Deft Scheduling of Dynamic Cloud Workflows with Varying Deadlines via Mixture-of-Experts
Authors: Ya Shen
Gang Chen
Hui Ma
Mengjie Zhang
Venue: ICLR 2026 Poster (2026)
Keywords: Cloud Computing
Dynamic Workflow Scheduling
Deep Reinforcement Learning
Primary area: optimization
TL;DR: We use Mixture-of-Experts to diversify policy behaviors in deep RL, enhancing adaptability and performance in dynamic scheduling.

Abstract: Workflow scheduling in cloud computing demands the intelligent allocation of dynamically arriving, graph-structured workflows with varying deadlines onto ever-changing virtual machine resources. However, existing deep reinforcement learning (DRL) schedulers remain limited by rigid, single-path inference architectures that struggle to handle diverse scheduling scenarios. We introduce $\textbf{DEFT}$ ($\textbf{D}$eadline-p$\textbf{E}$rceptive Mixture-o$\textbf{F}$-Exper$\textbf{t}$s), an innovative DRL policy architecture that leverages a specialized mixture of experts, each trained to manage different levels of deadline tightness. To our knowledge, DEFT is the first to introduce and validate a Mixture-of-Experts architecture for dynamic cloud workflow scheduling. By adaptively routing decisions through the most appropriate experts, DEFT is capable of meeting a broad spectrum of deadline requirements that no single expert can achieve. Central to DEFT is a $\textbf{graph-adaptive}$ gating mechanism that encodes workflow DAGs, task states, and VM conditions, using cross-attention to guide expert activation in a fine-grained, deadline-sensitive manner. Experiments on dynamic cloud workflow benchmarks demonstrate that DEFT significantly reduces execution cost and deadline violations, outperforming multiple state-of-the-art DRL baselines.

Published as a conference paper at ICLR 2026
DEFT SCHEDULING OF DYNAMIC CLOUD WORKFLOWS WITH VARYING DEADLINES VIA MIXTURE-OF-EXPERE
Ya Shen, Gang Chen, Hui Ma Mengjie Zhang
School of Engineering and Computer Science, Victoria University of Wellington Wellington, New Zealand (ya. shen, ren. chen, hui ma, mengjie zhang }@ecs
ABSTRACT
Workflow scheduling in cloud computing demands the intelligent allocation of dynamically arriving, graph-structured workflows with varying deadlines onto ever-changing virtual machine resources. However, existing deep reinforcement learning (DRL) schedulers remain limited by rigid, single-path inference archi- tectures that struggle to handle diverse scheduling scenarios. We introduce DEFT (Deadline-pErceptive
Mexture-oF--Exertts an innovative DRL policy architec- ture that leverages a specialized mixture of experts, each trained to manage dif- ferent levels of deadline tightness. To knowledge, DEFT is the first intro- duce and validate Mixture-of ofxpprre-f-Experts architecture for dynamic cloud workflow scheduling. By adaptively routing decisions through the most appropriate experts. DEFT is capable of meeting broad spectrum of deadline requirements that no single expert can achieve. Central to DEFT graph-adaptive gating mech- anism that encodes workflow deadlines and DAGs, task states, and VM condi- tions, using cross-attention to guide expert activation in a fine-grained, deadline- sensitive manner. Experiments dynamic cloud workflow benchmarks demon- strate that DEFT significantly reduces execution cost and deadline violations, outperforming multiple state-of-the art DRL baselines. The code is available at https///gtttbbbcomm/aaaeCCC////
INTRODUCTION
As cloud computing provides elastic and on-demand computation resources, it has become funda- mental platform for running large-scale applications efficiently (Buyya et al., 1a). Many of these applications take the form of workflows consisting of interdependent tasks, naturally modeled di- rected acyelic graphs (DAGs) where nodes represent tasks and edges define precedence constraints. Each workflow is associated with service-level agreement (SLA) deadline, missing which incurs financial penalties (Buyya et al.. 2011b; Shen et al., 2024). In practice, workflows arrive unpre- dictably, exhibit diverse structures, and have deadlines with varying levels of tightness, reflecting broad range of user expectations. This work tackles the Cost-Aware Dynamic Workflow Scheduling (CADWS) problem, aiming to minimize total execution cost by jointly minimizing virtual machine (VM) rental fees and deadline violation penalties under dynamic and uncertain conditions. The diagram of CADWS is shown in Figures (a) and (b).
Tackling the CADWS problem requires more than reactive scheduling. It demands intelligent poli- cies that can reason under uncertainty and make fine-grained, deadline-aware decisions in real time. The core challenge lies in navigating highly dynamic environment marked by fluctuating VM availability, diverse workflow structures, and, most critically, the wide spectrum of deadline tight- ness that governs workflow urgency. Schedulers must reason over complex task graphs, interpret shifting system states, and allocate resources in real time. These requirements quickly exceed the capabilities of traditional heuristics, which struggle to adapt such temporal and structural changes.
Deep reinforcement learning (DRL) has shown growing promise for dynamic workflow scheduling in cloud environments (Zhou et al., 2024a; Ngwu et al., 2025). By modeling the scheduler as

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agent that interacts with changing environment, DRL learns policies that optimize long-term cost and performance. In the CADWS setting, the agent observes system states and selects execution targets from dynamically evolving VM pool. DRL schedulers have demonstrated clear advantages over heuristic methods in cloud workflow orchestration tasks (Shen et al., 2024; Yang et al., 2025), offering improved adaptability to structural variation and timing uncertainty.
Despite recent progress, a key issue remains in DRL-based CADWS approaches: the inflexibility of their policy network architectures. Most existing methods adopt monolithic design, typically based on a single feedforward pathway (Huang et al., 2022; Shen et al., 2024). Once trained, these policies encode a static set of decision rules that are applied uniformly across different scheduling scenarios. While this can be effective in stable settings, such rigid architectures struggle to accommodate the wide variability in workflow deadline requirements, ranging from lenient to extremely tight. This lack of deadline awareness severely limits the scheduler's ability to allocate tasks appropriately under time pressure.
To overcome the limitations of rigid policy architectures, we propose DEFT (Deadline-pErceptive Mixpere-of-Experts), a novel policy network tailored for dynamic workflow scheduling. Instead of relying on single fixed inference pathway, DEFT dynamically selects from a pool of specialized subnetworks (experts), each trained to handle different levels of deadline tightness. Inspired by the Mixture-of -faturr--f-Experts (MoE) architecture in large language models (Shazeer et al., 2017), DEFT rein- terprets expert activation as adaptive policy modulation, enabling fine-grained scheduling strategies workflow urgency varies. It enhances the flexibility and responsiveness of DRL schedulers by diversifying action-priorit, mapping through three key innovations:
First MoE method for dynamic workflow scheduling. DEFT is the first approach to bring MoE architectures into dynamic workflow scheduling, introducing a new level of adaptiv- ity in deadline-awar policy design. Instead of relying single, rigid inference pathway, DEFT dynamically activates specialized experts based on the tightness of workflow dead- lines. This design enables scalable, deadline-sensitive scheduling that conventional DRL. schedulers fail to achieve.
Enhancing Policy Diversity and Generalization. DEFT employs novel two-phase train- ing strategy: the first phase, each expert trained independently to specialize spe- cific level of deadline tightness, learning tailored scheduling behaviors across the deadline spectrum. In the second phase, a route decisions through the most appropriate experts based on real-time workflow states, DAG structure, and VM conditions. During this phase, experts are further fine-tuned alongside the gating network to ensure consistent and generalizable performance across wide range of scheduling contexts.
gating network is trained to dynamically
Graph-adaptive Gating, DEFT is powered by a novel graph-adaptivy gating network that uses cross attention integrate structured workflow representations with real-time schedul- ing context. This mechanism enables fine-grained, deadline-aware expert activation at each decision step, allowing the policy fluidly adapt changing deadlines and resource con- ditions. To the best of our knowledge, our gating design is the first to combine graph neural representations with MoE routing in DRL scheduler, offering principled and scalable approach to structured, deadline-driven scheduling in dynamic cloud environments.
RELATED WORK
We begin by reviewing recent advances in DRL for CADWS, followed by an overview of MoE architectures and their integration into DRL policy networks.
2.1 DEEP REINFORCEMENT LEARNING FOR CADWS
DRL has shown strong potential in learning effective scheduling policies by leveraging the rep- resentation power of neural networks. Early DRL-based schedulers were developed for Job-Shop Scheduling (JSS) (Zhang et al., 2020; Song al., 2022) and Vehicle Routing Problems (VRP) (Wu et al., 2021; Xin et al., 2021), and have since been extended to the more complex CADWS set- ting (Huang et al., 2022; Jayanetti et al., 2024). These early CADWS studies demonstrated DRL's
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superiority over heuristic methods, though they relied simple FFN as the policy network, lim- iting policy expressiveness. Subsequent CADWS works improved policy network design by intro- ducing self-attention (Shen al., 2024) and GNNs (Shen et al., 2025; Yang et al., 2025) to capture task dependencies in workflows.
As shown in Figure (c), the policy networks in these studies often comprise of two key modules: a State Embedding Module (SEM) that encodes raw environment states into informative state embeddings, and a Priority Mapping Module (PMM) that further maps these embeddings to the action priorities for VM selection. Current CADWS studies mainly focus on SEM design, while PMMs are typically implemented as single Feed-Forward Network (FFN) with fixed inference pathway, which limits their ability to adapt to varying deadline tightness. This raises two key ques- tions: (1) Can a fixed-patwway PMM fully leverage rich state embeddings to capture the diverse scheduling needs imposed by varying deadline tightness? (2) Would set of specialized inference pathways provide stronger adaptability to dynamic workflow deadlines and resource conditions? To answer these questions, we propose DEFT, novel policy network that replaces the monolithic PMM with a MoE architecture. DEFT dynamically selects expert pathways based on workflow urgency, enhancing flexibility and generalization for deadline-senssee sensitive cloud scheduling.
2.2 EVOLUTION OF MIXTURE-O--EXPELS (MoE)
The MoE paradigm was first introduced by Jacobs et al. (1991), where a gating network assigns inputs to specialized expert networks. More recently, MoE architectures have been widely adopted in large-scale learning tasks, demonstrating their ability to improve model expressiveness and context sensitivity through dynamic expert selection (Shazeer et al., 2017; Fedus et al., 2022; Du et al., 2022).
