constant max C wi - log(1 + D max) is constructed. This construction ensures that the overall knowledge distance function satisfics the approximate triangle inequality, providing a theoretical guarantee for the quantitative evaluation of knowledge distance.
G.4. Theorem 1 Proof: Lower Bound of Expert-Task Mutual Information under Semantic Gap
Basic Definitions of Dynamic Multi-Agent Systems
In dynamic multi-agent systems, the interaction between the expert set and the task demand space based on three core assumptions: the Markovian evolution of task demands over time, the conditional independent decomposition of expert selection and tasks, and the decaying mutual information metric with the introduction of discount factor y. This framework is described by the joint distribution
plc, (c.tt.r)= = p(c) II p((tltte))p(ctt.
which characterizes the dynamic relationship between expert knowledge and task demands, providing a theoretical foundation for the subsequent analysis.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Step 2: Time Accumulation Form of Conditional Entropy
The accumulated conditional entropy of expert selection over an infinite time horizon is given by:
(( Jim
H(ET)).
T-o0
After introducing the discount factor y the weighted conditional entropy is:
H( Σ r-1 (((
Step 3: Extension of Fano's Inequality
For each time step 4, apply the classical Fano's Inequality:
H(E(T)) 2 -(E)) l12(P!
where h2) z log (1 2) log(1 x) is the binary entropy function, and P! P(E, ElTi) is the expert selection error rate at time t. When there is no prior knowledge (i.e., T(E; TT)) = 0), we have:
H(E[T)) 2 log K (P(
Step 4: Weighted Summation and Asymptotic Analysis
Substitute Fano's s inequality for the weighted conditional entropy:
(( =
(1(T))
Σ 1-1 log K I(E;T)) hp(
log K [(E:T)
1- (2(()))))
Under the assumption of long-term stability of the dynamic system (lim, p!O) 0), the asymptotic behavior of the error entropy is analyzed. By the convergence of the geometric series sum, it is shown that the weighted error entropy term Σ - hy (P( vanishes the limit. This result simplifies the lower bound of conditional entropy to the form of the difference between the entropy of the expert set and the mutual information:
Z log K
H(
((E:T).
1-7
which provides more concise thcoretical expression for system performance evaluation.
Step 5: Equivalent Form and Semantic Gap Explanation
Multiplying both sides of the inequality by (1 7) yields the final form:
T(E:T)
H(ETT)
2 log K
1 1-7
Conditional Entropy
(Semantic Uncertainty)
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Semantic Gap Limit: As T(E: T) 0+ (when there is semantic connection between experts and tasks), the lower bound of conditional entropy approaches log K, corresponding the maximum entropy of completely random selection.
Exploration Efficiency Bottleneck: The inequality shows that the exploration efficiency of traditional MAB (multi-armed (() When the semantic connection weakens (I )) or task dynamics increase (y 1), the exploration
bandit) is limited by I-n
cost increases dramatically.
G.S. Proof of Knowledge-Drice Driven Information Gain Theorem
1. Baseline Mutual Information Analysis
First, establish the baseline mutual information In I(E:T) when there no knowledge graph, which only depends on the direct association between experts and tasks.
2. Effect of Knowledge Graph Intervention: After introducing the knowledge graph G, the task generation process is reconstructed via the intermediary pattern of the knowledge graph:
= -
3. Mutual Information Gain Decomposition: Using the chain rule, the total mutual information introduced by the knowledge graph can be decomposed into: the original expert-task mutual information I(E;7) and the conditional mutual information contribution from the concept layer I(; T) Since G is fully determined by & and the information gain AI equals the conditional mutual information contribution from the concept layer, verifying that the knowledge graph improves the system's informational efficiency through the concept layer.
G.6. Derivation of the Concept Layer Information Gain Bound
Core Condition Analysis
Based on the two key properties of the knowledge graph: sparsity: the upper bound of the expert-concept association degree d = (C)C)) and balance: the minimum expert coverage of a concept [|]|/[C]]
Information Theoretic Derivation Process
Through the Markov chain - C analysis: Conditional Entropy Relation: H(T 2 H(T(C) (data processing inequality), (TTC) O(log (CI) (task sparsity). Mutual Information Lower Bound: Using the definition of conditional mutual information and the relationship with entropy, along with graph structure constraints, the lower bound is obtained:
log C V
IC: TIE) 2 Ω
This result quantifies the minimum information gain brought by the knowledge graph through the concept layer.
Step 2: Mathematical Representation of Accelerated Exploration Efficiency
(Upper Bound of Exploration Trials): the contextual Bandit framework, the expected number of exploration trials satisfies:
B B[Nesplore] =ō (vV
K Klog log [C|
A/
where = 1E], and AT Ω log [C] Viel
Proof.
Classical Bandit Exploration Complexity: Without knowledge graph, the exploration trials of traditional
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
MAB are:
e[Nexxtore]] O ( K log T
where is the expected reward gap between the optimal and suboptimal arms.
2. Knowledge-Driven Acceleration Mechanism: After introducing the knowledge graph, the reward gap is amplified by the information gain A/:
nnew c. VAT.
Substituting into the classical complexity formula:
K log T
K log T EA
esspppe
O
=0
now
log and assuming c = ((1/VK) (uniform exploration hypothesis), we obtain:
Combining with AT = Ω
V
(
K K log |C|
B[Neepphre] Ō
Al
G.7. Summary of the Information Gain Theorem Proof
By introducing structured knowledge graph through the concept layer C, the conditional mutual information I(;; T(E) provides the lower bound of the information gain A/ Ω
which reduces the exploration complexity from the traditional method of (()) to Ō (Vlog//C) log (i). This theoretical result rigorously verifies the acceleration advantage of knowledge-driven decision-making.
log [C]
G.8. Regret Upper Bound Derivation for Knowledge-Aware UCB (KABB)
Problem Framework Section 3.1 are extended with complete mathematical specifications of expert set & and task sequence (Ti
Selection process: S, at each step
Feedback mechanism: Obtain 0/
Success probability: Including knowledge distance Dist(S, (), time decay A and team synergy Synergy(S).
