Daily Papers

With the rapid growth in the number of Large Language Models (LLMs), there has been a recent interest in LLM routing, or directing queries to the cheapest LLM that can deliver a suitable response. Following this line of work, we introduce CARROT, a Cost AwaRe Rate Optimal rouTer that can select models based on any desired trade-off between performance and cost. Given a query, CARROT selects a model based on estimates of models' cost and performance. Its simplicity lends CARROT computational efficiency, while our theoretical analysis demonstrates minimax rate-optimality in its routing performance. Alongside CARROT, we also introduce the Smart Price-aware Routing (SPROUT) dataset to facilitate routing on a wide spectrum of queries with the latest state-of-the-art LLMs. Using SPROUT and prior benchmarks such as Routerbench and open-LLM-leaderboard-v2 we empirically validate CARROT's performance against several alternative routers.

We propose a learning algorithm for local routing policies that needs only a few data samples obtained from a single graph while generalizing to all random graphs in a standard model of wireless networks. We thus solve the all-pairs near-shortest path problem by training deep neural networks (DNNs) that efficiently and scalably learn routing policies that are local, i.e., they only consider node states and the states of neighboring nodes. Remarkably, one of these DNNs we train learns a policy that exactly matches the performance of greedy forwarding; another generally outperforms greedy forwarding. Our algorithm design exploits network domain knowledge in several ways: First, in the selection of input features and, second, in the selection of a ``seed graph'' and subsamples from its shortest paths. The leverage of domain knowledge provides theoretical explainability of why the seed graph and node subsampling suffice for learning that is efficient, scalable, and generalizable. Simulation-based results on uniform random graphs with diverse sizes and densities empirically corroborate that using samples generated from a few routing paths in a modest-sized seed graph quickly learns a model that is generalizable across (almost) all random graphs in the wireless network model.

By routing input tokens to only a few split experts, Sparse Mixture-of-Experts has enabled efficient training of large language models. Recent findings suggest that fixing the routers can achieve competitive performance by alleviating the collapsing problem, where all experts eventually learn similar representations. However, this strategy has two key limitations: (i) the policy derived from random routers might be sub-optimal, and (ii) it requires extensive resources during training and evaluation, leading to limited efficiency gains. This work introduces \HyperRout, which dynamically generates the router's parameters through a fixed hypernetwork and trainable embeddings to achieve a balance between training the routers and freezing them to learn an improved routing policy. Extensive experiments across a wide range of tasks demonstrate the superior performance and efficiency gains of \HyperRouter compared to existing routing methods. Our implementation is publicly available at {{https://github.com/giangdip2410/HyperRouter}}.

This paper discusses the system architecture design and deployment of non-stationary multi-armed bandit approaches to determine a near-optimal payment routing policy based on the recent history of transactions. We propose a Routing Service architecture using a novel Ray-based implementation for optimally scaling bandit-based payment routing to over 10,000 transactions per second, adhering to the system design requirements and ecosystem constraints with Payment Card Industry Data Security Standard (PCI DSS). We first evaluate the effectiveness of multiple bandit-based payment routing algorithms on a custom simulator to benchmark multiple non-stationary bandit approaches and identify the best hyperparameters. We then conducted live experiments on the payment transaction system on a fantasy sports platform Dream11. In the live experiments, we demonstrated that our non-stationary bandit-based algorithm consistently improves the success rate of transactions by 0.92% compared to the traditional rule-based methods over one month.

Recent advances in deep learning and large language models (LLMs) have facilitated the deployment of the mixture-of-experts (MoE) mechanism in the stock investment domain. While these models have demonstrated promising trading performance, they are often unimodal, neglecting the wealth of information available in other modalities, such as textual data. Moreover, the traditional neural network-based router selection mechanism fails to consider contextual and real-world nuances, resulting in suboptimal expert selection. To address these limitations, we propose LLMoE, a novel framework that employs LLMs as the router within the MoE architecture. Specifically, we replace the conventional neural network-based router with LLMs, leveraging their extensive world knowledge and reasoning capabilities to select experts based on historical price data and stock news. This approach provides a more effective and interpretable selection mechanism. Our experiments on multimodal real-world stock datasets demonstrate that LLMoE outperforms state-of-the-art MoE models and other deep neural network approaches. Additionally, the flexible architecture of LLMoE allows for easy adaptation to various downstream tasks.

As with other commodities, markets could help us efficiently produce machine intelligence. We propose a market where intelligence is priced by other intelligence systems peer-to-peer across the internet. Peers rank each other by training neural networks which learn the value of their neighbors. Scores accumulate on a digital ledger where high ranking peers are monetarily rewarded with additional weight in the network. However, this form of peer-ranking is not resistant to collusion, which could disrupt the accuracy of the mechanism. The solution is a connectivity-based regularization which exponentially rewards trusted peers, making the system resistant to collusion of up to 50 percent of the network weight. The result is a collectively run intelligence market which continual produces newly trained models and pays contributors who create information theoretic value.

This paper proposes a novel admission and routing scheme which takes into account arbitrarily assigned priorities for network flows. The presented approach leverages the centralized Software Defined Networking (SDN) capabilities in order to do so. Exact and heuristic approaches to the stated Priority Flow Admission and Routing (PFAR) problem are provided. The exact approach which provides an optimal solution is based on Integer Linear Programming (ILP). Given the potentially long running time required to find an exact and optimal solution, a heuristic approach is proposed; this approach is based on Genetic Algorithms (GAs). In order to effectively estimate the performance of the proposed approaches, a simulator that is capable of generating semi-random network topologies and flows has been developed. Experimental results for large problem instances (up 50 network nodes and thousands of network flows), show that: i) an optimal solution can be often found in few seconds (even milliseconds), and ii) the heuristic approach yields close-to-optimal solutions (approximately 95\% of the optimal) in a fixed amount of time; these experimental results demonstrate the pertinence of the proposed approaches.

The rapid advancement in large language models (LLMs) has brought forth a diverse range of models with varying capabilities that excel in different tasks and domains. However, selecting the optimal LLM for user queries often involves a challenging trade-off between accuracy and cost, a problem exacerbated by the diverse demands of individual queries. In this work, we present a novel framework that formulates the LLM selection process as a multi-armed bandit problem, enabling dynamic and intelligent routing of queries to the most appropriate model. Our approach incorporates a preference-conditioned dynamic routing mechanism, allowing users to specify their preferences at inference time, thereby offering a customizable balance between performance and cost. Additionally, our selection policy is designed to generalize to unseen LLMs, ensuring adaptability to new models as they emerge. Experimental results demonstrate that our method achieves significant improvements in both accuracy and cost-effectiveness across various LLM platforms, showcasing the potential of our framework to adaptively optimize LLM selection in real-world scenarios.