Applying MoE to DRL for combinatorial optimization remains relatively underexplored. Prior work by Kidambi et al. (2020) showed that MoE can enhance sample efficiency and generalization ca- pability of DRL agents. For example, recent studies have adopted MoE, such as MVMoE (Zhou et al., 2024b) and SHIELD (Goh et al., 2025), to solve multiple vehicle routing variants. Nev- ertheless, these early efforts are not well suited for CADWS. First, they focus on static settings, whereas CADWS involves continuously arriving workflows with varying deadline urgency. Second, their gating mechanisms are implemented by simple linear layers, unable to leverage the rich DAG structures and dynamic contexts needed for effective expert selection. We address these gaps with a novel MoE-based policy network tailored for CADWS, featuring a graph-adaptive gating module that adaptively routes decisions based workflow topology, task states, and deadline tightness.
3 PRELIMINARIES
This section defines the CADWS problem, presents its Markov Decision Process (MDP) formula- tion, and specifies the optimization objectives.
3.1 COST-AWARE DYNAMIC WORKFLOW SCHEDULING
The CADWS problem aims to schedule set of dynamically arriving workflows W for execution on VMs in a cloud environment. Each workflow W; W represented by a DAG W; = (Ow, Cw, ) where Ow, is the set of computational tasks and Cw. encodes precedence constraints as directed edges. Any directed edge (O.., Onj) ) E Cw; indicates that task On, must be completed before task Onz can begin. A task with all its predecessor tasks completed is considered the ready task, denoted as O,,,, and is eligible for immediate execution.
Tasks exhibit heterogeneous workloads. Each task O.. E Ow; has computational demand edo., E R+ Workflows arrive dynamically across time, each with an arrival time a, and a deadline d, derived from user-specified SLA. To model the varied urgency levels across workflows, we define each workflow's 's deadline as:
d, a + 7 minMMaksspan(W.).
(1)
where a; is the arrival time of workflow W., is deadline relaxation coefficient that controls the rightees of the deadline, and minMakespan (W;) denotes the minimum execution time achiev- able by allocating the fastest available VM to each task of W; without any delay. Smaller y values
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lead to tighter deadlines, posing greater challenges for the scheduler to meet timing constraints under dynamic resource availability.
The cloud infrastructure offers pool of VMs .M- {m1, m 77MM) change over time. Each VM my E .M has a processing speed V/ and an hourly rental cost Cj- Under pay-as-you-go model (Ibrahim et al., 2011), VMs can be provisioned on demand without predefined capacity constraints, enabling flexible but cost-sensitive resource allocation. A more detailed description of the problem definition can be found in Appendix A.
whose availability may
3.2 MARKOV DECISION PROCESS FORMULATION
We model the CADWS problem as a undiscounted Markov Decision Process (MDP) defined by the tuple A,, Pr, R). Each of its elements is introduced below.
State Space S: At any time step t. the state St E S captures the full system status, including: (I) Workflow information: workflow DAGs, arrival times, deadlines, task completion status, and workloads; and (2) VM information: current VM instances, their types, processing speeds, queue lengths, and existing lease time.
Action Space A: At each time step f, the action Or A specifies the assignment of the current ready task n to a VM instance for execution. The action space is dynamic and consists of two types of options: (1) assignment to an active (already leased) VM, and (2) provisioning and assignment to a new VM of any available type. This flexible formulation allows the DRL scheduler to dynamically lease new VMs demand, enabling adaptive resource scaling throughout the scheduling process.
Transition Probability Pr: The environment transition Pr(st+1 (t. ae) captures the stochastic evo- lution of workflow arrivals, VM availability, and task execution. The transition model is unknown to the DRL scheduler.
Reward Function R: The reward in CADWS is derived from two sources of costs the schedul- ing horizon T. At each time step I, the scheduler incurs an immediate VM rental cost Cy 2 0 for leasing all active VM instances. In addition, an episodic SLA penalty (WW) 2 0 computed the final time step to quantify the total penalty incurred by workflows that fail to meet their dead- lines. In line with these cost components, we define the total return (i.c., negative total cost) for trajectory as:
T-1
R(T)=-) - Σ
Cr Ci (W).
(2)
t=
with the VM rental cost calculated as:
cdo,.
C.m c
(3)
0j 3600
where is the hourly cost of VM my assigned to task On. and is its processing speed. Mean- while, the total SLA penalty is computed the sum over all workflows:
CW)) = Σ (W,),,
(4)
W.EW
C+.a B max (0, CT(W)) - d:},
(5)
where B is the penalty coefficient. CT(W)) is the actual completion time of workflow W; E W, and d, is the workflow's SLA deadline. Let J(T) = Ex>z [R(T)] be the expected total return under
policy и. The goal of the DRI. scheduler to learn an optimal policy x" that minimizes the total scheduling cost, equivalently, maximizes the overall return:
π arg max J (T).
(6)
x
METHODOLOGY
This section introduces DEFT approach in detail. Figure sketches the overall framework of DEFT. Figure 2 elaborates on the internal modules of DEFT. Algorithms in Appendixes C and D present two-phase strategy for training the DEFT policy.
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4.1 THE PROPOSED DEFT POLICY
As illustrated in Figure (c), DEFT enhances policy expressiveness by replacing the fixed policy mapping module (PMM) with MoE architecture (Jacobs et al., 1991). Instead of relying single inference pathway, DEFT trains a set of sparse sub-networks or experts, each specialized for different level of deadline tightness. At inference time, graph-adaptive gating network dynamically selects the most suitable expert based on the current scheduling context.
Figure 2 provides detailed view: panel (A) shows how MoE diversifies the inference pathway to support varied policy behaviors, while panel (B) illustrates our novel gating design that leverages workflow DAG structure, task states, and deadline urgency guide expert activation. This integra- tion empowers DEFT to flexibly align its scheduling strategy with a broad spectrum of dynamic, deadline-driven scenarios.
(a) The Dynamic Enviromment of CADWS
(b) All available VMs the cloud environment
Workflow with varying deadlines are arrving dynamically
Updated the information of completed takks
Transttion:
Queaeing tisks
Executing taoks
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errived
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Workflows state: Agenz rocelves the currest scheduling state of workdlows
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VMs state:
VMs states
Actions: Assign
VMs to ready tasks
W.
Sumbed Etill CAIIW
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tasks
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Store Eineediiigg Modal:: (SEM)
Espert
W4
schedullinn staee changing
Diaadlan Peecaptioe
(c) DRL Agent in CADWSS
Figure 1: The scheduling of dynamic workflows via DRL. (a) Workflows arrive over time, each associated with a distinct deadline; (b) The set available VMs the cloud fluctuates over time; and (c) The DRL agent selects appropriate VM resources for task execution by observing workflow and VM states. this work, our main contribution is to enhance the DRL policy network by incorporating ofxture--o--Expeff (MoE) architecture, enabling more intelligent decision decision-making.
4.2 DEADLINE-AWAN EXPERT DESIGN
MoE architectures are often used to partition the dense layers in neural networks into multiple lightweight MI.P-based experts, each trained handle different sub-tasks. DEFT, we tailor this paradigm for CADWS by assigning each expert particular deadline tightness regime.
Let E I' denote a discrete set deadline relaxation coefficients (e.g., I' (1.25, 1.75,2.25, 3.0)), which control the slackness of workflow deadlines. For each 7, E I' we instantiate corresponding expert EXP; and independently pre-tre pre-train it using only workflows whose deadlines are generated with that specific %. This enables each expert to learn scheduling behaviors optimal for its respective urgency level, ranging from aggressive early scheduling under tight deadlines to cost-efficient delay- tolerant strategies under relaxed ones.
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After expert pretraining, we freeze the expert structure and jointly fine-tune all experts along with a dedicated graph-adaptive gating network. This gating network takes as input: (1) the global workflow embedding produced by the SEM module, (2) the current task node embedding and its topological context (e.g., predecessors, successors), (3) system-level features such as VM availabil- ity, and (4) normalized deadline tightness score. These inputs fused via cross-attention layers to compute a sparse routing vector over the expert set, enabling the selection of the most appropriate expert each decision step.
As illustrated in Figure 2 (A), this design allows DEFT to dynamically adapt its inference pathway based on the urgency of each incoming workflow and the evolving system context. Crucially, expert activation is not static per workflow but evolves over time, facilitating fine-graine grained, deadline-ave awwre scheduling across numerous workflows.
(A): Experts activation in DEFT
(B): Graph-Adaptinn gating
Expert
(a)
current ready
State emtheddings
Wolihor Deadline
Gorph wereeeaaatie ontin
Wi (x)
VM
VM
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Ex(X)
Ws
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embestling
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Leurned state embeddlings from SEM
Linear
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Re- no-mmmmalize
Expert Weights
Priotly outpur
imposoration onds
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Sub-FEN Sub-FEN
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Wiar Wix
The MoE and graph-adaptiv gating network in DEFT. The SEM -eM-geeerated VM em- bedding is routed to the top-K experts selected by the gating network, and their weighted outputs are aggregated produce the scheduling priority. (b) The gating network encodes workflow DAG structure along with VM states, ready task features, and deadline tightness to form the query vector Q, while expert representations act as keys K and values V. (c) Cross-attention computes expert weights that guide expert selections.
Figure 2:
4.3 GRAPH-ADAPTIVE GATING NETWORK
The effectiveness of DEFT in CADW'S comes from its ability to activate the most suitable experts at each decision step, especially under dynamic workflows with heterogeneous deadlines. Since work- flows are naturally represented as DAGs with complex task dependencies, effective expert routing must account for this structure. Conventional MoE gating networks, based on simple linear projec- tions or shallow MLPs, cannot fully capture such topological and contextual information (Cai et al., 2025), making them inadequate for deadline-sensiin sensitive scheduling.
To address this challenge, we design a graph-adaptive gating network for aieeggriied, context- sensitive expert selection. each scheduling step, the workflow DAG encoded using graph attention network (GAT) (Veličković et al., 2017) to capture structural patterns and global depen- dencies. The resulting DAG embedding then fused with workflow deadline features. Then cross-attention mechanism processes this context weight and activate the most relevant experts. This design allows DEFT to dynamically route inference through the expert pathway best suited to the current scheduling scenario, illustrated in Figure 2 (B).
DAG Embedding Learning. As shown in Figure 2 (B), we employ a GAT to capture global corre- lations and task dependencies within the workflow, producing informative DAG embeddings. GAT's attention mechanism dynamically weights neighboring task nodes, enabling the model to focus on the most critical inter-node dependencies. The DAG embeddings produced by the GAT modules

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then used in cross-attention module to select the specific experts to activate. The detailed DAG embedding learning process is described in Appendix B.1.