exp -ist--is(SSs)) Aet Synergy(SS)
(3)
Historical expectation
Confidence Bound Construction This section elaborates the construction method of confidence bounds in the KABB algorithm, the definition of knowledge revision rewards, and their impact exploration weights. It supports the theoretical analysis in Section 3.2 regarding the limitations of traditional methods and the breakthroughs in knowledge-driven decision-making. The confidence-bourr construction extends traditional UCB through knowledge-aware reward correction:
2 log (
UCB
exp (-X Dist(8,())-744 Synergy (8)"
(4)
NO
Empirical mean
Knowledge-driven correction
Exploration term
where (00)
denotes the Bayesian estimate of historical success rate. The correction term adjusts the exploration weights through knowledge distance, time decay, and synergy effects.
as +
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
G.9. Regret Upper Bound Analysis
Total Regret Definition Appendix G.8 provides detailed analysis of the total regret decomposition and single-step regret properties for the KABB algorithm, corresponding the analysis in regarding the impact of team knowledge distance and complementarity algorithmic performance. The theoretical proofs and mathematical derivations presented follows:
The total regret is defined as:
T
R(T) = Σ
(5)
S.
where S" denotes the optimal expert subset and S, represents the selected subset at time step t, the analysis should follow these steps:
1. Characterize Single-Step Regret: First define the single-step regret:
7t 05 g!0 S.
(6)
and analyze its properties.
2. Analyze Regret Bound for Suboptimal Subsets: For any suboptimal subset S * S*, establish the upper bound of single-step regret.
3. Compose Total Regret Upper Bound: Investigate how to combine single-step regrets into the total regret upper bound.
Step 1: Per-Step Regret Decomposition For any suboptimal subset S + S*, the instantaneous regret satisfies:
A
(S Knowledge penalty
Optimal set
Suboptimal
Step 2: Exploration Acceleration Effect
Lemma G.6 (Exploration Count Upper Bound). For any suboptimal S, its selection count satisfies:
E [Ns(T)) (As. cxp(->Ds))² +0 (VTlogT)
8 log T
(8)
where Ds = max, Dist(S, f) and As 0s- 0ss-
Proof. The knowledge correction term exp(-ADg amplifies the reward gap As. thereby reducing the exploration demand inequality, combined with the
for suboptimal subsets. The estimation error is bounded via the exponential decay modification of exploration terms through knowledge distance. This upper bound formula reflects three key factors influencing regret:
Optimality gap term As: The term in the denominator represents the performance gap between suboptimal and optimal subsets. A larger gap leads to a smaller regret upper bound.
Knowledge distance penalty exp(-2XDs): The exponential term in the denominator reflects the impact of the knowledge graph. Larger D (i.e., greater knowledge discrepancy) increases the regret upper bound.
Combinatorial complexity term Oo (K)): Captures the combinatorial optimization nature of the problem, where:
VT T corresponds to the standard UCB term
represents the combinatorial complexity from selecting k experts out of K
This demonstrates that the regret upper bound is jointly determined by the knowledge structure (via Ds) and combinatorial optimization complexity.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
G.10. Core Differences from Classical UCB
Table 9. Comparison between Classical UCB and KABB
Dimension
Classical UCB
Knowledge-Aware UCB (KABB)
Exploration Design
Vlog./1 I/N
Multiplicative knowledge correction
Regret Dominant Term
(VKTTlog logT)
OlyTlog (k)
Theoretical Innovation
No structured prior
Knowledge graph integration
Key Assumption
IID rewards
Non-stationary rewards with synergy
The knowledge-aware UCB improves the traditional O T) regret bound of UCB through structured prior injection and dynamic correction mechanism, transforming into exponentially compressed form in the combinatorial space. The core innovation lies in the quantitative modeling of knowledge distance and synergy effects. This theorem represents the first strict integration of knowledge graphs and team collaboration theory within the Bandit framework.
G.11. Regret Bound and Exploration Efficiency Analysis
This section provides detailed description of the modules of the KABB algorithm, offering in- analysis of its cumulative regret bound and the relationship with exploration efficiency, supporting the algorithm derivation and convergence analysis in Appendix G.9. Additionally, Appendix G. 13 elaborates on the specific implementation modules of the KABB algorithm, along with its time and space complexities, providing empirical foundations and optimization strategies for the algorithm design and performance evaluation in the main text. Theorem G.7 (The cumulative regret R(T) of KABB).
L log(1 + D maxx) (wi tw2 wwy + ww))
AL logo
+0 (VT(M) log (
As = 1ts- 444
R(T) S
where
As
D Dmax max (S,
S45*
S.t
Additional complexity term due team site
k: |
Knowledge-driven exploration term
Explanation: The cumulative regret R(T) measures the performance loss caused by not selecting the optimal team S* over time steps:
Knowledge-driven exploration term: The exploration count is constrained by the knowledge distance. Its dominant
term 41.2 T shows that: 1) when the knowledge distance difference is significant (i.e., Dmax 1), the algorithm quickly
As
focuses high-quality teams through the exp(-XDist())) mechanism; when the team reward gap As the exploration intensity is adaptively adjusted via the log(1 + D mmxx) factor.
Team size complexity term: The complexity term O (VT()) log (+) includes the combination number (7) and its
variation with the expert set size N and optimal team size follows:
SO(N* /k!)
when & N
(N)
1(22
when N/2
G. Proof Framework
Step Reward Remapping
Define dual-modality adjusted reward:
jts lls expp(=DDiss(S,))) Synergy(S))
Knowledge decay
Synergy amplification
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
The knowledge decay term implements soft filtering through exp(->-), while the synergy gain term strengthens the competitive advantage of high-quality teams through the exponent 1j 1.
Step 2: Dynamic Sampling Probability Analysis
Based on the dual-time-scale update rule:
(1+1)
10)
+ + (M(
s
Instant Foodback Knowledge Memory
s
-ar
(1 + 8 (M(),t)
Negative Feedback Knowledge Forgetting
We derive the exponential convergence upper bound for the sampling count:
4T.2 log T
2 Ar
E[Ns(T)) s
E KM(S,T)
D
7
7)
Knowledge-matching driven accelerated convergence term
G.13. Algorithm Implementation and Complexity
Core Implementation Modules
Expert Subset Sampling:
S ThompsonSampling
0s
-exp -xp((ADDst(S,tt) Synergy(S)"
(10)
(1) ((t) ag +
Optimization implementation: The combinatorial space is compressed from O(2 to O N²* strategy.
through a greedy
Dynamic Parameter Update:
(1+1) (t) as a
+ r's + (.KKMS,))) 11==s))
(t)
(I))
((+11) -)>(g() + 1 rs +8. (1 KM(S,))) I(S-S.)