The Mixtures-of-Experts (MoE) model is a widespread distributed and integrated learning method for large language models (LLM), which is favored due to its ability to sparsify and expand models efficiently. However, the performance of MoE is limited by load imbalance and high latency of All-To-All communication, along with relatively redundant computation owing to large expert capacity. Load imbalance may result from existing routing policies that consistently tend to select certain experts. The frequent inter-node communication in the All-To-All procedure also significantly prolongs the training time. To alleviate the above performance problems, we propose a novel routing strategy that combines load balance and locality by converting partial inter-node communication to that of intra-node. Notably, we elucidate that there is a minimum threshold for expert capacity, calculated through the maximal angular deviation between the gating weights of the experts and the assigned tokens. We port these modifications on the PanGu-Sigma model based on the MindSpore framework with multi-level routing and conduct experiments on Ascend clusters. The experiment results demonstrate that the proposed LocMoE reduces training time per epoch by 12.68% to 22.24% compared to classical routers, such as hash router and switch router, without impacting the model accuracy.

The mixture of Expert (MoE) parallelism is a recent advancement that scales up the model size with constant computational cost. MoE selects different sets of parameters (i.e., experts) for each incoming token, resulting in a sparsely-activated model. Despite several successful applications of MoE, its training efficiency degrades significantly as the number of experts increases. The routing stage in MoE relies on the efficiency of the All2All communication collective, which suffers from network congestion and has poor scalability. To mitigate these issues, we introduce SMILE, which exploits heterogeneous network bandwidth and splits a single-step routing into bi-level routing. Our experimental results show that the proposed method obtains a 2.5x speedup over Switch Transformer in terms of pretraining throughput on the Colossal Clean Crawled Corpus without losing any convergence speed.

Low-rank adaptation (LoRA) and its mixture-of-experts (MOE) variants are highly effective parameter-efficient fine-tuning (PEFT) methods. However, they introduce significant latency in multi-tenant settings due to the LoRA modules and MOE routers added to multiple linear modules in the Transformer layer. To address this issue, we propose Mixture of Low-Rank Adaptation (MiLoRA), a novel and efficient LoRA variant. MiLoRA differs from previous MOE-style LoRA methods by considering each LoRA module as an expert and employing a prompt-aware routing mechanism. This mechanism calculates expert routing results once before generating the first new token and reuses these results for subsequent tokens, reducing latency. Extensive experiments and analysis on commonsense reasoning tasks, math reasoning tasks, and widely used LLM evaluation benchmarks demonstrate that MiLoRA consistently outperforms strong PEFT baselines with comparable tunable parameter budgets. Additionally, MiLoRA significantly reduces latency in multi-tenant settings compared to previous LoRA-based methods.

Sparsely activated neural networks with conditional computation learn to route their inputs through different "expert" subnetworks, providing a form of modularity that densely activated models lack. Despite their possible benefits, models with learned routing often underperform their parameter-matched densely activated counterparts as well as models that use non-learned heuristic routing strategies. In this paper, we hypothesize that these shortcomings stem from the gradient estimation techniques used to train sparsely activated models that use non-differentiable discrete routing decisions. To address this issue, we introduce Soft Merging of Experts with Adaptive Routing (SMEAR), which avoids discrete routing by using a single "merged" expert constructed via a weighted average of all of the experts' parameters. By routing activations through a single merged expert, SMEAR does not incur a significant increase in computational costs and enables standard gradient-based training. We empirically validate that models using SMEAR outperform models that route based on metadata or learn sparse routing through gradient estimation. Furthermore, we provide qualitative analysis demonstrating that the experts learned via SMEAR exhibit a significant amount of specialization. All of the code used in our experiments is publicly available.

The availability of performant pre-trained models has led to a proliferation of fine-tuned expert models that are specialized to particular domains. This has enabled the creation of powerful and adaptive routing-based "Model MoErging" methods with the goal of using expert modules to create an aggregate system with improved performance or generalization. However, existing MoErging methods often prioritize generalization to unseen tasks at the expense of performance on held-in tasks, which limits its practical applicability in real-world deployment scenarios. We observe that current token-level routing mechanisms neglect the global semantic context of the input task. This token-wise independence hinders effective expert selection for held-in tasks, as routing decisions fail to incorporate the semantic properties of the task. To address this, we propose, Global and Local Instruction Driven Expert Router (GLIDER) that integrates a multi-scale routing mechanism, encompassing a semantic global router and a learned local router. The global router leverages LLM's advanced reasoning capabilities for semantic-related contexts to enhance expert selection. Given the input query and LLM, the router generates semantic task instructions that guide the retrieval of the most relevant experts across all layers. This global guidance is complemented by a local router that facilitates token-level routing decisions within each module, enabling finer control and enhanced performance on unseen tasks. Our experiments using T5-based models for T0 and FLAN tasks demonstrate that GLIDER achieves substantially improved held-in performance while maintaining strong generalization on held-out tasks. We also perform ablations experiments to dive deeper into the components of GLIDER. Our experiments highlight the importance of our multi-scale routing that leverages LLM-driven semantic reasoning for MoErging methods.

One of the goals in Federated Learning (FL) is to create personalized models that can adapt to the context of each participating client, while utilizing knowledge from a shared global model. Yet, often, personalization requires a fine-tuning step using clients' labeled data in order to achieve good performance. This may not be feasible in scenarios where incoming clients are fresh and/or have privacy concerns. It, then, remains open how one can achieve just-in-time personalization in these scenarios. We propose FedJETs, a novel solution by using a Mixture-of-Experts (MoE) framework within a FL setup. Our method leverages the diversity of the clients to train specialized experts on different subsets of classes, and a gating function to route the input to the most relevant expert(s). Our gating function harnesses the knowledge of a pretrained model common expert to enhance its routing decisions on-the-fly. As a highlight, our approach can improve accuracy up to 18\% in state of the art FL settings, while maintaining competitive zero-shot performance. In practice, our method can handle non-homogeneous data distributions, scale more efficiently, and improve the state-of-the-art performance on common FL benchmarks.