Cross-Attention for Expert Selection. As shown in Figure 2 (B), the gating network leverages a cross-attention mechanism to perform fine-grained, dcadline-aware expert selection. Specifically, the Query (Q) is formed by concatenating four components: the learned DAG embedding, the feature representation of the current ready task, the VM state embeddings from the SEM, and the workflow's dynamic deadline information. The feature embeddings of all experts are and Value (V) in the attention operation. The resulting attention scores are normalized to form probability distribution over experts guide expert selection.
both the Key (K)
This cross-attention design allows the gating network to make deeply contextualized expert selec- tions. each decision step, it integrates the workflow DAG, the current ready task, and most importantly deadline urgency to choose the suitable expert for VM action prioritization. In doing so, the gating network learns an expert-routing policy that leverages structural and temporal signals to deliver accurate, deadline-aware scheduling decisions. The cross-attention procedure is detailed Appendix B.2.
4.4 TRAINING METHOD
Our proposed DEFT method adopts a two-phase pipeline effectively train the MoE policy net- work. In the Expert Pre-training phase, multiple experts are individually pre-trained to tackle spe- cialized scheduling scenarios with varied deadline tightness. In the subsequent Gating Network Training phase, these experts are integrated into DEFT and further improved together with the gat- ing module and the SEM module make adaptive end-to-end scheduling decisions in dynamic cloud environments.
4.4.1 EXPERT PRE-TRAINING
To ensure that each expert in DEFT acquires diversified expertise for varied deadline settings, pre-train the policy network with multiple different 7, e.g., Y E {1.25, 1.75, 2.25, 5.0). For each setting y, the policy network is trained via conventional RL methods till convergence. Afterwards, the trained policy parameters are extracted and stored. These pre-trained parameters enable us to establish multiple experts. Each expert is initialized with knowledge specific a class of deadline tightness before being integrated into the full DEFT architecture. Appendix C gives the detailed training steps of each expert.
4.4.2 GATING NETWORK TRAINING
After the above phase, all pre-trained experts are loaded into the DEFT policy form the expert pool. Subsequently, both the gating network and the SEM module are trained simultaneously to- gether with all the experts. The gating network routes tasks the most suitable expert in line with the workflow DAG and deadline, while the SEM refines the representation of context-aware schedul- ing states. this phase, we continue to fine-tune experts for enhanced adaptability. Meanwhile, the gating network is trained to accurately identify and select the most suitable experts to handle the respective workflow deadlines. This hybrid training strategy enables DEFT to combine specialized expertise with adaptive gating, delivering robust scheduling across diverse and dynamic deadline scenarios. The detailed algorithm for training the gating network can be found in Appendix D.
5 EXPERIMENTS
This section evaluates DEFT's performance, starting with the experimental setup and baseline methods, followed by comprehensive comparisons under dynamic workflow scenarios examine DEFT's key components.
5.1 PROBLEM SETTINGS AND EXPERIMENT CONFIGURATION
Workflow in CADWS. We evaluate the proposed DEFT method on the CADWS problem using widely adopted simulator (Shen et al., 2025; 2024; Huang et al., 2022). The simulator models

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heterogeneous VM instances (detailed in Appendix E) and four representative workflow patterns: CyberShake, Montage, Inspiral, and SIPHT (Deelman et al., 2015). Workflows are categorized into small (S), medium (M). and large (L) scales according to the number of tasks per workflow, thereby reflecting& a wide range of scheduling complexities. Workflow arrivals are generated using Poisson process with rate À = 0.01, which captures the dynamic and stochastic nature of real- world cloud environments (Huang et al., 2022; Shen et al., 2024). The SLA deadline of workflows governed by two coefficients: y for deadline tolerance and 8 0.24/hour (Shen al., 2024) for penalty severity. Larger values relax deadlines, while larger 3 amplify penalty costs. They together demand scheduling policies strike a balance between renting cheaper VMs and avoiding deadline violations.
Baselines. We experimentally compare DEFT with five baselines, including ProLis (Wu et al., 2017) and GRP-HEFT (Faragardi et al., 2019) as popular priority-based heuristic approaches, as well as ES-RL (Huang et al., 2022), SPN-CWS (Shen et al., 2024), and, GATES (Shen et al., 2025) as state-of-the-art DRL techniques for CADWS. Particularly, SPN-CWS adopts Transformer-base policy network. GATES uses GNNs to model its trained policy networks. Since GATES has shown cutting-edge performance on CADWS, DEFT builds on its neural network architecture and directly inherits its GNN- policy network as its SEM module, as illustrated in Figure I (c).
Parameters of DEFT. To demonstrate the reliability of DEFT, we adopt directly the hyperparameter settings recommended in GATES (Shen et al., 2025) without additional fine-tuning. We construct the graph-adaptive gating network in DEFT with two GAT layers. OpenAI-ES (Salimans et al., 2017) is utilized to train the DEFT policy. This algorithm uses a population size of 40, 3000 generations, an initial learning rate of 0.01, and Gaussian noise with a standard deviation of 0.05.
Two-phase training. (Phase-1: Expert pre-training) We train four experts on S-scale instances under fixed deadlines Y E {1.25, 1.75, 2.25, 5.0). each expert specializing in single deadline regime. Every training instance contains 10 workflows with identical 7. OpenAI-ES evaluates 0.01). (Phase-2: Gating network training with expert fine-tuning) Starting from the pre-trained experts, we jointly optimize the SEM, gating network, and experts on S-scale instances. For each training instance, the deadline sampled from y E {1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.0}, ensuring that the gating network learns to adapt expert selection to varying deadline tightness. Additionally, all baselines are trained on the same mixed- deadline dataset as DEFT's 2 training. This ensures that all methods learn under the same data distribution.
one instance per generation with Poisson arrivals
Testing. We test on S/M/L scales with 30 instances per scale; each instance contains 10 workflows with their y sampled from the same set as above. This setting evaluates DEFT under instances with varying deadline regimes and its generalization from small-scale workflows larger-scale work- flows. All testing is based on 10 independent runs. Additional details are provided in Appendix F.
5.2 MAIN RESULTS UNDER DYNAMIC DEADLINES
Total cost. Table reports results where each test instance is assigned a different deadline, aim- ing to evaluate the algorithm's scheduling performance under highly varying deadline conditions. DEFT has the lowest total cost at all sizes (S/M/L: 52.46 86.60 / 137.69). The margin over the strongest baseline (GATES) grows with scale: improves by 0.49 (52.95 95-45.246 0.9%). M by 11.16 (97.76-86.66 with scale 665.99-255.46 While SPN-CWS beats ES-RL at M (87.69 vs. 109.23), it still trails GATES and DEFT. In short: DEFT achieves strong scalability since its total cost rises more slowly as workflows grow and deadlines tighten. In contrast, heuristic schedulers such as ProLis and GRP- HEFT perform much worse across all scales, showing costs three to ten times higher than -bLed approaches, indicating their inability to cope with dynamic deadlines.
11.4%), and by 57.96 (195.65 199.655-137.66
29.6%). ES-RL degrades sharply
VM/SLA balance. By observing Table 1, ProLis suffers high penalties despite moderate VM fees, while GRP-HEFT avoids violations by overusing costly VMs, making both inferior to DRL methods. In S, GATES excels at minimizing VM fees (20.65) and DEFT focuses more on minimizing SLA (31.45); DEFT's slightly higher VM (21.01) is offset by its lower SLA, yielding superior total cost (52.46 52.95). In M and L. DEFT shifts to cutting VM most (41.06, 70.88), while GATES aims to reduce SLA penalty (42.42, 50.45). Even though DEFT's SLA is not minimal in M/L (45.54, 66.81), the VM savings dominate, so its total cost still leads the competition (86.60 vs. 97.76; 137.69
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195.65). The takeaway is prominent: minimizing one component (VM or SLA) is insufficient; DEFT adapts the trade-off with scale and wins on the overall cost.
Since all DRL methods are trained on the same S-scale data with identical mixed- deadline settings, their performance on the S-scale test set is naturally similar. DEFT still achieves consistent improvement in this in-distribution setting, but its primary advantage appears when evaluated on M and L scales. The markedly larger gains on these unseen scales highlight DEFT's stronger generalization ability, which is the intended benefit of its expert specialization and graph- adaptive gating design.
Generalization:
Table 1: Total cost (mean) with VM fees SLA penalties under dynamic deadlines.
Semartio
Prolis VMISL
GRP 1IEUT
ES RL
SPN CWS
GATES VMISLA
DUPT
Cost
Cost
VMISLA
Cost
VMILL
Cost
VAUSLA
Cost
Cost
VM/SLA
(8)
183.44
79.01 10
297.5 58
297.58/ 55.0.00
65. 39
20.12/ 16.27
54,99
23.31 (3.68
$2.95
20,68
722300 30300
$2.46
21.01 33.45
AAX)
304,08
176.34/ 127.09
495.64
495.64/ 0.00
109.23
63.75 /5.448
$7.68
44.05 43.64
91.76
55.36/ / 42.42
86.00
41.06/ 45.54
12
755.21
279.45/ 447.78
1064.34
1054.34/ 0.00
225.46
170:45 55.01
149.26
90.64/ 58.62
195.65
145.20/50.5
137.09
70.88/
70.88/66.81
5.3
TEST PERFORMANCE ON SCENARIOS WITH DIFFERENT DEADLINES
Total cost comparison. Table 2 fixes the deadline across all test instances to evaluate scalability with workflow size. DEFT consistently achieves the lowest total cost, while heuristic schedulers (ProLis, GRP-HEFT) either overspend on VMs or incur large penalties. ES-RL and SPN-CWS perform less stably, confirming DEFT's superiority. In contrast, DEFT handles both tight and relaxed deadlines well, yielding robust cost reduction beyond single-expert methods. This advantage comes directly from DEFT's MoE design: the graph-adaptive gating network can select the most suitable expert in line with the current deadline levels, allowing DEFT to minimize total cost across diverse scenarios.
VM/SLA balance. As shown in Table 2, the VM and SLA results reveal distinct biases among exist- ing algorithms: GRP-HEFT meets deadlines at very high VM cost; ProLis incurs large SLA penal- ties; and SPN-CWS cuts VM usage aggressively but suffers frequent deadline violations. GATES achieves more balanced trade-off, but DEFT surpasses it by delivering consistently lower costs. DEFT's MoE with graph-adaptive gating dynamically routes tasks to experts based on deadline tightness, simultaneously avoiding excessive VM usage and large SLA penalties. Its adaptive expert selection capabilities keep both VM cost and SLA penalties at a low level. resulting in the lowest total cost. More results regarding convergence and stability can be found in Appendix G.