(6)
where I is the indicator function, enabling sparse updates.
Complexity Analysis
*Time Complexity:
T(N,T) o
+T o (
O
((*) log (+)
Initialization compuupttaaiio
Sampling + Evaluation (Per step)
Sorting
(lcP)
Graphi Update (Dijkstra)
T-
((²) log N
(k) + 1
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Space Complexity:
M(N) o ((M)
+ O (1CF²)
+ + (w.
Parameters (a,0)
Knowlodge Graph (Adjacency Matrix)
Sliding Window (Depth W)
o (x)
+ (CP)
(when W < |e
Storage Optimization
Knowledge Graph Compression: Adjacency matrix -> adjacency list, reducing space from O((CP) to O(IC) + (8]).
Parameter Sharing: Share (u: 3) parameters for teams satisfying (i, <e.
Incremental distance updates via streaming updates: Store only ADist instead of the full distance matrix, allowing for more efficient memory usage and reducing computational overhead.
G.14. Summary
The supplementary proofs, through systematic chapter definitions and key point organization, comprehensively support and extend the discussion of the knowledge-driven Dynamic Bayesian Multi-Armed Bandit (KABB) model presented in Section 3. Each supplementary section corresponds to specific part of the main text, covering critical content such as problem definitions, confidence-bound construction, regret-bound analysis, and algorithm and complexity analysis. These sections provide readers with a comprehensive resource for deeply understanding the theoretical foundations and implementation details of the KABB algorithm.
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KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Table 5. Case: Some models produce high-quality answers on AlpacaFval
User Prompt
Who created the Superman cartoon character?
Expert
Model
Preference
Output
Interaction
LLaMa-3-70B-Instie
0.0001 12313
Superman, the iconic cartoon character, was created by writer Jerry Siegel and artist Joe Shuster. They were both high school students in Cleveland, Ohio, when they came up with the idea for the character in 1933....
Analyst
Dialogue Specialist
Qwen2-72B-Instee
0.9998820091 ...
They created Superman in 1933, and the character first appeared in print in Action Comics #1 in June 1938, pub- lished by DC Comics....
Humanities
M-
0.9999975912
...errann quickly became cultural icon and often credited with helping to create the superhero genre as we know today.
Scholar
The character's success led to various adaptations across multiple media, including radio serials, television shows, movies, and-of course coure--nnimatd cartoons.
Cultural Interpreter
Gemma-2-27B-it
0.2356933747
It's a fascinating story that highlights how cultural con- text and collaboration shape creative works. ... If you't d like to delve deeper into any specifie aspect of Super- man's creation, such as the social anxicties of the Great Depression reflected in the character, the evolution of his powers and morality over time, feel free to ask!
Aggregator
Qwen2-72B-Instruee Instruct
0.9999988203
Superman, the iconic cartoon character, was created by writer Jerry Siegel and artist Joe Shuster. The duo, who were high school students in Cleveland, Ohio, came up with the idea for the character in 1933 Superman first appeared in print in Action Comics #1 in June 1938, pub- lished by National Allied Publications, which later hecame DC Comics.
Siegel and Shuster's s creation quickly became cultural icon, leading to various adaptations in comic books, TV shows, movies, and animated cartoons.
Superman's 's creation is story of collaboration, influenced by the cultural context of the 1930s. If you't 'd like to explore any specific aspect of Superman's 's creation or history, feel free to ask!
28

---

KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Table 6, Case: Some models produce low-quality answers Arena-Hard
User Prompt
Write a chrome plugin that saves the contents of the current page.
Expert
Model
Score
Output
Creative Strategist
LLaMa-3-70B- Instructt
GPT
>>
KABB
Al-powered content analysis: Integrate machine learning algorithm that analyzes the saved page's content, providing users with insights, such as keyword extraction, sentiment analysis, or topic modeling.
User
Qwen2-72B-Instree
GPT >> KABB
Content Script: =#eebbbckk ** Provide visual feed- back when the user interacts with the plugin...
Experience
Consultant
Implementation Qwen2-72B-Instrucct
GPT >> KABB
4. **est and iterate**; Conduct thorough testing to ensure the plugin works as intended, and iterate on the design and functionality based on user feedback.
Advisor
Technical Architect
W
GPT KABB
The manifest file should look like this: 'json
inanifest_versionn 3,
"name": "Page Saver Plugin",
Aggregator
Qwen2-72B 72Bt-ntttuctt
GPT KABB
3. **Define Plugin Permissions:** Update 'manifest.json with plugin metadata, per- missions (e.g.. "active'Tab", "downloads"), and content scripts.
Test the plugin in various scenarios to ensure reliabil-
ity.
Implement visual feedback, progress indicators, and error handling.
Incorporate Al-powered content analysis for in- sights or collaboration feature for annotations. Regularly update the plugin with bug fixes and feature enhancements based on user feedback...
Reference
GPT-4 (03/14)
N/A
2. Inside the "SavePageContentt" folder, create new file called "manifest json" and add the following code: 'sson
maniifest version": 2,
"name": "Save Page Content",
Judgment
GPT-4 Preview (11/06)
N/A
GPT's answer is slightly better because it provides actionable code snippets and clear example that users can follow to create the plugin. However, KABB's answer is also of high quality, offering broader overview of the process and additional creative suggestions....
29

---

KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Table Error Analysis
Inappropriate Domain Expert Selection AlpacaEval 2.0
User Prompt
What type of soil is suitable for cactus?
Expert
Model
Preference
Output
Humanities
Qwen2-72B-Instruee
0.0041602948
Cacti are native to arid and semi-arid regions, primar- ily in the Americas, from Patagonia Canada. ... From cultural perspective, the cultivation of cacti in various societies has led the development of specific soil mixes that mimic their native conditions. ... For optimal growth, cacti require soil mix that is well-draining and porous. A common recipe for a cactus soil mix includes a combi- nation of the following components: 1. Pumice or Perlite: Understanding this context can enrich our appreciation of the cactus as both biological organism and cultural symbol.