To enhance the efficiency and practicality of federated bandit learning, recent advances have introduced incentives to motivate communication among clients, where a client participates only when the incentive offered by the server outweighs its participation cost. However, existing incentive mechanisms naively assume the clients are truthful: they all report their true cost and thus the higher cost one participating client claims, the more the server has to pay. Therefore, such mechanisms are vulnerable to strategic clients aiming to optimize their own utility by misreporting. To address this issue, we propose an incentive compatible (i.e., truthful) communication protocol, named Truth-FedBan, where the incentive for each participant is independent of its self-reported cost, and reporting the true cost is the only way to achieve the best utility. More importantly, Truth-FedBan still guarantees the sub-linear regret and communication cost without any overheads. In other words, the core conceptual contribution of this paper is, for the first time, demonstrating the possibility of simultaneously achieving incentive compatibility and nearly optimal regret in federated bandit learning. Extensive numerical studies further validate the effectiveness of our proposed solution.

In this paper, we introduce a novel predict-and-optimize method for profit-driven churn prevention. We frame the task of targeting customers for a retention campaign as a regret minimization problem. The main objective is to leverage individual customer lifetime values (CLVs) to ensure that only the most valuable customers are targeted. In contrast, many profit-driven strategies focus on churn probabilities while considering average CLVs. This often results in significant information loss due to data aggregation. Our proposed model aligns with the guidelines of Predict-and-Optimize (PnO) frameworks and can be efficiently solved using stochastic gradient descent methods. Results from 12 churn prediction datasets underscore the effectiveness of our approach, which achieves the best average performance compared to other well-established strategies in terms of average profit.

Budget management strategies in repeated auctions have received growing attention in online advertising markets. However, previous work on budget management in online bidding mainly focused on second-price auctions. The rapid shift from second-price auctions to first-price auctions for online ads in recent years has motivated the challenging question of how to bid in repeated first-price auctions while controlling budgets. In this work, we study the problem of learning in repeated first-price auctions with budgets. We design a dual-based algorithm that can achieve a near-optimal O(T) regret with full information feedback where the maximum competing bid is always revealed after each auction. We further consider the setting with one-sided information feedback where only the winning bid is revealed after each auction. We show that our modified algorithm can still achieve an O(T) regret with mild assumptions on the bidder's value distribution. Finally, we complement the theoretical results with numerical experiments to confirm the effectiveness of our budget management policy.

Large Language Models (LLMs) typically generate outputs token by token using a fixed compute budget, leading to inefficient resource utilization. To address this shortcoming, recent advancements in mixture of expert (MoE) models, speculative decoding, and early exit strategies leverage the insight that computational demands can vary significantly based on the complexity and nature of the input. However, identifying optimal routing patterns for dynamic execution remains an open challenge, limiting the full potential of these adaptive methods. To address this need, we study adaptive computation in LLMs more systematically. We propose a novel framework that integrates smaller auxiliary modules within each Feed-Forward Network layer of the LLM. This design enables dynamic routing of tokens based on task complexity: tokens can be processed by either the small or big modules at each layer, or even bypass certain layers entirely. This allows us to introduce a novel notion of a token's difficulty, defined by its potential to benefit from additional computational resources. Importantly, by employing oracles to identify optimal patterns of adaptive computations, we gain valuable insights into the internal workings of LLMs and the routing processes in a simplified heterogeneous MoE setup. We show that trained routers operate differently from oracles and often yield suboptimal solutions. Notably, activating a large module in just one layer outperforms models that use large modules across all layers, underscoring the gap between practical implementations of routing in MoE models and theoretical optima for adaptive computation.

The sparsely-activated models have achieved great success in natural language processing through large-scale parameters and relatively low computational cost, and gradually become a feasible technique for training and implementing extremely large models. Due to the limit of communication cost, activating multiple experts is hardly affordable during training and inference. Therefore, previous work usually activate just one expert at a time to alleviate additional communication cost. Such routing mechanism limits the upper bound of model performance. In this paper, we first investigate a phenomenon that increasing the number of activated experts can boost the model performance with higher sparse ratio. To increase the number of activated experts without an increase in computational cost, we propose SAM (Switch and Mixture) routing, an efficient hierarchical routing mechanism that activates multiple experts in a same device (GPU). Our methods shed light on the training of extremely large sparse models and experiments prove that our models can achieve significant performance gain with great efficiency improvement.

Optimization problems over dynamic networks have been extensively studied and widely used in the past decades to formulate numerous real-world problems. However, (1) traditional optimization-based approaches do not scale to large networks, and (2) the design of good heuristics or approximation algorithms often requires significant manual trial-and-error. In this work, we argue that data-driven strategies can automate this process and learn efficient algorithms without compromising optimality. To do so, we present network control problems through the lens of reinforcement learning and propose a graph network-based framework to handle a broad class of problems. Instead of naively computing actions over high-dimensional graph elements, e.g., edges, we propose a bi-level formulation where we (1) specify a desired next state via RL, and (2) solve a convex program to best achieve it, leading to drastically improved scalability and performance. We further highlight a collection of desirable features to system designers, investigate design decisions, and present experiments on real-world control problems showing the utility, scalability, and flexibility of our framework.

Stochastic optimization is one of the central problems in Machine Learning and Theoretical Computer Science. In the standard model, the algorithm is given a fixed distribution known in advance. In practice though, one may acquire at a cost extra information to make better decisions. In this paper, we study how to buy information for stochastic optimization and formulate this question as an online learning problem. Assuming the learner has an oracle for the original optimization problem, we design a 2-competitive deterministic algorithm and a e/(e-1)-competitive randomized algorithm for buying information. We show that this ratio is tight as the problem is equivalent to a robust generalization of the ski-rental problem, which we call super-martingale stopping. We also consider an adaptive setting where the learner can choose to buy information after taking some actions for the underlying optimization problem. We focus on the classic optimization problem, Min-Sum Set Cover, where the goal is to quickly find an action that covers a given request drawn from a known distribution. We provide an 8-competitive algorithm running in polynomial time that chooses actions and decides when to buy information about the underlying request.