Table 2: Total cost (mean) and VM rental fees / SLA penalties across every single deadline scenario.
Scenario
ProLis
GRP.HEFT
BS-RL
SPN-CWS
GATES
DEPT
Cost
VMMSSLA
Cost
VMISLA
Cost
VMISL
Cost
VMISLA
Cost
VM/SLA
Cost
VMUSLA
1.0.55 5)
L33.74
83.
$3.25/55.49 49
222.90
222. 9..90000000
54.31
30.91/23.40
40
45.37
18:45/26.92
44.58
18.80/25.7 78
41.58
17.74/3388 84
1.0. .z)
203.70
50.02/113
13.74
339.05
339.63 599.65/0.00
30.37
58.72
06772/77.0 45
72.86
36. 06.14336,2 72
67.53
35.43/32.5 30
66.45
33.89/22.59
1.0. F3)
311.70
179 91-991111100 80
519.50
519. 51/.000000
131.12
103. 65777 .47
112.78
64. 70440448800 08
103.00
65.76/58 14
100.47
57.21/43.22 36
11 25. 5)
118.17
50.58/57.50 58
196.95
196.59 05..00
47.33
01.52/1..8
40.58
17.74/22.8 84
39.39
17.79/216 60
37,43
17.34/20.09
190.02
108, 108.34/2222
317.70
317.7040.00
77.07
06.76/2112
43
33.85/29.17 71
61.53
32.47/29.06
421.52
31/1966111
52685
192.89
112.37
05.98446.99
105
68.72/36.61
99.16
57.43/41.73
115.5 80
152.44
68/56.76 76
190.55
150.5500.00
72/77/
30.53
17 07.66-11 67
38 11
17.99/2011
36.87
17.74/1.11
1.5. (2)
187.65
94.21/93.44
375.30
375. 30.00000000 00
$0.33
52.12/27.91
65.68
34. 38/31
50
62.56
31,05/28.5 51
61.37
32. $2.95/8840 42
1.5. 1)
306.09
330.53995.00 76
$10.15
510. 1540.00
198.61
104-76/33.0 85
114.46
68. 03.55145.000 99
102.00
C5. 88/38 15
98.51
58.02/4013 29
1 1.75. 8)
149.24
63 85/85.80 30
186.55
186. 5540.0
$2.68
30 54/33. 34
10:14
1N.42/20.7
72
37.91
18.61/16.
70
36.75
18. 46/1 29
11.75 3/)
187.17
122 16/64.11
374.34
354.35.0.00
96.93
65 65.84/31.09
64.52
34.55/29.99
97
62.39
34,71/27 68
60.57
[1 E)
119.36
239 559.551159.88
$24.20
$34.2000.00
212.36
171.14/11.2 224
109.96
66 46640443.56 5.56
104.85
69.41/35.1 41
96.20
59 39..6638.1 74
(2.0.
96.12
(22222255,4 AD
192.24
192. 220.22/0000
47.91
86.20111.11
37.04
18.19/18.85
37
34,63
18.0/16.57
22.0.
232.36
383.54
$2/29.20
12.11//7.22 25
57
32.37/25
56,
31 81.88/5.00 06
2)
265.92
443.20
443.2000.00
62
161 161.33/40.29
102.00
61.59/40.41
97.09
63.62/33.
93.90
56.71/37.09
2:255 81
125.22
68443.24
157.40
4100.00
44.50)
16/19,34
35.31
17.9517.36
34.79
18.36/16.49
33,01
17.75/15.26
2:225 M]
465
79 98/R5/ 47
330.90
90/0000
$2.73
$8.59
32. 02.51/26.00 08
56 30
32.13/24 67
55.45
31.56/33 89
22:25, F)
352.08
179.9/172.1 15
440. 10
440. 10/0.00
201 48
162. 72/98 76
103.
63. 71/77410000 80
95.05
63.32/52 61
92.55
56. 25/36 30
3.0. 5)
97.44
59. 19..793799 95
191,88
19415800000
4
23 21/8858
32.76
17.80V15.16 16
32.48
18.17/14.31
30.74
17.53/13.21
3.0 MZ)
166.55
93. 36/75.99
277.75
277. 750000
76.03
S01 10225.95
55.57
32. 022.22233.55 34
55.54
33,34/22 20
52.32
31.44/20.85 SS
(3.0. F)
293,10
157. 89/135.11
488.50
458. 5t00.00
163.45
128 03/35.4
100.52
65.42/35.11 10
97.70
67.29/30.41 41
93.69
53.0633.63
5.4 ABLATION STUDIES
We evaluate DEFT on the same testing scenarios by analyzing its gating design, the effect of replac- ing the PMM of GATES with a deeper MLP, and its average per-step inference overhead. The results show that DEFT delivers the best overall performance while keeping inference overhead modest.

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Published as a conference paper at ICLR 2026
Comparing Gating Mechanisms. We first isolate the effect of the gating network inside DEFT. All gating networks receive the same input embedding; they differ only in how they score experts. As summarized in Table 3, the linear gating performs the worst, the MLP gating improves but still falls behind, and the graph-adaptive gating used by DEFT consistently achieves the lowest total cost on all S/M/L scales. This confirms that CADWS benefits from the proposed graph-adaptive gating that is aware of workflow structure and deadline pressure, and that simple linear or MLP gating cannot fully exploit expert specialization.
Table 3: Performance and average per-step inference overhead on different testing scales.
Total Cost
Average Inference Overhead (second/step)
Method
S
M
S
M
L
Overall (S+M+L)
GATES (original PMM)
52.95
97.76
195.65
0.0616
0.1610
0.4250
0.2159
GATES deep MLP-PMM
52.91
98.41
194.77
0.0674
0.1267
0.6979
0.2973
DEFT + Linear gating
52.85
88.41
142.27
0.0608
0.1453
0.4467
0,2176
DEFT + Graph-adaptive gating (ours)
52.46
86.60
137.69
0.0648
0.1482
0.4525
0,2218
DEFT + MLP gating
52.70
87.34
141.62
0.0777
0.1586
0.5206
0,2523
MoE-PMM vs. MLP-PMM. To check whether DEFT's gain over GATES comes merely from using more MLP experts in MoE, we compare DEFT with the original GATES and stronger GATES with a deeper MLP-PMM. Table shows that GATES and GATES+deep-MLP PMM achieve nearly identical performance, whereas DEFT clearly outperforms both across all scenar- ios. This indicates that the improvement stems from MoE's s ability to select specialized policies per decision step, rather than from simply increasing network capacity.
Inference Overhead. Table 3 also reports the per-step inference overhead on all testing scales. As expected, the original GATES model the fastest overall, because it does not include any MoE component and therefore avoids extra routing computation. Adding MoE top of GATES (all DEFT variants) inevitably introduces some overhead, but the increase is small. DEFT with linear gating and DEFT with graph-adaptive gating are only slightly slower than GATES, while achieving much lower total cost. Among the DEFT variants, linear gating is the cheapest to run; our graph-adaptive gating adds only small overhead because it only computes attention weights for expert selection (see Appendix B.2); MLP gating is the most expensive because it must learn new embeddings through multiple fully connected layers at every decision step. Finally, GATES deep MLP-PMM is the slowest method overall, because it infers through deeper MLP at each decision step.
Overall, these ablations show that adding an McE-PMM to GATES reliably improves scheduling performance. Our proposed DEFT offers the best performance and moderate latency, benefiting from its lightweight cross-attention design. Additional ablation studies, including sensitivity to the number experts and Top-k routing and pre-training 7, are provided in Appendix H.
CONCLUSION
This paper presented DEFT, the first Mixture-of-Experts architecture for dynamic cloud workflow scheduling. DEFT trains multiple experts specialized for different levels of deadline tightness and employs a graph-adaptin gating network that utilizes workflow DAGs, VM states, and more im- portantly deadline urgency activate the most appropriate experts. This combination enables DEFT to adapt its scheduling strategy across diverse scenarios with both flexibility and precision. Extensive experiments demonstrated that DEFT can consistently achieve the lowest overall cost, outperform- ing heuristic and sfate-of-the-an DRL baselines by delivering a superior balance between VM rental fees and deadline penalties.
Looking ahead, future research may extend DEFT to multi-tenant cloud environments, integrate explainability into expert routing, and explore broader applications of graph-adaptive MoE models for large-scale resource management.
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ETHICS STATEMENT
Our research focuses on dynamic workflow scheduling in cloud computing environments. The work does not involve human subjects, personally identifiable information, sensitive data. The exper- iments are conducted entirely on synthetic and publicly available benchmark datasets. Potential societal impacts are positive, as the proposed methods improve energy and cost efficiency in cloud systems. We do not foresee any negative ethical implications from this research.
REPRODUCIBILITY STATEMENT
To ensure reproducibility, we provide: (I) full description of the problem formulation and al- gorithm design in Sections 3; (2) detailed experimental settings, including datasets, baselines, and hyperparameters, in Section 5 and Appendix F; and (3) complete pseudo-code for the training algo- rithm in Appendices C and D. The source code and scripts for reproducing all experiments will also be released publicly upon acceptance.
LLM USAGE STATEMENT
During manuscript preparation, we used large language model to assist with language polishing, grammar correction, and rephrasing. We carefully reviewed and edited the L.M--generted text to ensure accuracy and originality. LLM was never used to generate experimental results, algorithm designs, neural network architectures and other core technical contributions.
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A DETAILED PROBLEM FORMULATION
This section provides a more detailed description of the Cost-Aware Dynamic Workflow Scheduling (CADWS) problem, complementing the concise formulation presented in Section 3.
A.1 WORKFLOWW MODEL.
A workflow W E W is represented by directed acyclic graph (DAG) W; = (Ow, Cw., ). where Ow, is the of tasks and Cw, the set of precedence edges. Each directed edge (O Ong) E Cw, indicates that task Ozi must finish before task Ony can begin. A task becomes a ready task, denoted by On-, once all its predecessors have completed. Each task Oni E Ow, has a computational demand edo.. E RRt which measures the amount of work required. Workflows arrive dynamically with an arrival time a, and a deadline
dj a; + minMakespan Wi),
where 7 2 1 is the deadline relaxation coefficient, and minMakespan( (W,)) is the minimum execution time achievable all tasks are processed on the fastest VM without waiting.