Scholar
Cultural Interpreter
Gemma-2-27B-it
0.0000614221 Cacti, like many cultural phenomena, have adapted to thrive in very specific conditions. ...For countless gener- ations, Indigenous peoples of the Americas have deeply respected cacti, utilizing them for healing, ceremonies, and everyday purposes. ... Cacti generally prefer well- draining soil that replicates their natural, arid habitats. Think sandy or gritty soils with good acration to prevent root rot, which can be detrimental to these resilient plants.
Aggregator
Civen277B-Innstreeen
0.0180713022 Cacti thrive in soil that closely resembles the arid con- ditions of their native environments. The ideal soil for cacti should have the following characteristics: 1. Good Drainage: Understanding the cultural and historical context of cactus cultivation enriches our appreciation for these plants. Indigenous communities the Americas have long revered cacti for their medicinal, spiritual, and practical uses, and the knowledge of cactus care has been passed down through generations. ... This approach not only reflects scientific understanding but also respects and incorporates traditional ecological wisdom.
30

---

KABB: Knowledge-Aware Bandits in Multi-Agent Systems
Table Error Analysis Partial Recovery Through Team Expansion on AlpacaEval 2.0
User Prompt
What type of soil is suitable for cactus?
Expert
Model
Preference
Output
Analysis Expert
M-2-x2L
0.8940661652
...Cacti are adapted to survive in arid conditions with minimal water, and as such, they require well-draining soil that doesn't retain moisture for extended periods. The ideal soil for cacti typically has the following characteris- ties: 1. Good Drainage .... Gritty Texture ...A common potting míx for cacti might include: 2 parts potting soil By providing the right type of soil and appropriate care, you can create an environment where cacti can thrive.
Humanities Scholar
Qwen2-72B-Insee Ins-rutt
0.0041602948
... Cacti are native to arid and semi-arid regions, primarily in the Americas, from Patagonia Canada. ... .or opti- mal growth, cacti require soil mix that is well-draining and porous. A common recipe for cactus soil mix in- cludes a combination of the following components: 1. Pumice or Perlite: Understanding this context can en- rich our appreciation of the cactus as both a biological organism and a cultural symbol.
Cultural Interpreter
Gemma-2-27B-it
0.0000614121
Cacti, like many cultural phenomena, have adapted to thrive in very specific conditions. ... Cacti generally prefer well-draining soil that replicates their natural, arid habitats. Think sandy or gritty soils with good aeration to prevent root rot, which can be detrimental to these resilient plants.
Aggregator
Qwen2-72B -2B--utttuctt
0.9153241218 Cacti adapted to thrive in environments with limited water and extreme temperatures, primarily found in arid and semi-arid regions. Here are the key characteristics of suitable soil mix for cacti: 1. Well-draining Soil: ... ....rit Texture; ... For gardeners and landscapers, a recommended soil mix for cacti might include a blend of regular potting soil, sand, and perlite. ... Understanding and creating the proper soil conditions for cacti not only supports their growth but also reflects the rich history and cultural significance these plants hold in various societies that have thrived in arid landscapes.
31


Reviews:
[{"review_id": "INKBEEgvR6", "reviewer": "Reviewer_DfAR", "summary": "In this paper, authors propose Knowledge-Aware Bayesian Bandits (KABB), a model that improves multi-agent system coordination through semantic understanding and dynamic adaptation. There are three key contributions in the work: a three-dimensional knowledge distance model for deep semantic understanding, a dual-adaptation mechanism for continuous expert optimization, and a knowledge-aware Thompson Sampling strategy for efficient expert selection. Authors provide various experiment results, as well as their source code.", "questions": "", "limitations": "", "rating": 4, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing our contributions and novelty.\n\n**Q1**: More detailed architecture of KABB in Figure 2\n\n**A1**: Sorry for the confusion. We have refined Figure 2 in the revised paper. Please see our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials?tab=readme-ov-file#overview-of-kabb-updated-figure-2-in-paper).\n\n---\n\n**Q2**: Ablation studies of the KABB's architecture component\n\n**A2**: Thank you very much for your valuable suggestion.  Ablations for architecture components:  [Table s1 in our repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials?tab=readme-ov-file#table-s1-ablation-study-results) shows the detailed contribution of each component of KABB on AlpacaEval 2.0. To further justify the superiority of the Knowledge-Aware module, we replace it with the recently open-sourced SOTA method, i.e., EmbedLLM  [r1], and denote it as EmbedLLM (MAB) for dynamic MAB routing and select the top‑3 experts before integrating their responses using an Aggregator. Combined with the ablation studies presented in the original paper (see Table 2), we believe these additional experiments provide sufficient evidence for the effectiveness of each component of KABB.\n\n---\n\n**Q3**: Moving some contents from the Appendix into the main paper\n\n**A3**: We have refined our paper by organizing more content from the supplementary file. Specifically, we shrink Sec. 4-5 of our paper and move the key findings of Sec. C after Sec. 4.3.\n\n---\n**Q4**: Missing References and Discussions\n\n**A4**: As for the mentioned references, we have refined the related work section by including more discussions about knowledge graphs and fundamental works in knowledge representation learning. \nResearch in knowledge representation and graph-based learning has centered on knowledge graphs (KGs) as a foundational framework. KGs serve as powerful structures for encoding complex, machine-readable relationships between entities (Wang et al., 2017 [r2], Hogan et al., 2021 [r3]). Recent advances in KG representation address challenges like entity and relation heterogeneity using multisource hierarchical neural networks (Jiang et al., 2024 [r4]). KG embeddings have been explored with models like M2GNN and DGS using mixed-curvature spaces to capture hierarchical and cyclic patterns (Wang et al., 2021 [r5]; Iyer et al., 2022 [r6]). Yang et al. (2023) [r7] proposed a contextualized KG embedding method combining neighbor semantics and meta-paths to improve explainability in talent training course recommendations. Temporal aspects of KGs have been addressed through Large Language Models-guided Dynamic Adaptation (LLM-DA), which combines LLMs' temporal reasoning capabilities with dynamic rule adaptation (Wang et al., 2024 [r8]).\n\nThank you for your time and effort in reviewing our paper. Your comments and suggestions are greatly appreciated and have helped us to improve the quality of our work.