In recent years, microservices have gained widespread adoption in IT operations due to their scalability, maintenance, and flexibility. However, it becomes challenging for site reliability engineers (SREs) to pinpoint the root cause due to the complex relationships in microservices when facing system malfunctions. Previous research employed structured learning methods (e.g., PC-algorithm) to establish causal relationships and derive root causes from causal graphs. Nevertheless, they ignored the temporal order of time series data and failed to leverage the rich information inherent in the temporal relationships. For instance, in cases where there is a sudden spike in CPU utilization, it can lead to an increase in latency for other microservices. However, in this scenario, the anomaly in CPU utilization occurs before the latency increase, rather than simultaneously. As a result, the PC-algorithm fails to capture such characteristics. To address these challenges, we propose RUN, a novel approach for root cause analysis using neural Granger causal discovery with contrastive learning. RUN enhances the backbone encoder by integrating contextual information from time series, and leverages a time series forecasting model to conduct neural Granger causal discovery. In addition, RUN incorporates Pagerank with a personalization vector to efficiently recommend the top-k root causes. Extensive experiments conducted on the synthetic and real-world microservice-based datasets demonstrate that RUN noticeably outperforms the state-of-the-art root cause analysis methods. Moreover, we provide an analysis scenario for the sock-shop case to showcase the practicality and efficacy of RUN in microservice-based applications. Our code is publicly available at https://github.com/zmlin1998/RUN.

Deploying Large Language Models (LLMs) on resource-constrained (or weak) devices presents significant challenges due to limited resources and heterogeneous data distribution. To address the data concern, it is necessary to fine-tune LLMs using on-device private data for various downstream tasks. While Federated Learning (FL) offers a promising privacy-preserving solution, existing fine-tuning methods retain the original LLM size, leaving issues of high inference latency and excessive memory demands unresolved. Hence, we design FedSpine, an FL framework that combines Parameter- Efficient Fine-Tuning (PEFT) with structured pruning for efficient deployment of LLMs on resource-constrained devices. Specifically, FedSpine introduces an iterative process to prune and tune the parameters of LLMs. To mitigate the impact of device heterogeneity, an online Multi-Armed Bandit (MAB) algorithm is employed to adaptively determine different pruning ratios and LoRA ranks for heterogeneous devices without any prior knowledge of their computing and communication capabilities. As a result, FedSpine maintains higher inference accuracy while improving fine-tuning efficiency. Experimental results conducted on a physical platform with 80 devices demonstrate that FedSpine can speed up fine-tuning by 1.4times-6.9times and improve final accuracy by 0.4%-4.5% under the same sparsity level compared to other baselines.

Congestion is a common failure mode of markets, where consumers compete inefficiently on the same subset of goods (e.g., chasing the same small set of properties on a vacation rental platform). The typical economic story is that prices solve this problem by balancing supply and demand in order to decongest the market. But in modern online marketplaces, prices are typically set in a decentralized way by sellers, with the power of a platform limited to controlling representations -- the information made available about products. This motivates the present study of decongestion by representation, where a platform uses this power to learn representations that improve social welfare by reducing congestion. The technical challenge is twofold: relying only on revealed preferences from users' past choices, rather than true valuations; and working with representations that determine which features to reveal and are inherently combinatorial. We tackle both by proposing a differentiable proxy of welfare that can be trained end-to-end on consumer choice data. We provide theory giving sufficient conditions for when decongestion promotes welfare, and present experiments on both synthetic and real data shedding light on our setting and approach.

The bandits with knapsack (BwK) framework models online decision-making problems in which an agent makes a sequence of decisions subject to resource consumption constraints. The traditional model assumes that each action consumes a non-negative amount of resources and the process ends when the initial budgets are fully depleted. We study a natural generalization of the BwK framework which allows non-monotonic resource utilization, i.e., resources can be replenished by a positive amount. We propose a best-of-both-worlds primal-dual template that can handle any online learning problem with replenishment for which a suitable primal regret minimizer exists. In particular, we provide the first positive results for the case of adversarial inputs by showing that our framework guarantees a constant competitive ratio alpha when B=Omega(T) or when the possible per-round replenishment is a positive constant. Moreover, under a stochastic input model, our algorithm yields an instance-independent O(T^{1/2}) regret bound which complements existing instance-dependent bounds for the same setting. Finally, we provide applications of our framework to some economic problems of practical relevance.

Web3Recommend is a decentralized Social Recommender System implementation that enables Web3 Platforms on Android to generate recommendations that balance trust and relevance. Generating recommendations in decentralized networks is a non-trivial problem because these networks lack a global perspective due to the absence of a central authority. Further, decentralized networks are prone to Sybil Attacks in which a single malicious user can generate multiple fake or Sybil identities. Web3Recommend relies on a novel graph-based content recommendation design inspired by GraphJet, a recommendation system used in Twitter enhanced with MeritRank, a decentralized reputation scheme that provides Sybil-resistance to the system. By adding MeritRank's decay parameters to the vanilla Social Recommender Systems' personalized SALSA graph algorithm, we can provide theoretical guarantees against Sybil Attacks in the generated recommendations. Similar to GraphJet, we focus on generating real-time recommendations by only acting on recent interactions in the social network, allowing us to cater temporally contextual recommendations while keeping a tight bound on the memory usage in resource-constrained devices, allowing for a seamless user experience. As a proof-of-concept, we integrate our system with MusicDAO, an open-source Web3 music-sharing platform, to generate personalized, real-time recommendations. Thus, we provide the first Sybil-resistant Social Recommender System, allowing real-time recommendations beyond classic user-based collaborative filtering. The system is also rigorously tested with extensive unit and integration tests. Further, our experiments demonstrate the trust-relevance balance of recommendations against multiple adversarial strategies in a test network generated using data from real music platforms.

Sparsely-activated Mixture-of-experts (MoE) models allow the number of parameters to greatly increase while keeping the amount of computation for a given token or a given sample unchanged. However, a poor expert routing strategy (e.g. one resulting in load imbalance) can cause certain experts to be under-trained, leading to an expert being under or over-specialized. Prior work allocates a fixed number of experts to each token using a top-k function regardless of the relative importance of different tokens. To address this, we propose a heterogeneous mixture-of-experts employing an expert choice method. Instead of letting tokens select the top-k experts, we have experts selecting the top-k tokens. As a result, each token can be routed to a variable number of experts and each expert can have a fixed bucket size. We systematically study pre-training speedups using the same computational resources of the Switch Transformer top-1 and GShard top-2 gating of prior work and find that our method improves training convergence time by more than 2x. For the same computational cost, our method demonstrates higher performance in fine-tuning 11 selected tasks in the GLUE and SuperGLUE benchmarks. For a smaller activation cost, our method outperforms the T5 dense model in 7 out of the 11 tasks.