(;)
The proposed DEFT operates in concurrent multi-workflow setting where all workflows share the same VM pool. At each decision step, it observes global state that includes all ready tasks across workflows, VM statuses, and workflow deadlines, so inter-workflow resource contention is treated as part of the scheduling problem itself. The state embedding module and graph-adaptive gating network are both defined on this global state, enabling DEFT learn how workflows interact and to coordinate their execution without any extra cross- cross- workflow coordination module.
A.2 CLOUD ENVIRONMENT
The cloud provides a pool VMs M = {mi, m2.......... M each characterized by a processing speed 2 and an hourly rental cost cj. VMs can be provisioned on demand without fixed capacity limits, but the cost grows with the number leased instances. If task On is assigned to VM my. its execution time is:
cdo.:
Toke O
(8)
Uj
Let Tatart be its start time, then the completion time of Oni
is:
Toom
Totart + my,
(9)
The completion time of a workflow W, is the finish time of its last task:
CT(W:) max Teomp, O.EDOw,
(10)
A.3 VM RENTAL COST AND SLA PENALTY
At each time step f, executing the ready task On- on VM my incurs a cost:
cdo.-
C =
(1I)
0j
3600
and the cumulative VM rental cost across the scheduling horizon T'is:
T-1
Cr
[o.T]
C.T,,
(12)
2
Each workflow W; is associated with penalty if it misses its deadline. The penalty is defined as: Crlaa = 3 max(0, CT(W)) - -d
(13)
where B is the penalty coefficient. The total SLA penalty over all workflows is:
Cale
Σ Cgl)(W
(14)
W.EW
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B THE DETAILS OF GRAPH-ADAPTIVE GATING NETWORKS
B.1 DAG-EMBEDDING LEARNING
Each workflow W; is represented by a directed acyclic graph (DAG), denoted as W; (Ow, ; Cw: ) where Ow, is the set of task nodes and Cw, is the set of precedence edges. For a task node On E Ow. let (Onss) denote the set of its neighboring task nodes the DAG. The input feature of On is represented as ho... E IR..
To capture dependencies among tasks, we employ a Graph Attention Network (GAT), The attention coefficient from task On to one of its neighbors Onj is defined as
exp (Lea [Who || Who.,))
aij Σ (O..N) exp (LeakyReLU(a [Who..: || Who...))
(15)
where W is learnable transformation matrix, is trainable attention vector, and denotes catenation.
The hidden embedding of node One is then obtained by aggregating messages from its neighbors with attention weights:
bo... =0 Σ
Oij Who
(16)
(OsEN((O..)
where (-) is non-linear activation function, e.g., ReLU.
Once all nodes in W3 are updated. we compute the workflow-level DAG embedding by applying a mean pooling over the task embeddings:
hw, 10w. On.EOw;
Σ
ho....
(17)
The resulting hw, R serves as a compact representation of the workflow DAG, capturing both task-specific features and structural dependencies among tasks. This embedding is later used by DEFT inform scheduling decisions.
B.2 CROSS-ATTENTION FOR EXPERT SELECTION
At each decision step, rank E parallel experts via cross-attention mechanism that maps contex- tual features to per-expert weights. Consider a batch of N actions with embeddings A E R Daes. Let g R x Rax be the learned DAG embedding,
R RIxDready the ready-task embedding, and the SLA deadline coefficient. We broadcast (g, 7) across the batch and form queries:
E R x1x1
Q
Wy [A:g:r:/ E IR Nxd
(18)
where [ denotes concatenation and W, is a learned projection. Each row of Q is the query for one VM action.
Q/K/V in cross attention. We maintain a learnable token table Exd with one d-dimensional token per expert. For each action in the batch, the attention inputs are:
== 4r E R 1lxd
K= Exd
V=TEREN
In standard self-attention, the attention output is:
Attention(Q, K, V) softmax
QKT Vd
V.
(19)
However, in our gating scenario, we only require the attention weights to rank experts, and the multiplication by V (which would produce a new representation) is unnecessary. So, let qn be the n-th row of Q, the scaled dot-product attention gives:
On softmax
q. KT Vd
E
E
(20)
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where an [n..1........................... 0n, RR, and Onee denotes the weight assigned to expert for action (e L)....E).. Stacking over N actions yields E RN
Sparse Top-k routing. For each action n, we select the index set the top-k experts
(x)
TopK(an)),
k
and re- re-normalize the selected components to form mixture weights
Wn.e
Ejerp
Σ
On
On.
(e (eE2
&
Σ
Wn,e = 1.
(21)
2EER
The routed output for action is
Σ EEE
Wn.e fe(.),
(22)
where fe(-) denotes the forward network of expert
C TRAINING OF EACH EXPERT UNDER DIFFERENT DEADLINES
Following existing works Shen et al. (2024; 2025), train each expert under a different workflow urgency to learn specific knowledge under this deadline scenario. OpenAl ES is population-based optimization technique known for its robustness against hyperparameter sensitivity, insensitivity to the design of reward signals, and suitability for parallel implementation, making it particularly effective for policy optimization tasks in dynamic environ- ments Salimans et al. (2017); Khadka & Tumer (2018). The main procedure involves the following key steps:
the OpenAl ES Salimans et al. (2017) to
(1) In each training generation, we first sample population of N individuals centered around the current policy parameters 0 from Gaussian distribution. Specifically, the parameter vector for individual is generated as:
0 0 - 4 N(O,
(23)
(2) Next, we evaluate the fitness F0,) of each individual parameter 0,, which defined as the negative of the total scheduling cost (including VM rental fees and SLA violation penalties) obtained by using the policy network parameterized by 0₂:
F(O,) = R(T) - Σ C C
(24)
t=
(3) Subsequently, we update the current policy parameter ê by estimating the gradient to maximize the expected fitness of the population, thereby minimizing the total scheduling cost:
TOBenNon oe:)) ~
F(O oe:)es
(25)
No
This process of sampling, evaluating, and updating parameters repeats until maximum number of generations is reached. The training procedure is outlined in Algorithm 1.
D TRAINING OF GRAPH-ADAPTIVE GATING NETWORK
Let (ch 1K be the pre-trained MLP experts obtained in Appendix C, where K denotes the number of experts. During the second-stage training, we jointly optimize the graph-adaptive gating network with parameters 89, the State Embedding Module (SEM) with parameters 0*, and all pre-trained experts (ox1 We pack all trainable parameters into a single vector:
θ
[00; 0º; [k
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Algorithm OpenAl ES for policy training
Population size: N, max number of generation: Gen, initial parameters of policy with DEFT: 8, initial learning rate: a, and the Gaussian standard noise deviation:
Input:
Output: The trained policy
1: while the current number of generation <= Gen do
2: Randomly sample a CADWS training instance: Pro.
3: for each individual (i=1.2..... in N do
4: Sample a 6 (0, I).
5:
The parameters of 7; represented by individual i: 0; = d6; 6: Evaluate the fitness value of F(0,) using equation 24 based on Pro
7:
end for
8: Estimate the policy gradient V Vgl N(00,00 F(..)
F(0.) using equation 25. 1 Σ [F + oa)a).
9: Update parameters π: + 0 + No
end while
11:
return the trained policy æ
Given a state 9; (DAG embedding, ready-task features, VM features. and deadline), the SEM pro- duces context vector h, = fe (8z), the gating network outputs expert weights w, = geo (St, ht) with =k=1 Wi,k 1, and the DEFT policy mixes expert output as:
ADEFT(a:(s:) Σ W (x(alss:
(26)
The fitness is the negative total scheduling cost in equation 24. The pseudo-code is shown in Algo- rithm
Algorithm DEFT Training (SEM + Gating + Experts via OpenAl ES)
Inputs:
Pre-trained experts føx k== (to be fine-tuned); initial gating params 89; initial SEM params
0%; CADWS training distribution D; population size N; ES hyperparameters (learning rate a, noise standard deviation a, generations Gen).
Output:
Trained (09,05 0*, ; (dx }
1: Define the trainable parameter vector é - [09; 0"; (0xx [
Note: In OpenAl ES, each individual is sampled as O, θ + with NNO0 (); Algo- rithm handles sampling and gradient estimation.
2: Define FITNESS(O,):
3: Load θ - (89, 8", { into DEFT
4: Sample CADWS instance Pro D
5: Roll out #DEFT on Pro: for each step f,, compute h4 = So (8t). w. goo (Se, h4), and
k= Wt,k TT& (T (arlss; Φu) 6: Return FITNESS ((TNESS((O))) using equation 24
(DEFF(aa)s:) >x
7: Optimize θ by invoking Algorithm 1 with population size N, noise a, learning rate a, genera- tions Gen, and FITNESS the evaluator
8: return the optimized (09, 0", (0x {
E VM CONFIGURATION AND WORKFLOW PATTERNS
VM Configuration. We adopt six Amazon EC2 VM types ranging from m5. large to m5. 12xlarge, varying in computational power and cost. Table 4 lists their specifications.
Workflow Patterns. We simulate four workflow types (CyberShake, Montage, Inspiral, SIPHT) with different DAG structures, as shown in Figure 3. The number of tasks per workflow varies with the scale, shown in 5.
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Table 4: The configuration of VM instances.
VM Type
vCPU/Memory (GB)
Cost (S/hour)
m5. large
2/8
0.096
m5 xlarge
4/16
0.192
m5 2xlarge
8/32
0.384
m5 4xlarge
16/64
0.768
m5 8xlarge
32/128
1.536
m5 15.12x1arge
48/192
2.304
Table 5: Workflow patterns and sizes.
Scale CyberShake
Montage
Inspiral/IIPHT
Small
30
25
30
Medium
50
50/60
Large
100
100
100
F ADDITIONAL TRAINING AND TESTING DETAILS
Training and testing use instances of 10 workflows with a Poisson arrival process (A = 0.01). Within any single instance, all workflows share the same deadline y; across instances, varies by phase. In Stage-1, 1, each expert is pre-trained on S-scale instances at fixed deadline chosen from {1.25, 1.75, 2.25, 5.0). In Stage-2, the state embedding network, gating network, and pre-trained experts networks are jointly optimized on S-scale instances where the per-instance deadline is sam- pled from (1.0, 1. 1.25, 1.5, 1.75, 2.0, 2.25, 3.0). Although experts are pre-trained discrete 7 values, phase-2 training uses mixed-deadline distribution that exposes all experts and the gating network to various y values (c.g.. 1.5, 2.0). Through this phase, the gating network learns a smooth mapping from varied deadlines and state features to suitable expert choices. For intermediate deadlines such as y = 1.5 or = 2.0, the gating network does not simply pick the nearest experts, also considers the current scheduling pressure, deciding whether SLA risk VM should be prioritized. As result, it adaptively selects between the experts whose behaviors best match the ongoing context.