\n\n---\n\n**References**\n\n[r1] Zhuang, Richard, et al. \"EmbedLLM: Learning Compact Representations of Large Language Models\". The Thirteenth International Conference on Learning Representations, 2025.\n\n[r2] Wang, Quan, et al. \"Knowledge graph embedding: A survey of approaches and applications.\" IEEE transactions on knowledge and data engineering 29.12 (2017): 2724-2743.\n\n[r3] Hogan, Aidan, et al. \"Knowledge graphs.\" ACM Computing Surveys (Csur) 54.4 (2021): 1-37.\n\n[r4] Jiang, Dan, et al. \"Multisource hierarchical neural network for knowledge graph embedding.\" Expert Systems with Applications 237 (2024): 121446.\n\n[r5] Wang, Shen, et al. \"Mixed-curvature multi-relational graph neural network for knowledge graph completion.\" Proceedings of the web conference 2021. 2021.\n\n[r6] Iyer, Roshni G., et al. \"Dual-geometric space embedding model for two-view knowledge graphs.\" Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. 2022.\n\n[r7] Yang, Yang, et al. \"Contextualized knowledge graph embedding for explainable talent training course recommendation.\" ACM Transactions on Information Systems 42.2 (2023): 1-27.\n\n[r8] Wang, Jiapu, et al. \"Large language models-guided dynamic adaptation for temporal knowledge graph reasoning.\" Advances in Neural Information Processing Systems 37 (2024): 8384-8410.", "claims_and_evidence": "The paper presents a lot of novelty, and the formulas are correct. Figure 2 needs to be improved to include more details about the architecture.", "methods_and_evaluation_criteria": "While Thompson Sampling is a known technique, the knowledge graph distance function is interesting as it is integrating several key dimensions including difficulty scaling, semantic mismatch, dependency complexity, historical effectiveness, and team complementarity. \nThe Joint Knowledge-Time-Team Sampling Strategy is also a novel component. \n\nIt would help if the authors could provide some ablation studies indicating the effect that each of their novel architecture components has on overall model performance. I currently do not see this type of analysis in the paper.", "theoretical_claims": "See above.", "experimental_designs_or_analyses": "Experiment results are thorough and show good performance. \n\n(From above section)\n\nWhile Thompson Sampling is a known technique, the knowledge graph distance function is interesting as it is integrating several key dimensions including difficulty scaling, semantic mismatch, dependency complexity, historical effectiveness, and team complementarity. \nThe Joint Knowledge-Time-Team Sampling Strategy is also a novel component. \n\nIt would help if the authors could provide some ablation studies indicating the effect that each of their novel architecture components has on overall model performance. I currently do not see this type of analysis in the paper.", "relation_to_broader_scientific_literature": "There are three key contributions in the work: a three-dimensional knowledge distance model for deep semantic understanding, a dual-adaptation mechanism for continuous expert optimization, and a knowledge-aware Thompson Sampling strategy for efficient expert selection. Authors provide various experiment results, as well as their source code. This work is of interest and relevance to the research community and will help to advance frontiers in machine learning.", "essential_references_not_discussed": "The Introduction and Related work sections are missing discussions about knowledge graphs, and fundamental works in knowledge representation learning. Authors should include this discussion as that is part of their core model and providing this context to the reader is necessary. Some recent works in the domain of knowledge graphs include: \n\n[KDD 2022] Dual-Geometric Space Embedding Model for Two-View Knowledge Graphs. In Proceedings of the 28th ACM SIGKDD Conference on Knowledge Discovery and Data Mining (KDD '22). Association for Computing Machinery, New York, NY, USA, 676–686. https://doi.org/10.1145/3534678.3539350\n\n[WWW 2021] Mixed-Curvature Multi-Relational Graph Neural Network for Knowledge Graph Completion. In Proceedings of the Web Conference 2021 (WWW '21). Association for Computing Machinery, New York, NY, USA, 1761–1771. https://doi.org/10.1145/3442381.3450118", "other_strengths_and_weaknesses": "N/A", "other_comments_or_suggestions": "N/A", "questions_for_authors": "See above sections.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "PZ4v6Zy9dV", "reviewer": "Reviewer_ymVy", "summary": "This paper proposes a graph-guided router based on the knowledge-aware Thompson sampling strategy for the mixture of agents. The methods and experiments have their merits but still lack some key comparisons and discussions.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for your valuable time and insightful comments.\n\n**Q1**: Trying LLM-based representations in ablation study.\n\n**A1**: To further justify the superiority of the Knowledge-Aware module, we replace it with the recently open-sourced SOTA method, EmbedLLM (ICLR 2025) [r1], and denote it as EmbedLLM (MAB) for dynamic MAB routing and select the top‑3 experts before integrating their responses using an Aggregator. EmbedLLM learns compact vector representations of LLMs, facilitating model routing. Table s1 in our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials) shows the results. Despite this LLM‐based configuration, its performance still lags behind our original KABB.\n\n--------------\n\n**Q2**: No performance comparisons among the strategies in FrugalGPT, HybridLLM, COKE, etc.\n\n**A2**: In our original paper, we compared KABB only with MoA since both aggregate responses from multiple experts to harness collective intelligence rather than routing queries to a single model. \nAccording to your suggestion, we’ve added comparisons with FrugalGPT [r2], EmbedLLM [r1], and HybridLLM [r3] (Please see Table s2 in our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials). We exclude COKE [r4] due to its lack of an open-source version and reproducibility issues. All experiments used the KABB w/o Deepseek configuration to avoid API update biases. As shown in Table s2, our KABB outperforms conventional routing methods, as further evidenced by comparisons with MoA, the GPT-Series, and other single models (Fig. 4 in our paper).\n\n\n--------------\n**Q3**: Differences between KABB and COKE.\n\n**A3**: Our KABB and COKE differ in:\n- **Knowledge Representation**: COKE relies on a separate KGMs cluster for knowledge graph operations; KABB directly embeds knowledge into the routing mechanism through knowledge distance vectors and semantic matching.\n- **Routing**: COKE uses a two-tier routing strategy (cluster-level between LLMs and KGMs, then model-level); KABB operates at the expert level with a comprehensive knowledge distance metric, emphasizing team synergy and knowledge complementarity.