Inventory Routing Problem (IRP) is a crucial challenge in supply chain management as it involves optimizing efficient route selection while considering the uncertainty of inventory demand planning. To solve IRPs, usually a two-stage approach is employed, where demand is predicted using machine learning techniques first, and then an optimization algorithm is used to minimize routing costs. Our experiment shows machine learning models fall short of achieving perfect accuracy because inventory levels are influenced by the dynamic business environment, which, in turn, affects the optimization problem in the next stage, resulting in sub-optimal decisions. In this paper, we formulate and propose a decision-focused learning-based approach to solving real-world IRPs. This approach directly integrates inventory prediction and routing optimization within an end-to-end system potentially ensuring a robust supply chain strategy.

In online ad markets, a rising number of advertisers are employing bidding agencies to participate in ad auctions. These agencies are specialized in designing online algorithms and bidding on behalf of their clients. Typically, an agency usually has information on multiple advertisers, so she can potentially coordinate bids to help her clients achieve higher utilities than those under independent bidding. In this paper, we study coordinated online bidding algorithms in repeated second-price auctions with budgets. We propose algorithms that guarantee every client a higher utility than the best she can get under independent bidding. We show that these algorithms achieve maximal coalition welfare and discuss bidders' incentives to misreport their budgets, in symmetric cases. Our proofs combine the techniques of online learning and equilibrium analysis, overcoming the difficulty of competing with a multi-dimensional benchmark. The performance of our algorithms is further evaluated by experiments on both synthetic and real data. To the best of our knowledge, we are the first to consider bidder coordination in online repeated auctions with constraints.

Most methods for Personalized PageRank (PPR) precompute and store all accurate PPR vectors, and at query time, return the ones of interest directly. However, the storage and computation of all accurate PPR vectors can be prohibitive for large graphs, especially in caching them in memory for real-time online querying. In this paper, we propose a distributed framework that strikes a better balance between offline indexing and online querying. The offline indexing attains a fingerprint of the PPR vector of each vertex by performing billions of "short" random walks in parallel across a cluster of machines. We prove that our indexing method has an exponential convergence, achieving the same precision with previous methods using a much smaller number of random walks. At query time, the new PPR vector is composed by a linear combination of related fingerprints, in a highly efficient vertex-centric decomposition manner. Interestingly, the resulting PPR vector is much more accurate than its offline counterpart because it actually uses more random walks in its estimation. More importantly, we show that such decomposition for a batch of queries can be very efficiently processed using a shared decomposition. Our implementation, PowerWalk, takes advantage of advanced distributed graph engines and it outperforms the state-of-the-art algorithms by orders of magnitude. Particularly, it responses to tens of thousands of queries on graphs with billions of edges in just a few seconds.

We consider a class of assortment optimization problems in an offline data-driven setting. A firm does not know the underlying customer choice model but has access to an offline dataset consisting of the historically offered assortment set, customer choice, and revenue. The objective is to use the offline dataset to find an optimal assortment. Due to the combinatorial nature of assortment optimization, the problem of insufficient data coverage is likely to occur in the offline dataset. Therefore, designing a provably efficient offline learning algorithm becomes a significant challenge. To this end, we propose an algorithm referred to as Pessimistic ASsortment opTimizAtion (PASTA for short) designed based on the principle of pessimism, that can correctly identify the optimal assortment by only requiring the offline data to cover the optimal assortment under general settings. In particular, we establish a regret bound for the offline assortment optimization problem under the celebrated multinomial logit model. We also propose an efficient computational procedure to solve our pessimistic assortment optimization problem. Numerical studies demonstrate the superiority of the proposed method over the existing baseline method.

As the range of applications for Large Language Models (LLMs) continues to grow, the demand for effective serving solutions becomes increasingly critical. Despite the versatility of LLMs, no single model can optimally address all tasks and applications, particularly when balancing performance with cost. This limitation has led to the development of LLM routing systems, which combine the strengths of various models to overcome the constraints of individual LLMs. Yet, the absence of a standardized benchmark for evaluating the performance of LLM routers hinders progress in this area. To bridge this gap, we present RouterBench, a novel evaluation framework designed to systematically assess the efficacy of LLM routing systems, along with a comprehensive dataset comprising over 405k inference outcomes from representative LLMs to support the development of routing strategies. We further propose a theoretical framework for LLM routing, and deliver a comparative analysis of various routing approaches through RouterBench, highlighting their potentials and limitations within our evaluation framework. This work not only formalizes and advances the development of LLM routing systems but also sets a standard for their assessment, paving the way for more accessible and economically viable LLM deployments. The code and data are available at https://github.com/withmartian/routerbench.

Cascading bandits have gained popularity in recent years due to their applicability to recommendation systems and online advertising. In the cascading bandit model, at each timestep, an agent recommends an ordered subset of items (called an item list) from a pool of items, each associated with an unknown attraction probability. Then, the user examines the list, and clicks the first attractive item (if any), and after that, the agent receives a reward. The goal of the agent is to maximize the expected cumulative reward. However, the prior literature on cascading bandits ignores the influences of user states (e.g., historical behaviors) on recommendations and the change of states as the session proceeds. Motivated by this fact, we propose a generalized cascading RL framework, which considers the impact of user states and state transition into decisions. In cascading RL, we need to select items not only with large attraction probabilities but also leading to good successor states. This imposes a huge computational challenge due to the combinatorial action space. To tackle this challenge, we delve into the properties of value functions, and design an oracle BestPerm to efficiently find the optimal item list. Equipped with BestPerm, we develop two algorithms CascadingVI and CascadingBPI, which are both computationally-efficient and sample-efficient, and provide near-optimal regret and sample complexity guarantees. Furthermore, we present experiments to show the improved computational and sample efficiencies of our algorithms compared to straightforward adaptations of existing RL algorithms in practice.

In Causal Bayesian Optimization (CBO), an agent intervenes on an unknown structural causal model to maximize a downstream reward variable. In this paper, we consider the generalization where other agents or external events also intervene on the system, which is key for enabling adaptiveness to non-stationarities such as weather changes, market forces, or adversaries. We formalize this generalization of CBO as Adversarial Causal Bayesian Optimization (ACBO) and introduce the first algorithm for ACBO with bounded regret: Causal Bayesian Optimization with Multiplicative Weights (CBO-MW). Our approach combines a classical online learning strategy with causal modeling of the rewards. To achieve this, it computes optimistic counterfactual reward estimates by propagating uncertainty through the causal graph. We derive regret bounds for CBO-MW that naturally depend on graph-related quantities. We further propose a scalable implementation for the case of combinatorial interventions and submodular rewards. Empirically, CBO-MW outperforms non-causal and non-adversarial Bayesian optimization methods on synthetic environments and environments based on real-word data. Our experiments include a realistic demonstration of how CBO-MW can be used to learn users' demand patterns in a shared mobility system and reposition vehicles in strategic areas.