For testing, use 30 instances per scale (S/M/L.); each instance draws single deadline from the same sampled set and applies it to all workflows. This protocol exposes the gating network to deadline variation while permitting mild expert fine-tuning. Additionally, in this work, we the parameters of Top-k as 1, meaning that we only select one pre-trained expert by the gating network every decision step. Top-1 routing enables the gating network to directly activate the expert whose behavior best fits the current scheduling state, while still rotating across different experts over the full trajectory. The benefit of this Top-1 routing behavior is illustrated in Appendixes H. and Table 6 summarizes the detailed configuration of training and testing.
Montage
Cyber
Inspiral
Figure 3: The workflows studied in this work.
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Table 6: Training and testing setup. "Scale" indicates the workflow scale/size. "Card." stands for cardinality.
Phase
Updated Params
Scale
Card.
Stage-1 train
Experts
S
Fixed
{1.25, 1.75, 2.25, 5.0)
Stage-2 train
SEM+Gatc+Exp
S
Sampled
{1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.0]
S test
None
S
Sampled
{1.0, 1.25, 1.5, 1.75, 2.0, 2.25.
M test
None
M
Sampled
11.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.0g
test
None
L
Sampled
[1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.0)
G ADDITIONAL EXPERIMENTS ON CONVERGENCE AND STABILITY
Convergence analysis. Figure shows the convergence curves of ES-RL, SPN-CWS, GATES, and DEFT small- and medium-scale workflows. ES-RL exhibits slow and unstable learning, with large fluctuations and much lower solution quality in both cases. SPN-CWS converges faster but plateaus at higher total costs, reflecting its limited policy expressiveness. GATES shows more stable convergence and better final performance, yet still lags behind DEFT. In contrast, DEFT not only converges quickly but also reaches the lowest total cost with reduced variance, confirming that its MoE architecture and graph-adaptive gating enable more effective policy learning across different workflow scales.
Convergence S scale workflows
Convergence scale workflows
-Tbbl cost)
ES RL GATES
ES-RL RL GATES
-00
DEFT
DEFT
400
800
1200
1600 Generation
2000
2400
2800
0
400
800
1200
1600 Generation
2000
2400
2000
(a) Small workflow
(b) Medium workflow
Figure 4: Convergence of testing performance under dynamic workflow deadlines.
Performance stability analysis. Figure 5 compares the distribution of total costs across indepen- dent runs on small- and medium-scale workflows. ES-RL exhibits the largest variance, with widely scattered results and frequent extreme outliers, indicating unstable learning behavior. SPN-CWS shows moderate improvement but still suffers from noticeable variability as workflow size increases. GATES achieves tighter distributions with fewer outliers, reflecting more stable scheduling perfor- mance. DEFT demonstrates the most concentrated distribution across both scales, with consistently lower variance and narrower interquartile ranges. This highlights that the combination of MoE spe- cialization and graph-adaptive gating not only reduces average total cost but also ensures robust performance stability, which is crucial for real-world deployment.
H ADDITIONAL ABLATION STUDIES
We present additional ablation studies examining three key parameters in DEFT: (i) the number of experts, (ii) the choice of Top-k routing, and (iii) the selection of y values for expert pretraining. Together, these results verify the architectural choices of DEFT and demonstrate that the proposed graph-adaptin MoE architecture provides consistent and meaningful gains in CADWS. All these ablation experiments are under small setting with 10 instances, each composed of 5 workflows.
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WF Size=S
WF Size=M
1.40
140
Total Cune
1200
85-R1
SPR-EWS
GATES
DEFT
ES-RL
SPM--WW
GATES
DEFT
Algorithm
Algonttim
(a) Small workflow
(h) Medium workflow
Figure 5: Stability the testing set with dynamic workflow deadlines.
H.1 JOINT ABLATION ON THE NUMBER OF EXPERTS AND ToP-k ROUTING
To obtain a complete understanding of how the proposed DEFT behaves under different architectural settings in CADWS, we conduct joint ablation over representative combinations of expert numbers {2, 4, 8) and Top-k routing choices {1, 2, 4). This results in 8 configurations in total. Table 7 reports the scheduling performance of each configuration.
Table 7: Effect of varying expert counts and Top-k routing choices in DEFT.
S
M
L
#Experts
Top-k
Total Cost
VM
SLA
Total Cost
VM
SLA
Total Cost
VM
SLAA
1
19.80
9.11
10.69
32.09
16.66
15.43
49.09
25.05
24.04
2
2
20.56
9.47
11.09
35.13
18.25
16.88
53.36
26.43
26.93
1
20.18
9.17
11.01
28.32
16.73
11.59
45.20
24.04
21.16
4
2
19.86
9,08
10.78
31,48
17.09
14.39
48.76
25.24
23.52
4
20.60
9.62
10.98
30.88
16.89
13.99
48.79
25.95
22.84
19.61
9.20
10.41
32.67
17.08
15.59
49.02
25.25
23.77
8
2
20.69
9.38
11.31
32,80
17.26
15.54
53.90
28.08
25.82
4
20.75
9.86
10.89
33.12
17.88
15.24
50.50
28.03
22.47
Effect of Expert numbers. As shown in Table 7, configurations with only two experts consistently underperform on most testing scenarios, particularly in and L, regardless of the choice of Top-k. The limited deadline coverage during pre-training forces the experts absorb broad and hetero- geneous scheduling patterns, leading to coarse- coarse-grained -rained behaviors with insufficient specialization. As a result, the gating network has few meaningful routing options, and increasing &: offers benefit.
Conversely, eight-expert configurations suffer from excessive redundancy. Many pre-training val- close, leading experts converge to nearly identical policies. This redundancy increases routing ambiguity, as multiple experts provide almost the same policy behaviors, making the expert selection harder for the gating network and causing overall performance to degrade across all Top-k settings.
Effect of Top-k Routing, Top-1 routing consistently performs best across most settings accord- ing to Table 7. Activating only the highest-scoring expert preserves the specialization encoded in each expert policy and avoids the noise introduced by averaging multiple experts' outputs. Increas- ing l generally weakens this specialization signal and yields diminishing negative performance, especially when the expert pool already contains overlapping behaviors, as the 8-expert case.
4 Experts Top-1. The joint ablation reveals clear and consistent pattern: the number of experts determines how many distinct scheduling policies the DEFT can express, while the Top-k value controls how precisely the gating network of DEFT can leverage that diversity. Their interaction therefore essential, as experts only perform well under specific Top-k settings and vice versa. Among all nine tested combinations, the configuration with experts and Top-1 routing achieves the strongest overall performance in CADWS. With four experts, the policy pool is diverse enough to include clearly separated SIAA-saving and VM-saving strategies, yet compact enough to avoid
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redundancy. Top-1 routing then allows the gating network cleanly choose the expert whose policy best matches the current state, resulting in more stable and clearer scheduling decisions. As shown in Table 7, this combination achieves the lowest total cost, especially in M and L testing scenarios. These results indicate that DEFT performs better when expert diversity is meaningful and the gating network can decisively pick the right expert, which is precisely why we adopt the 4-expert Top-1 configuration in this paper.
To further analyze the Top-1 phenomenon, we performed transparency analysis that logs the VM selection by every expert, as detailed in Appendix I. The results show that Top-1 routing can ac- tivate the experts whose policy behaviors best match the current scheduling state, providing better performance than higher Top-k in our CADWS settings.
H.2 THE CHOICE OF FOR EXPERT PRE-TRAINING
As the previous ablation in Appendix H.1 has identified the 4-expert Top-1 configuration the most effective design in DEFT, the following y study conducted under this setting. We evaluate three configurations of y values for expert pre-training: (1) evenly spaced values, (2) randomly sampled values, and (3) compact cluster values. These 7-sets differ primarily in how broadly they cover the full spectrum of deadline tightness. Table summarizes the results under the ablation testing scenario.
Table 8: Effect of different sets for DEFT expert pre-training.
S
L
set for expert pre-trae pre-training
cost
VM
SLA
cost
VM
SLA
cost
VM
SLA
Evenly spaced: [1.25, 1.75, 2.25, 5.0]
20.18
9.17
11.01
28.32
16.73
11.59
45,20
24.04
21.16
Randomly sampled: [1.25, 1.5, 3.0, 3.0, 5.0]
20.61
9.67
10.94
32.70
17.92
14.78
53.41
28.70
24.71
Compact cluster: [1.0, 1.25, 1.5, 1.75]
21.04
9.21
11.83
34.39
18.09
16.30
53.49
28.16
25.33
The experiments show a consistent pattern. Both the evenly spaced and the randomly sampled 7-sets y-sets span wide range of deadline conditions, which exposes each expert to sufficiently different deadline regimes during pre-training. As a result, the experts learn clearly differentiated scheduling styles, from strongly SLA-saving to VM-saving. giving the gating network a diverse and well-separated expert portfolio. This diversity directly translates into better scheduling performance, improving performance compared with the compact cluster set.
In contrast, the manually crafted 7-set clusters most values in a narrow interval. This restricted coverage causes experts to receive nearly identical training signals, leading them to converge to overly similar policy behaviors. The resulting homogenized expert pool provides little meaningful variation for the gating network to exploit, making expert routing less informative and ultimately degrading scheduling quality.
Overall, these results indicate that DEFT does not require precise tuning of the 7 values. What matters is simply that the selected ry-set adequately spans the diversity of deadline tightness levels. Whenever this condition satisfied, such as with uniformly spaced or randomly sampled values, the expert specialization remains well-structured, and the proposed graph-adaptive gating network can reliably differentiate between experts and select the fittest one at each decision step.
H.3 SUMMARY
Overall, these ablation studies lead to three clear conclusions about the design of DEFT. First, the MoE architecture of DEFT is effective only when the expert pool provides genuinely diverse scheduling behaviors and the gating network can reliably select among them. The joint ablation over the numbers of experts and Top-k routing shows that this balance is achieved most robustly by the 4-expert Top-1 configuration in CADWS problem. Lastly, the choice of pre-training y values does not require careful tuning, DEFT remains stable as long as the selected pre-training set spans broad range of all deadline tightness.