\n- **Sampling**: KABB’s enhanced Thompson Sampling incorporates knowledge metrics for more informed expert selection; COKE relies on historical success/failure data.\nThese make KABB better suited for scenarios requiring robust multi-agent coordination and deep semantic understanding.\n\n\n-------------\n**Q4**: How to ensure expertise diversity?\n\n**A4**: We have selected 6 open-source LLMs with various architectures, training data and knowledge cutoffs, as shown in 4.1.Experimental Setup. For example, Gemma emphasizes scientific knowledge. R1 excels in reasoning while V3 in general tasks; etc. \n\nEnsemble diversity is ensured with a data-driven process: each LLM is represented by a normalized performance vector (from benchmarks and API metrics) that captures its strengths and weaknesses; a synergy metric penalizes overlapping expertise and rewards complementary skills; and continuous updates let the ensemble adapt to evolving behaviors.\n\n\n--------------\n**Q5**: The construction of knowledge graphs makes limited sense.\n\n**A5**: We respectfully note that your concern reflects a misunderstanding of our framework's design. Specifically:\n1. **Rapid Matching**: We use ability vectors for quick expert-task matching, while KGs enhance this by capturing deeper semantic relationships (see Eq. 4, where the distance metric merges vector overlap and graph dependencies).\n2. **Modeling Team Dynamics**: KGs model dependency path complexity, quantify team synergy (Eq. 6), and capture hierarchical relationships. Graph updates are minimal, as only the Beta distribution parameters (Eq. 5) change, keeping the computational overhead negligible.\n3. **Unified Confidence Function**: Our parameterized mapping integrates historical performance, knowledge distance, temporal decay, and team synergy into an adaptive sampling strategy.\nIn essence, KGs enable our KABB to capture complex team dynamics that vectors alone cannot represent.\n\nWe appreciate your constructive criticism. We carefully considered your comments and believe our paper is greatly improved.\n\n**References**\n\n[r1] Zhuang, Richard, et al. \"EmbedLLM: Learning Compact Representations of Large Language Models.\" The Thirteenth International Conference on Learning Representations, 2025.\n\n[r2] Chen, Lingjiao, et al. \"FrugalGPT: How to Use Large Language Models While Reducing Cost and Improving Performance.\" Transactions on Machine Learning Research, 2024.\n\n[r3] Ding, Dujian, et al. \"Hybrid llm: Cost-efficient and quality-aware query routing.\" The Twelfth International Conference on Learning Representations, 2024.\n\n[r4] Dong, Junnan, et al. \"Cost-Efficient Knowledge-Based Question Answering with Large Language Models.\" Advances in Neural Information Processing Systems, edited by A. Globerson et al., vol. 37, Curran Associates, Inc., 2024, pp. 115261–115281.", "claims_and_evidence": "There is sufficient evidence for the claims.", "methods_and_evaluation_criteria": "1. The construction of knowledge graphs makes limited sense since LLMs could be directly represented by the ability vector.\na) there are no clear structured relations among the concepts that have to be represented as the graphs.\nb) the dynamic updates on graphs is also a challenging and inefficient task.\nc) there are no tailored graph learning techniques over the KG to ensure the learning performance of complex relations.\nd) the more important thing is to establish parameterized relations to map the query and expertise.", "theoretical_claims": "There is a sufficient theoretical analysis.", "experimental_designs_or_analyses": "1. SentenceBert is not a convincing substitute for knowledge graphs as an ablation study. Authors should try LLM-based representations to make the ablation study more technically sound.\n\n2. Since the authors have realized the relatedness of this paper with previous routing methods like FrugalGPT. No performance comparisons among the strategies in FrugalGPT, HybridLLM(ICLR23), COKE (NeurIPS24), etc.\n\n3. Since COKE is also a router based on Thompson Sampling and MAB, can authors discuss the differences between them?\n\n4. The selection of different LLMs is not discussed. Authors should balance the heterogeneous expertise in the expert set to ensure an effective selection. How can authors ensure the diversity of expertise in the ensemble?", "relation_to_broader_scientific_literature": "Closely related", "essential_references_not_discussed": "HybridLLM, COKE are a series of cost-effective methods for model routers but not discussed in the paper.", "other_strengths_and_weaknesses": "NA", "other_comments_or_suggestions": "NA", "questions_for_authors": "please check the comments and weaknesses", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "zsAi6oJUVJ", "reviewer": "Reviewer_S13Y", "summary": "This paper introduces KABB, a framework for multi-agent system coordination with knowledge graphs. It addresses issues in large language models and multi-agent systems with a knowledge distance model and dynamic Bayesian MAB framework. Experiments on multiple benchmarks show its high performance and cost-effectiveness.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "Thank you for recognizing the value of our contributions.\n\n**Q1**: The motivation for formulas.\n\n**A1**: We appreciate the opportunity to clarify the motivation, necessity, and uniqueness of our definitions.\n\n- **Knowledge Distance (Eq. 4)**: Our formulation integrates semantic, structural, and historical dimensions using logarithmic scaling to balance task complexity. The added synergy term explicitly captures team complementarity.\n- **Dynamic Parameter (Eq. 5)**: We use an exponential time decay ($\\gamma^{\\Delta t}$) to discount outdated data while incorporating a knowledge matching term. This approach effectively balances historical performance, immediate feedback, and knowledge priors, addressing non-stationarity.\n- **Comprehensive Confidence (Eq. 6)**: This function combines historical performance, knowledge alignment, and team synergy multiplicatively, with exponential penalties on knowledge distance. The integration of time decay allows for faster adaptation compared to standard Thompson sampling.\n- **Learning Costs**: Our model uses a modest number of parameters relative to deep learning models. Once optimized, the weights remain stable across similar tasks, amortizing the initial learning cost.\n\n---\n\n**Q2**: Explanation for results not exceeding DeepSeek-R1.\n\n**A2**: Regarding our results compared to DeepSeek-R1:\n\n- **Performance & Cost**: Although KABB's AlpacaEval 2.0 LC win rate is slightly lower than DeepSeek-R1's (77.9% vs. 80.1%), KABB achieves a higher MT-Bench score (9.65 vs. 9.30) and does so at significantly lower cost due to avoiding overly verbose responses from Deepseek-R1 (Fig. 4).