Sparse mixture of experts (SMoE) offers an appealing solution to scale up the model complexity beyond the mean of increasing the network's depth or width. However, effective training of SMoE has proven to be challenging due to the representation collapse issue, which causes parameter redundancy and limited representation potentials. In this work, we propose a competition mechanism to address this fundamental challenge of representation collapse. By routing inputs only to experts with the highest neural response, we show that, under mild assumptions, competition enjoys the same convergence rate as the optimal estimator. We further propose CompeteSMoE, an effective and efficient algorithm to train large language models by deploying a simple router that predicts the competition outcomes. Consequently, CompeteSMoE enjoys strong performance gains from the competition routing policy while having low computation overheads. Our extensive empirical evaluations on two transformer architectures and a wide range of tasks demonstrate the efficacy, robustness, and scalability of CompeteSMoE compared to state-of-the-art SMoE strategies.

RAG systems consist of multiple modules to work together. However, these modules are usually separately trained. We argue that a system like RAG that incorporates multiple modules should be jointly optimized to achieve optimal performance. To demonstrate this, we design a specific pipeline called SmartRAG that includes a policy network and a retriever. The policy network can serve as 1) a decision maker that decides when to retrieve, 2) a query rewriter to generate a query most suited to the retriever, and 3) an answer generator that produces the final response with/without the observations. We then propose to jointly optimize the whole system using a reinforcement learning algorithm, with the reward designed to encourage the system to achieve the best performance with minimal retrieval cost. When jointly optimized, all the modules can be aware of how other modules are working and thus find the best way to work together as a complete system. Empirical results demonstrate that the jointly optimized SmartRAG can achieve better performance than separately optimized counterparts.

Excellent tail performance is crucial for modern machine learning tasks, such as algorithmic fairness, class imbalance, and risk-sensitive decision making, as it ensures the effective handling of challenging samples within a dataset. Tail performance is also a vital determinant of success for personalized recommender systems to reduce the risk of losing users with low satisfaction. This study introduces a "safe" collaborative filtering method that prioritizes recommendation quality for less-satisfied users rather than focusing on the average performance. Our approach minimizes the conditional value at risk (CVaR), which represents the average risk over the tails of users' loss. To overcome computational challenges for web-scale recommender systems, we develop a robust yet practical algorithm that extends the most scalable method, implicit alternating least squares (iALS). Empirical evaluation on real-world datasets demonstrates the excellent tail performance of our approach while maintaining competitive computational efficiency.

The advent of large language models has revolutionized natural language processing, but their increasing complexity has led to substantial training costs, resource demands, and environmental impacts. In response, sparse Mixture-of-Experts (MoE) models have emerged as a promising alternative to dense models. Since training MoE models from scratch can be prohibitively expensive, recent studies have explored leveraging knowledge from pre-trained non-MoE models. However, existing approaches have limitations, such as requiring significant hardware resources and data. We propose a novel algorithm, LaDiMo, which efficiently converts a Transformer-based non-MoE model into a MoE model with minimal additional training cost. LaDiMo consists of two stages: layer-wise expert construction and routing policy decision. By harnessing the concept of Knowledge Distillation, we compress the model and rapidly recover its performance. Furthermore, we develop an adaptive router that optimizes inference efficiency by profiling the distribution of routing weights and determining a layer-wise policy that balances accuracy and latency. We demonstrate the effectiveness of our method by converting the LLaMA2-7B model to a MoE model using only 100K tokens, reducing activated parameters by over 20% while keeping accuracy. Our approach offers a flexible and efficient solution for building and deploying MoE models.

Stock Price Trend Prediction (SPTP) based on Limit Order Book (LOB) data is a fundamental challenge in financial markets. Despite advances in deep learning, existing models fail to generalize across different market conditions and struggle to reliably predict short-term trends. Surprisingly, by adapting a simple MLP-based architecture to LOB, we show that we surpass SoTA performance; thus, challenging the necessity of complex architectures. Unlike past work that shows robustness issues, we propose TLOB, a transformer-based model that uses a dual attention mechanism to capture spatial and temporal dependencies in LOB data. This allows it to adaptively focus on the market microstructure, making it particularly effective for longer-horizon predictions and volatile market conditions. We also introduce a new labeling method that improves on previous ones, removing the horizon bias. We evaluate TLOB's effectiveness using the established FI-2010 benchmark, which exceeds the state-of-the-art by an average of 3.7 F1-score(\%). Additionally, TLOB shows improvements on Tesla and Intel with a 1.3 and 7.7 increase in F1-score(\%), respectively. Additionally, we empirically show how stock price predictability has declined over time (-6.68 absolute points in F1-score(\%)), highlighting the growing market efficiencies. Predictability must be considered in relation to transaction costs, so we experimented with defining trends using an average spread, reflecting the primary transaction cost. The resulting performance deterioration underscores the complexity of translating trend classification into profitable trading strategies. We argue that our work provides new insights into the evolving landscape of stock price trend prediction and sets a strong foundation for future advancements in financial AI. We release the code at https://github.com/LeonardoBerti00/TLOB.

Despite their remarkable achievement, gigantic transformers encounter significant drawbacks, including exorbitant computational and memory footprints during training, as well as severe collapse evidenced by a high degree of parameter redundancy. Sparsely-activated Mixture-of-Experts (SMoEs) have shown promise to mitigate the issue of training efficiency, yet they are prone to (1) redundant experts due to representational collapse; and (2) poor expert scalability for inference and downstream fine-tuning, primarily due to overfitting of the learned routing policy to the number of activated experts during training. As recent research efforts are predominantly focused on improving routing policies to encourage expert specializations, this work focuses on exploring the overlooked scalability bottleneck of SMoEs and leveraging it to effectively scale dense transformers. To this end, we propose a new plug-and-play training framework, SMoE-Dropout, to enable scaling transformers to better accuracy in their full capacity without collapse. Specifically, SMoE-Dropout consists of a randomly initialized and fixed router network to activate experts and gradually increases the activated expert number as training progresses over time. Transformers trained by SMoE-Dropout naturally exhibit a self-slimmable property subject to resource availability, offering smooth and consistent performance boosts with an increase in activated experts during inference or fine-tuning. Our extensive experiments demonstrate the superior performance and substantial computation savings of SMoE-Dropout, compared to dense training baselines with equivalent parameter counts. In particular, our trained BERT outperforms its densely trained counterpart with consistent improvements of {1.03%, 0.78%, 1.09%} on challenging reasoning tasks {ASDiv-A, MAWPS, SVAMP}, respectively.