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1 THE CHOICE OF TOP-1 ROUTING IN DEFT
From Appendix H.1, we already know that the Top-1 routing in DEFT shows more stable and good performance than higher Top-k. To further understand this phenomenon, we performed a trans- parency experiment that logs the VM selected by each expert. When the current number of VM actions becomes larger than the previous state, these newly appearing corresponds to the newly rented VMs at the current state, which allows us to see whether expert prefers renting reusing VMs. We also record the VM occupation rate as an indicator system load: a high VM occupation rate means the VM pool is heavily occupied with long queues, while a low occupation rate means the system has abundant free VM capacity. Table 9 presents six representative examples from dif- ferent scheduling states and reveals expert behaviors that explain why Top-1 routing is better suited to CADWS than Top-k (k > 1).
Table 9: Transparency experiment. At each decision step, we log the VM chosen by each expert, the current and previous numbers of available VM actions, the current VM occupation rate, and the deadline coefficient y.
Example
VM selection per expert
current VM numbers
previous VM numbers
VM occupation
?
[28, 28, 28]
27
0,91
1.25
2
[47, 47,47, 47,
46
0.82
2.25
3
[25. 8, 8, 48]
52
52
0,23
1.25
4
[6, 26, 18, 21]
33
33
0.078
2.25
[34, 34, 25]
33
0.43
1.25
[54, 48]
61
0.62
2.25
1.1 EXPERT BEHAVIOR ACROSS EXTREME AND TRADE-OFF STATES
Examples 1-4 show two types of extreme scheduling states in which experts tend to converge to similar decision. Examples and 2 correspond to SLA-critical situations with very high VM occu- pation rate (0.91 and 0.82). In Example 1, fight deadlines (7 1.25) make reusing existing VMs likely to trigger SLA violations, and all experts select to rent a new VM (index 28). In Example 2, even with a more relaxed deadline (7 2.25), the high VM occupation rate keeps SLA violation risky, and most experts again choose to rent a new VM (47), with only one expert opting for using an existing VM (38). Examples 3 and represent VM-abundant states with low occupation rate (0.23 and 0.078). Under such conditions, the system already has enough idle VM capacity, so rent- ing another new VM tends to increase cost while offering few benefits for avoiding SLA penalties. In these cases, experts naturally agree on reusing existing VMs such as indices 6, 8, 18, or 25, re- gardless deadline tightness. These four examples demonstrate that under both extreme states, SLA-critical and VM-abundant states, experts gravitate toward similar or even the same VM action, making Top-1 and Top-k produce nearly identical decisions.
By contrast, Examples and reflect intermediate trade-off states where neither SLA pressure nor VM cost fully dominates. In Example 5, moderate occupation rate (0.43) and a tight deadline (7 = 1.25) cause experts to split between renting the new VM (34) and reusing existing ones (24 or 25). Example 6 shows similar divergence at a slightly higher occupation rate (0.62) with relaxed deadline (7 2.25). These trade-off states exactly where the experts behave differently: some choose the newly rented VM to avoid possible SLA violations, while others reuse existing VMs to keep the VM cost low.
1.2 WHY T IS A BETTER FIT FOR CADWS
In CADWS, the action space discrete. The scheduler should select one VM at each decision step. This means the gating network cannot "blend" expert recommendations. For example, in Table 10, Expert I strongly prefers VM B and Expert prefers VM C. mixing their action distributions under Top- can artificially raise the probability of an entirely different VM (e.g.. VM D). This blended action distribution misled the gating network to pick a VM that none of the experts actually recommended. This limitation has little impact in extreme states (Examples 1-4), where all experts tend to agree on the same VM. However, the situation changes in trade-off states (Examples and 6), where experts genuinely disagree: some prefer renting new VM stay safe SLA
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violation, while others would rather reuse existing VMs to save VM cost. Top-k (k > 1) mixes these conflicting opinions and often blurs the strongest action signal, which can push the scheduler toward less suitable VM.
Table 10: Top-k blending can select a VM that no expert actually prefers (expert weights w1 w1=0.4, W2 0.6))
Action probability distributions
Who prefers this VM?
VM
Expert (a)
Expert (a)
Mixed Tiix
Expert
Expert
Top-k 2) mixing
A
0.10
0.05
0.07
PC
0,45
0.10
0.24
Yes
0.05
0.50
0.32
Yes
0.40
0.35
0.37
Yes
The transparency analysis in Table 9 and the examples in Table 10 reveal that: When the system is in an extreme state, Top-1 and Top-k behave almost the same because experts reach natural agreement. When the system enters trade-off state, Top-k becomes unreliable because it smooths away the expert differences that actually matter. Top-1 avoids this problem by letting the gating network choose the single expert that best understands the current situation, leading clearer and more stable decisions, renting VMs when deadlines are tight, and reusing VMs when saving VM cost matters more. This makes Top-I a better match our CADWS problem.
1.3 EXPERT SELECTION ACROSS TIME
Using Top-1 does not eliminate the benefits of multi-expert architecture from MoE. In CADWS, full scheduling process consists of thousands to tens of thousands of decision steps, and the gating network frequently selects among experts in context-dependent manner. When VM occupation rate rises and workflow deadlines tighten, the gating network chooses towards SLA-saving experts; when deadlines relax, shifts towards VM-saving experts. Thus, DEFT does leverage diverse expert policies and mixes them across the whole scheduling process, which is exactly how MoE delivers gains in CADWS.
ARCHITECTURAL-LEVER ADVANCES BEYOND GATES
Although DEFT reuses the GNN encoder from GATES, it introduces fundamentally different decision-making mechanism. GATES relies single-path priority mapping module (PMM), which restricts the scheduler to one static scheduling mode. contrast, DEFT replaces this fixed PMM with MoE architecture by incorporating graph-adaptive gating network and set of spe- cialized experts, as shown in Figure (c). The gating network selects the most suitable expert based on the evolving deadline pressure, workflow structure, and VM cost state, enabling DEFT to select policy behaviors dynamically over the whole scheduling horizon. This adaptive, multi-mode expert policy cannot be expressed by GATES. Therefore, DEFT is not minor modification of GATES but framework that expands the expressive power of the scheduling policy through expert specialization and deadiine-conditioned expert routing.
To further clarify, in our CADWS setting, deadline tightness is the main factor driving scheduling performance, so we use as the primary dimension for expert specialization in our MoE design. In other scenarios where workflow size, task heterogeneity, or resource type have a stronger impact on scheduling, these attributes could also used to deñine expert specializations.
23


Reviews:
[{"review_id": "6ClYOKF5KE", "reviewer": "Reviewer_3WxC", "summary": "This paper introduces DEFT, an innovative DRL policy architecture that leverages a specialized mixture of experts for dynamic cloud workflow scheduling. By adaptively routing decisions through the most appropriate experts, DEFT is capable of meeting a broad spectrum of deadline requirements that no single expert can achieve. Central to DEFT is a graph-adaptive gating mechanism that encodes workflow DAGs, task states, and VM conditions, using cross-attention to guide expert activation in a fine-grained, deadline-sensitive manner. Experiments on dynamic cloud workflow benchmarks demonstrate that DEFT significantly reduces execution cost and deadline violations, outperforming multiple state-of-the-art DRL baselines.", "questions": "1.\tCan the proposed approach handle inter-workflow dependencies or coordination?\n\n2.\tCould other factors—such as workflow size, task heterogeneity, or resource type—also guide expert assignment?\n\n3.\tAs the number of workflows or task dimensions increases, how does the method scale in terms of computational cost and expert routing efficiency?", "limitations": "", "rating": 6, "confidence": 4, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The paper introduces Mixture-of-Experts (MoE) into DRL-based workflow scheduling for different deadline tightness, and explicitly considers workflow-level characteristics.", "weaknesses": "1.\tIn real-world cloud environments, scheduling decisions often involve multiple concurrent workflows and cross-workflow resource contention. It would be helpful to clarify whether the proposed approach can handle inter-workflow dependencies or coordination.\n\n2.\tThe paper assigns each expert to a specific deadline tightness regime. However, it is unclear why deadline tightness was chosen as the sole dimension for expert specialization. Could other factors—such as workflow size, task heterogeneity, or resource type—also guide expert assignment?\n\n3.\tThe scalability of the proposed MoE framework remains uncertain. As the number of workflows or task dimensions increases, how does the method scale in terms of computational cost and expert routing efficiency?", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "NflrDnb9rT", "reviewer": "Reviewer_A9tJ", "summary": "This paper presents DEFT, a novel DRL-based scheduling framework for dynamic cloud workflows with varying deadlines. By leveraging a MoE architecture, each expert specializes in a specific level of deadline urgency. A graph-adaptive gating network with cross-attention dynamically selects the most suitable expert based on workflow structure, task states, VM conditions, and deadline tightness. Experiments demonstrate that DEFT significantly reduces execution cost and deadline violations, outperforming existing DRL and heuristic baselines, especially on large-scale workflows.", "questions": "The paper does not report inference latency or computational overhead. Given the complexity of the MoE + GNN + attention-based gating architecture, it is unclear whether DEFT is suitable for real-time scheduling scenarios. What is the inference latency of DEFT compared to simpler DRL baselines?", "limitations": "", "rating": 6, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 3, "strengths": "The proposed MoE architecture tailored for dynamic cloud workflow scheduling, where each expert is specialized for a specific level of deadline urgency. This design enhances adaptability over traditional monolithic DRL approaches. Additionally, the proposed graph-adaptive gating mechanism effectively integrates workflow DAG structures and real-time system context via cross-attention, enabling fine-grained, deadline-aware expert selection and improving scheduling precision.", "weaknesses": "1. Degraded MoE with K=1 Routing: The use of Top-1 routing (K=1 in Part F. Additional Training And Testing Details) turns the MoE into a hard selection of a single expert, preventing any combination of expert behaviors. This limits the model’s flexibility and may reduce its ability to generalize to intermediate deadline scenarios.\n\n\n2. Lack of Justification for Gating Complexity: The paper does not compare the complex gating network with simpler baselines. Without such comparisons, it is unclear whether the added computational and implementation cost is justified by actual performance improvements.