\n\n- **Scalability**: Scaling KABB to 6 selected experts not only surpasses DeepSeek-R1's performance but also maintains the cost advantage. This confirms that intelligent expert routing, rather than just increasing model size, yields efficient performance gains.\n\n---\n\n**Q3**: Potential overfitting concerns.\n\n**A3**: KABB reduces overfitting through dynamic Bayesian updating with time decay (Eq. 5), Thompson sampling for continuous exploration, and a knowledge-aware sampling strategy that balances historical performance, knowledge distance, time decay, and team synergy (Eq. 6). Theoretical guarantees (Theorem 3.3) confirm convergence to an ε-optimal solution with bounded regret.\n\n---\n\n**Q4**: How the different components of the framework interact with each other in real-world scenarios?\n\n**A4**: In real-world scenarios like AlpacaEval 2.0 tasks (e.g., \"Who created the Superman cartoon character?\"), KABB’s components interact dynamically. The knowledge distance metric parses the task into concepts (e.g., comics, history) and scores expert subsets across five dimensions—semantic match, dependencies, synergy, history—using learnable weights. Knowledge-aware Thompson sampling then selects experts from a Beta distribution. The dynamic MAB mechanism updates parameters with feedback (e.g., preference scores) and time decay, refining the knowledge graph. Finally, the aggregator (e.g., Qwen2-72B) integrates outputs, resolving conflicts via the graph for coherence. This closed-loop process—metric guiding selection, sampling choosing experts, adaptation evolving the model, and integration ensuring quality—offers transparency through its five dimensions. Ablation studies (see Sec. 4 and Table s1 in our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials)) confirm each component’s role.\n\n---\n\n**Q5**: The impact of the knowledge distance metric in different task-specific contexts. \n\n**A5**: Our design is transparent: the knowledge distance metric uses five dimensions (Eq. 4)—task difficulty ($d_t$), semantic matching ($\\omega_1$), dependency ($\\omega_2$), historical effectiveness ($\\omega_3$), and synergy ($\\omega_4$). We examined the experimental results and found that in factual tasks like AlpacaEval 2.0, $\\omega_1$ often leads as stats favor domain precision. In reasoning tasks like MATH, $d_t$ rises and $\\omega_2$ and $\\omega_4$ dominate, integrating concepts per data trend. For complex tasks like, $\\omega_3$ tends to rise. Thompson sampling adapts via these stats, optimizing expert fit.\n\n---\n\n**Q6**: The generalizability of the KABB framework across different types of tasks and domains.\n\n**A6**: KABB’s generalizability shines across diverse tasks and domains (e.g., writing, dialogue, programming, math, reasoning), as shown by evaluations on the six benchmarks. Its domain-agnostic knowledge distance metric and adaptive Bayesian updates allow seamless extension to new areas by expanding the knowledge graph and setting fresh performance priors.\n\nWe appreciate your insightful review, which has strengthened our revised paper.", "claims_and_evidence": "The main innovations are supported by theories. However, there are still two concerns:\n1. The motivation for the mathematical form of the main components is unclear, such as formulas 4, 5, and 6. The author should give the reason for such definitions and explain their necessity and uniqueness. In addition, the multiple weights in the definition increase the learning cost.\n2. Some experimental results do not exceed DeepSeek-R1. In addition to the explanation in the text, more convincing reasons should be given.", "methods_and_evaluation_criteria": "Yes", "theoretical_claims": "Theorem 3.1", "experimental_designs_or_analyses": "Yes", "relation_to_broader_scientific_literature": "RAGs and MBA-RAG.", "essential_references_not_discussed": "NA", "other_strengths_and_weaknesses": "The idea of using knowledge to enhance the multi-agent system is interesting and useful. The paper is well-written and easy to follow. Given the high costs of scaling large language models, the proposed KABB framework provides a more cost-effective alternative. By enabling efficient expert coordination. However, there are still some concerns:\n1. Potential overfitting concerns. With the use of learnable weights in the knowledge distance metric and the dynamic parameter updates in the Bayesian MAB algorithm, there is a potential risk of overfitting. The paper does not provide sufficient analysis on how to mitigate this risk. For example, cross-validation techniques are used, but their effectiveness in preventing overfitting, especially in the context of the complex interactions between the model components, is not thoroughly discussed.\n2. Lack of in-depth interpretability analysis. Although the KABB framework has some transparent components, like the knowledge distance metric as well as each part inside it, there is a lack of in-depth interpretability analysis. The case study cannot prove this. It is not clear how the different components of the framework interact with each other in real-world scenarios. For example, the impact of the knowledge distance metric on the overall performance of the system in different task-specific contexts is not fully explored. This makes it difficult for users to understand and trust the decision-making process of the model in complex situations.\n3. Unclear generalizability. The experiments mainly focus on a specific and limited number of benchmarks. This may not fully represent the entire spectrum of real-world tasks. As a result, the generalizability of the KABB framework across different types of tasks and domains remains uncertain.", "other_comments_or_suggestions": "Please see above.", "questions_for_authors": "Please see above.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}, {"review_id": "m5N76rShOk", "reviewer": "Reviewer_22fq", "summary": "This paper introduces Knowledge-Aware Bayesian Bandits (KABB) as a novel framework for improving dynamic expert coordination in multi-agent systems, which defines a five-dimensions of information of knowledge distance function, and leverages a dynamic Bayesian MAB algorithm together to select expert subset for outcome. The authors evaluate KABB on multiple benchmarks, including AlpacaEval 2.0, MT-Bench, and FLASK-Hard, demonstrating its ability to maintain high performance with lower computational cost compared to baselines.", "questions": "", "limitations": "", "rating": 3, "confidence": null, "soundness": null, "presentation": null, "contribution": null, "strengths": "", "weaknesses": "", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "We appreciate your thoughtful suggestions to improve the quality of our paper.\n\n**Q1**: Supplementary Material\n\n**A1**: The supplementary material is included at the end of the paper. Please let us know if there are any issues accessing it.