Many applications must provide low-latency LLM service to users or risk unacceptable user experience. However, over-provisioning resources to serve fluctuating request patterns is often prohibitively expensive. In this work, we present a best-effort serving system that employs deep reinforcement learning to adjust service quality based on the task distribution and system load. Our best-effort system can maintain availability with over 10x higher client request rates, serves above 96% of peak performance 4.1x more often, and serves above 98% of peak performance 2.3x more often than static serving on unpredictable workloads. Our learned router is robust to shifts in both the arrival and task distribution. Compared to static serving, learned best-effort serving allows for cost-efficient serving through increased hardware utility. Additionally, we argue that learned best-effort LLM serving is applicable in wide variety of settings and provides application developers great flexibility to meet their specific needs.

Applying reinforcement learning (RL) to combinatorial optimization problems is attractive as it removes the need for expert knowledge or pre-solved instances. However, it is unrealistic to expect an agent to solve these (often NP-)hard problems in a single shot at inference due to their inherent complexity. Thus, leading approaches often implement additional search strategies, from stochastic sampling and beam search to explicit fine-tuning. In this paper, we argue for the benefits of learning a population of complementary policies, which can be simultaneously rolled out at inference. To this end, we introduce Poppy, a simple training procedure for populations. Instead of relying on a predefined or hand-crafted notion of diversity, Poppy induces an unsupervised specialization targeted solely at maximizing the performance of the population. We show that Poppy produces a set of complementary policies, and obtains state-of-the-art RL results on four popular NP-hard problems: traveling salesman, capacitated vehicle routing, 0-1 knapsack, and job-shop scheduling.

Motivated by concerns about making online decisions that incur undue amount of risk at each time step, in this paper, we formulate the probably anytime-safe stochastic combinatorial semi-bandits problem. In this problem, the agent is given the option to select a subset of size at most K from a set of L ground items. Each item is associated to a certain mean reward as well as a variance that represents its risk. To mitigate the risk that the agent incurs, we require that with probability at least 1-delta, over the entire horizon of time T, each of the choices that the agent makes should contain items whose sum of variances does not exceed a certain variance budget. We call this probably anytime-safe constraint. Under this constraint, we design and analyze an algorithm {\sc PASCombUCB} that minimizes the regret over the horizon of time T. By developing accompanying information-theoretic lower bounds, we show that under both the problem-dependent and problem-independent paradigms, {\sc PASCombUCB} is almost asymptotically optimal. Experiments are conducted to corroborate our theoretical findings. Our problem setup, the proposed {\sc PASCombUCB} algorithm, and novel analyses are applicable to domains such as recommendation systems and transportation in which an agent is allowed to choose multiple items at a single time step and wishes to control the risk over the whole time horizon.

Algorithmic Recourse (AR) is the problem of computing a sequence of actions that -- once performed by a user -- overturns an undesirable machine decision. It is paramount that the sequence of actions does not require too much effort for users to implement. Yet, most approaches to AR assume that actions cost the same for all users, and thus may recommend unfairly expensive recourse plans to certain users. Prompted by this observation, we introduce PEAR, the first human-in-the-loop approach capable of providing personalized algorithmic recourse tailored to the needs of any end-user. PEAR builds on insights from Bayesian Preference Elicitation to iteratively refine an estimate of the costs of actions by asking choice set queries to the target user. The queries themselves are computed by maximizing the Expected Utility of Selection, a principled measure of information gain accounting for uncertainty on both the cost estimate and the user's responses. PEAR integrates elicitation into a Reinforcement Learning agent coupled with Monte Carlo Tree Search to quickly identify promising recourse plans. Our empirical evaluation on real-world datasets highlights how PEAR produces high-quality personalized recourse in only a handful of iterations.

Major Internet advertising platforms offer budget pacing tools as a standard service for advertisers to manage their ad campaigns. Given the inherent non-stationarity in an advertiser's value and also competing advertisers' values over time, a commonly used approach is to learn a target expenditure plan that specifies a target spend as a function of time, and then run a controller that tracks this plan. This raises the question: how many historical samples are required to learn a good expenditure plan? We study this question by considering an advertiser repeatedly participating in T second-price auctions, where the tuple of her value and the highest competing bid is drawn from an unknown time-varying distribution. The advertiser seeks to maximize her total utility subject to her budget constraint. Prior work has shown the sufficiency of Tlog T samples per distribution to achieve the optimal O(T)-regret. We dramatically improve this state-of-the-art and show that just one sample per distribution is enough to achieve the near-optimal tilde O(T)-regret, while still being robust to noise in the sampling distributions.

Many real-world multi-label prediction problems involve set-valued predictions that must satisfy specific requirements dictated by downstream usage. We focus on a typical scenario where such requirements, separately encoding value and cost, compete with each other. For instance, a hospital might expect a smart diagnosis system to capture as many severe, often co-morbid, diseases as possible (the value), while maintaining strict control over incorrect predictions (the cost). We present a general pipeline, dubbed as FavMac, to maximize the value while controlling the cost in such scenarios. FavMac can be combined with almost any multi-label classifier, affording distribution-free theoretical guarantees on cost control. Moreover, unlike prior works, it can handle real-world large-scale applications via a carefully designed online update mechanism, which is of independent interest. Our methodological and theoretical contributions are supported by experiments on several healthcare tasks and synthetic datasets - FavMac furnishes higher value compared with several variants and baselines while maintaining strict cost control. Our code is available at https://github.com/zlin7/FavMac

Conditional computing processes an input using only part of the neural network's computational units. Learning to execute parts of a deep convolutional network by routing individual samples has several advantages: Reducing the computational burden is an obvious advantage. Furthermore, if similar classes are routed to the same path, that part of the network learns to discriminate between finer differences and better classification accuracies can be attained with fewer parameters. Recently, several papers have exploited this idea to take a particular child of a node in a tree-shaped network or to skip parts of a network. In this work, we follow a Trellis-based approach for generating specific execution paths in a deep convolutional neural network. We have designed routing mechanisms that use differentiable information gain-based cost functions to determine which subset of features in a convolutional layer will be executed. We call our method Conditional Information Gain Trellis (CIGT). We show that our conditional execution mechanism achieves comparable or better model performance compared to unconditional baselines, using only a fraction of the computational resources.