\n\n---\n\n**Q2**: The importance of each model component\n\n**A2**: Table s1 in our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials) shows the detailed contribution of each component of KABB on AlpacaEval 2.0. To further justify the superiority of the Knowledge-Aware module, we replace it with the recently open-sourced SOTA method, EmbedLLM (ICLR 2025) [r1], and denote it as EmbedLLM (MAB) for dynamic MAB routing and select the top‑3 experts before integrating their responses using an Aggregator. Combined with the ablation studies presented in the original paper (see Table 2), we believe these additional experiments provide sufficient evidence for the importance of each component of KABB.\n\n---\n\n**Q3**: The used knowledge graphs (KGs)\n\n**A3**: Our main contribution is the theoretical foundation and empirical validation of our KABB, not an extensive treatment of the KGs. In brief, our curated KG comprises 1319 units across 12 conceptual domains. Nodes are embedded using semantic similarity, with interconnections weighted by our knowledge distance (Eq. 5) and adjusted via Thompson sampling. The Representative Visualization of Knowledge Graph (three of the core concepts and some key nodes) is provided in our [repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials). \n\n---\n\n**Q4**: The dual adaptation mechanism\n\n**A4**: \nOur mechanism combines (1) Bayesian Parameter Adaptation—using exponential time decay to weight recent interactions for setting the Beta distribution parameters—and (2) Knowledge Graph Evolution—which continuously updates concept relationships and team synergy based on task outcomes.\n\nExperimental Validation in Table s5 over five sequential batches with induced quality drifts (30% of experts), our KABB can \n- Reduce expert selection stabilization time by 46%.\n- Improve LC win rate from 67.4% to 75.7%.\n- Reduce performance degradation to 2.1% (versus 7.8% for the baseline).\n\n### Table s5: Experimental Validation of Dual Adaptation Mechanism on AlpacaEval 2.0 \n| **Condition**         | **Avg. Stabilization Time (Tasks)** | **Avg. LC win. (%)** | **Avg. Performance Degradation (%)** |\n| --- | --- | --- | --- |\n| **Dual Adaptation (Ours)**   | 5.31 | 75.7   | 2.1  |\n| **Bayesian-only**  | 8.73 |  71.8   | 5.2 |\n| **Static Parameters** | 9.82 | 67.4 | 7.8 |\n\nWe have included these results in the revised paper.\n\n---\n\n**Q5**: The difference with related studies\n\n**A5**: Our KABB introduces Knowledge-aware Thompson sampling. For example, as discussed in our response to Reviewer ymVy (and in our comparisons with methods like COKE (NeurIPS 24), our design fundamentally differs from prior works. We have explicitly compared our contributions with related studies in the revised paper.\n\n---\n\n**Q6**: The error analyses when failed to select the best experts\n\n**A6**: Our analysis for the query \"What type of soil is suitable for cactus\" (see [Table s3-s4 in our repository](https://github.com/KABBAnonymous/KABB_icml774_SupplementaryMaterials?tab=readme-ov-file#table-s3-error-analysis-case-1)) revealed two key failure cases:\n1. Inappropriate Domain Expert Selection: KABB initially selected a team without the necessary botanical expertise (e.g., Humanities Scholar and Cultural Interpreter), leading to very low scores.\n2. Partial Recovery Through Team Expansion: By including an Analysis Expert with broader scientific knowledge, the aggregator effectively weighted this high-quality input (preference score 0.89), improving the final response score to 0.91. This demonstrates our system’s ability to leverage better contributions even if the initial selection is suboptimal.\n\nWe focus on overall system performance because a slight increase in expert numbers can largely mitigate the impact of a single misselection. Nevertheless, we have included a quantitative breakdown of error types (cold start gaps, semantic drift, and over-reliance on historical performance) in the revised paper.\n\n---\n\n**Q7**: Integrating RL for KABB\n\n**A7**: While RL is promising, our experiments show that the current Bayesian MAB in KABB is good enough. It achieves the cumulative regret as stated in Theorem G.7 (Line 1269) and outperforms RL methods like A2C, PPO, and MCTS (see Table 2). Although RL could address more dynamic scenarios, its increased complexity and tuning requirements make the pure Bayesian MAB approach preferable for balancing cost, performance, and adaptability in our current scope. We recognize RL’s potential and will explore it in future work.\n\n**References**\n\n[r1] Zhuang, Richard, et al. \"EmbedLLM: Learning Compact Representations of Large Language Models.\" The Thirteenth International Conference on Learning Representations, 2025.", "claims_and_evidence": "Yes.", "methods_and_evaluation_criteria": "Yes.", "theoretical_claims": "I didn't check the theoretical part in this paper, which is beyond my research area.", "experimental_designs_or_analyses": "Yes.", "relation_to_broader_scientific_literature": "The paper relates to existing research on multi-agent collaboration on LLMs, especially the new strategy for agent collaboration.", "essential_references_not_discussed": "No.", "other_strengths_and_weaknesses": "Strengths:\n* The evaluation covers diverse real-world benchmarks.\n* The cost-effectiveness analysis provides a practical insight into real-world applications.\n\nWeaknesses:\n* Ablation study is incomplete: The importance of each model component (knowledge distance, dual adaptation, Thompson sampling) is not separately evaluated.\n* The used knowledge graphs in paper are not presented, which is quite unclear.\n* The details and impacts of the dual adaptation mechanism needs clearer clarification and results.", "other_comments_or_suggestions": "* The difference with related studies is not clear, which needs further clarified.\n* More transparent error analysis is needed, particularly regarding cases where KABB fails to select the best experts.\n* Would integrating reinforcement learning improve KABB over pure Bayesian MAB?", "questions_for_authors": "Please see my comments and weakness points.", "summary_of_paper": "", "summary_of_recommendation": "", "technical_quality": "", "clarity_of_presentation": "", "potential_impact": "", "robotics_focus": "", "quality_of_limitations": "", "questions_for_rebuttal": "", "reasons_to_accept": "", "reasons_to_reject": "", "questions_to_authors": "", "extra_scores": {}}]

Author rebuttal:

Meta-review: All four reviewers indicate a positive stance toward acceptance, with three assigning Weak Accept and one giving Accept. The proposed KABB framework is recognized for its contributions to multi-agent coordination, especially its cost-effective design. The authors' rebuttal addresses several concerns, including limited ablation studies and comparisons with existing methods. Given the overall agreement among the reviewers, I would recommend acceptance.
Decision: Accept (poster)