Continuous control tasks often involve high-dimensional, dynamic, and non-linear environments. State-of-the-art performance in these tasks is achieved through complex closed-box policies that are effective, but suffer from an inherent opacity. Interpretable policies, while generally underperforming compared to their closed-box counterparts, advantageously facilitate transparent decision-making within automated systems. Hence, their usage is often essential for diagnosing and mitigating errors, supporting ethical and legal accountability, and fostering trust among stakeholders. In this paper, we propose SMOSE, a novel method to train sparsely activated interpretable controllers, based on a top-1 Mixture-of-Experts architecture. SMOSE combines a set of interpretable decisionmakers, trained to be experts in different basic skills, and an interpretable router that assigns tasks among the experts. The training is carried out via state-of-the-art Reinforcement Learning algorithms, exploiting load-balancing techniques to ensure fair expert usage. We then distill decision trees from the weights of the router, significantly improving the ease of interpretation. We evaluate SMOSE on six benchmark environments from MuJoCo: our method outperforms recent interpretable baselines and narrows the gap with noninterpretable state-of-the-art algorithms

Transformer-based Mixture-of-Experts (MoE) models have been driving several recent technological advancements in Natural Language Processing (NLP). These MoE models adopt a router mechanism to determine which experts to activate for routing input tokens. However, existing router mechanisms allocate a fixed number of experts to each token, which neglects the varying importance of different input tokens. In this study, we propose a novel dynamic router mechanism that Dynamically Allocates a variable number of experts for Mixture-of-Experts (DA-MoE) models based on an effective token importance measure. First, we show that the Transformer attention mechanism provides a natural and effective way of calculating token importance. Second, we propose a dynamic router mechanism that effectively decides the optimal number of experts (K) and allocates the top-K experts for each input token. Third, comprehensive experiments on several benchmark datasets demonstrate that our DA-MoE approach consistently outperforms the state-of-the-art Transformer based MoE model on the popular GLUE benchmark.

This research proposes a new recommender system algorithm for online grocery shopping. The algorithm is based on the perspective that, since the grocery items are usually bought in bulk, a grocery recommender system should be capable of recommending the items in bulk. The algorithm figures out the possible dishes a user may cook based on the items added to the basket and recommends the ingredients accordingly. Our algorithm does not depend on the user ratings. Customers usually do not have the patience to rate the groceries they purchase. Therefore, algorithms that are not dependent on user ratings need to be designed. Instead of using a brute force search, this algorithm limits the search space to a set of only a few probably food categories. Each food category consists of several food subcategories. For example, "fried rice" and "biryani" are food subcategories that belong to the food category "rice". For each food category, items are ranked according to how well they can differentiate a food subcategory. To each food subcategory in the activated search space, this algorithm attaches a score. The score is calculated based on the rank of the items added to the basket. Once the score exceeds a threshold value, its corresponding subcategory gets activated. The algorithm then uses a basket-to-recipe similarity measure to identify the best recipe matches within the activated subcategories only. This reduces the search space to a great extent. We may argue that this algorithm is similar to the content-based recommender system in some sense, but it does not suffer from the limitations like limited content, over-specialization, or the new user problem.

We consider the problem of recommending relevant content to users of an internet platform in the form of lists of items, called slates. We introduce a variational Bayesian Recurrent Neural Net recommender system that acts on time series of interactions between the internet platform and the user, and which scales to real world industrial situations. The recommender system is tested both online on real users, and on an offline dataset collected from a Norwegian web-based marketplace, FINN.no, that is made public for research. This is one of the first publicly available datasets which includes all the slates that are presented to users as well as which items (if any) in the slates were clicked on. Such a data set allows us to move beyond the common assumption that implicitly assumes that users are considering all possible items at each interaction. Instead we build our likelihood using the items that are actually in the slate, and evaluate the strengths and weaknesses of both approaches theoretically and in experiments. We also introduce a hierarchical prior for the item parameters based on group memberships. Both item parameters and user preferences are learned probabilistically. Furthermore, we combine our model with bandit strategies to ensure learning, and introduce `in-slate Thompson Sampling' which makes use of the slates to maximise explorative opportunities. We show experimentally that explorative recommender strategies perform on par or above their greedy counterparts. Even without making use of exploration to learn more effectively, click rates increase simply because of improved diversity in the recommended slates.

Inverse reinforcement learning (IRL) offers a powerful and general framework for learning humans' latent preferences in route recommendation, yet no approach has successfully addressed planetary-scale problems with hundreds of millions of states and demonstration trajectories. In this paper, we introduce scaling techniques based on graph compression, spatial parallelization, and improved initialization conditions inspired by a connection to eigenvector algorithms. We revisit classic IRL methods in the routing context, and make the key observation that there exists a trade-off between the use of cheap, deterministic planners and expensive yet robust stochastic policies. This insight is leveraged in Receding Horizon Inverse Planning (RHIP), a new generalization of classic IRL algorithms that provides fine-grained control over performance trade-offs via its planning horizon. Our contributions culminate in a policy that achieves a 16-24% improvement in route quality at a global scale, and to the best of our knowledge, represents the largest published study of IRL algorithms in a real-world setting to date. We conclude by conducting an ablation study of key components, presenting negative results from alternative eigenvalue solvers, and identifying opportunities to further improve scalability via IRL-specific batching strategies.

Influence maximization (IM) is formulated as selecting a set of initial users from a social network to maximize the expected number of influenced users. Researchers have made great progress in designing various traditional methods, and their theoretical design and performance gain are close to a limit. In the past few years, learning-based IM methods have emerged to achieve stronger generalization ability to unknown graphs than traditional ones. However, the development of learning-based IM methods is still limited by fundamental obstacles, including 1) the difficulty of effectively solving the objective function; 2) the difficulty of characterizing the diversified underlying diffusion patterns; and 3) the difficulty of adapting the solution under various node-centrality-constrained IM variants. To cope with the above challenges, we design a novel framework DeepIM to generatively characterize the latent representation of seed sets, and we propose to learn the diversified information diffusion pattern in a data-driven and end-to-end manner. Finally, we design a novel objective function to infer optimal seed sets under flexible node-centrality-based budget constraints. Extensive analyses are conducted over both synthetic and real-world datasets to demonstrate the overall performance of DeepIM. The code and data are available at: https://github.com/triplej0079/DeepIM.