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "8QZ6WV6wUI", "reviewer": "Reviewer_BnPy", "summary": "### **Review Summary**\n\nThis paper introduces DEFT, a Deep Reinforcement Learning (DRL) agent for Cost-Aware Dynamic Workflow Scheduling (CADWS). The central hypothesis is that monolithic DRL policies are inflexible and perform poorly when faced with a wide spectrum of workflow deadline requirements. The proposed solution, DEFT, replaces the final policy-mapping module with a Mixture-of-Experts (MoE) architecture. The model includes multiple \"expert\" sub-networks, each pre-trained to handle a specific deadline tightness ($\\gamma$), and a \"graph-adaptive gating network\" that routes tasks to the most suitable expert based on the workflow's DAG structure, task state, and deadline. The authors present a two-phase training strategy and show that their model outperforms prior SOTA baselines, including GATES, on benchmark cloud scheduling tasks.\n\nWhile the core idea of applying MoE to this problem is interesting, the paper's contributions are undermined by a lack of critical ablation studies, an incremental design, and a complete omission of inference cost analysis. The added complexity of the MoE and the graph-adaptive gate is not sufficiently justified, making the performance gains appear marginal in some cases and the overall contribution feel incomplete.", "questions": "No questions", "limitations": "", "rating": 4, "confidence": 3, "soundness": 3, "presentation": 3, "contribution": 2, "strengths": "### **Strengths**\n\n1.  **Problem Motivation:** The paper correctly identifies a practical and significant limitation of existing DRL schedulers: a single, fixed policy struggles to be optimal for the diverse range of deadline tightness found in real-world scenarios (e.g., a cost-saving policy will miss tight deadlines, while an aggressive policy will overspend on lenient ones) [cite: 77, 143-145].\n2.  **Novelty of MoE Application:** Applying a Mixture-of-Experts (MoE) architecture to DRL for this *specific* scheduling domain appears to be a novel contribution[cite: 6]. The idea of specialising experts for different deadline regimes is intuitive and logical[cite: 5, 147].\n3.  **Strong Scalability Results:** The empirical results in Table 1 are a clear strength. DEFT outperforms the SOTA GATES baseline, and this performance gap widens significantly as the problem scale increases (from a 0.9% improvement at small scale to a 29.6% improvement at large scale), demonstrating the scalability and robustness of the MoE approach [cite: 771-772].", "weaknesses": "### **Weaknesses and Questions**\n\n1.  **Incremental Contribution:** The paper builds directly on the GATES architecture, explicitly stating that it \"directly inherits its GNN-based policy network as its SEM module\"[cite: 756]. The core contribution is replacing the final Priority Mapping Module (PMM) with the MoE-gate assembly[cite: 226]. This makes the work feel like a highly incremental improvement to a 2025 baseline (GATES) [cite: 755] rather than a fundamentally new framework.\n2.  **Missing Critical Ablation Studies:** The paper fails to provide the necessary ablations to justify its core design choices. This is its most significant weakness.\n    * **Gating Network Complexity:** The \"graph-adaptive gating network\" is a major new component, using a GAT and cross-attention [cite: 8, 156, 485, 595-598] that must be executed *at every scheduling step*. [cite_start]The paper claims simpler gating networks are \"inadequate\" [cite: 594] but provides no experimental comparison. How does this complex gate compare to a simple MLP gate that only looks at the workflow's deadline $\\gamma$ as input? Without this baseline, the value of the complex GAT-based router is unproven.\n    * **MoE Hyperparameters:** The model uses four experts [cite: 480-481, 761]. This number is a critical hyperparameter, yet it is presented without any justification or sensitivity analysis. How does performance change with two experts, or eight? [cite_start]Furthermore, Appendix F reveals that $k=1$ (hard routing) was used for expert selection[cite: 1455]. This is a major simplification of the MoE paradigm and is not justified. Did the authors experiment with soft mixtures or $k>1$, and if so, how did it impact performance and (presumably) inference cost?\n3.  **No Inference Cost Analysis:** For a paper on real-time dynamic scheduling, the complete omission of any inference latency analysis is a critical flaw. The proposed DEFT model adds a GAT and a cross-attention mechanism *on top of* the existing GATES GNN, all of which runs at *every decision step* [cite: 595-598]. This added complexity must have a non-trivial impact on the decision-making time. Without a direct runtime comparison to the GATES baseline, the practical value of the model is impossible to assess.\n4.  **Marginal Gains at Trained Scale:** The model is pre-trained and fine-tuned on Small (S) scale instances[cite: 761, 763]. However, on the S-scale test set, the performance gain over the GATES baseline is marginal (52.95 vs. 52.46, a 0.9% improvement) [cite: 771-772]. This suggests that all this added complexity (MoE, GAT-gate, cross-attention) provides almost no benefit for the data distribution it was actually trained on, questioning the cost/benefit ratio of the proposed architecture.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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": "BbllWvYQq3", "reviewer": "Reviewer_Fb6P", "summary": "This paper addresses the problem of Cost-Aware Dynamic Workflow Scheduling (CADWS) in cloud computing. The goal is to intelligently assign dynamically arriving graph-structured workflows (DAGs) with varying deadlines to virtual machines (VMs) to minimize total cost (including VM rental fees and deadline violation penalties).\n\nThe authors point out that existing deep reinforcement learning (DRL) schedulers often use rigid, single-path policy networks (i.e., a single Priority Mapping Module, PMM), making it difficult for them to adapt to variable deadline tightness.\n\nTo solve this problem, the paper proposes DEFT (Deadline-pErceptive Mixture-oF-Experts), an innovative DRL policy architecture. To the best of the authors' knowledge, DEFT is the first work to apply a Mixture-of-Experts (MoE) architecture to dynamic cloud workflow scheduling.\n\nIts core contributions include:\n\n1. An MoE policy network where each \"expert\" is specialized to handle a specific level of deadline tightness (controlled by a $\\gamma$ coefficient).\n2. A novel \"graph-adaptive gating mechanism.\" It uses a Graph Attention Network (GAT) to encode the workflow's DAG structure and combines VM state and deadline information to dynamically select the most appropriate expert via a cross-attention mechanism.\n3. A two-stage training strategy: first, pre-training each expert independently on specific $\\gamma$ values, and then jointly training the gating network and fine-tuning all experts in an environment with mixed $\\gamma$ values.\n\nExperimental results show that DEFT significantly outperforms existing SOTA DRL baselines (such as GATES, SPN-CWS) on several CADWS benchmarks. The advantage of DEFT in reducing total cost is particularly evident on medium-to-large scale (M/L) workflows.", "questions": "1. **Regarding the GATES baseline:** Was the GATES baseline (used for comparison in Tables 1 and 2) trained on the same mixed deadline distribution as DEFT's stage 2 (i.e., with $\\gamma$ sampled from {1.0, ..., 3.0})? If not, could you please provide the performance of a GATES or DEFT variant with a single PMM (instead of MoE) trained on this same mixed dataset, to fairly evaluate the true gains from the MoE architecture?\n2. **Regarding expert generalization:** The stage-1 pre-trained experts target specific $\\gamma$ values. When new $\\gamma$ values (like 1.0, 1.5, 2.0) are encountered in stage 2 and during testing, which expert(s) does the gating network tend to select? For example, when $\\gamma=1.5$, does it choose the $\\gamma=1.25$ expert or the $\\gamma=1.75$ expert? Does this rely entirely on the stage-2 fine-tuning?\n3. **Regarding Top-k = $k=1$:** Why was $k=1$ chosen instead of $k=2$ or higher? Does using $k=1$ mean that DEFT forgoes the ability to \"mix\" experts and instead just \"switches\" between them?\n4. **Regarding the number and selection of experts:** How was the number of experts (4) and the choice of $\\gamma$ values ({1.25, 1.75, 2.25, 5.0}) determined? Could you provide a sensitivity analysis on the number of experts (e.g., 2 or 6 experts) or their $\\gamma$ value selection? Or add a section explaining the reasoning for these hyperparameter choices.", "limitations": "", "rating": 4, "confidence": 4, "soundness": 3, "presentation": 4, "contribution": 2, "strengths": "1. **Originality:** This paper is the first to introduce a Mixture-of-Experts (MoE) architecture to the field of dynamic cloud workflow scheduling (CADWS). The idea of dedicating different experts to handle scheduling strategies for different levels of deadline tightness directly addresses the \"one-size-fits-all\" pain point of existing DRL schedulers.\n\n2. **Quality:** The core component, the \"graph-adaptive gating mechanism,\" is very well-designed. It not only uses GAT to encode the DAG topology of the workflow but also skillfully integrates VM status, task features, and the critical deadline information, performing expert routing via cross-attention. This design is highly aligned with the characteristics of the CADWS problem domain.\n\n3. **Clarity:** The paper is clearly written. The problem definition, related work, and methodology are well-articulated. The appendix is detailed and aids in reproducibility.\n\n4. **Significance:** The CADWS problem solved in this paper has significant practical importance and challenges in cloud computing resource management. The method demonstrates strong performance, especially on medium (M) and large (L) scale workflows, indicating good scalability and practical value.", "weaknesses": "1. Insufficient Baseline Comparison and Ablation: A major weakness of the paper is the lack of a rigorous ablation study on the contribution of the MoE architecture itself. DEFT is built upon the SEM from GATES, with the main modification being the replacement of GATES's PMM with an MoE-PMM. A crucial baseline is missing: one that uses the same SEM as GATES, but where the PMM is a single, deeper, or wider FFN (or the original GATES PMM), trained end-to-end on the mixed-deadline dataset (i.e., the stage-2 dataset). It is currently unclear if the GATES baseline was trained on this mixed dataset. If not, DEFT's advantage might partially stem from a richer data distribution or longer training (two-stage), rather than solely from the MoE architecture.\n\n2. Furthermore, DEFT uses a two-stage training process: stage 1 pre-trains experts on fixed $\\gamma$ values, and stage 2 trains the gate and fine-tunes experts on mixed $\\gamma$ values. However, the paper does not explicitly state whether its SOTA baselines (especially GATES) were also trained or fine-tuned on the same mixed $\\gamma$ value dataset (the stage-2 dataset). If GATES was trained on a single $\\gamma$ value or a simpler dataset, then DEFT's performance advantage (especially on M/L scales) might simply come from exposure to more diverse training data, rather than from its MoE architecture.\n\n3. **Expert Generalization:** The expert pre-training (stage 1) uses a fixed set of $\\gamma$ values ({1.25, 1.75, 2.25, 5.0}), but during the gating network training (stage 2) and testing, $\\gamma$ is sampled from a different, denser set ({1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 3.0}). The authors do not adequately explain how the gating network handles $\\gamma$ values not seen during pre-training (e.g., 1.0, 1.5, 2.0, 3.0). Does the gating network interpolate between these points? Or does it rely primarily on the stage-2 fine-tuning? An analysis of how the gate makes decisions when encountering these unseen $\\gamma$ values would be valuable.\n\n4. **Simplification of Top-k Routing:** The paper states in Appendix F that the Top-k setting is $k=1$ in experiments. This means that at each decision step, the gating network selects only one expert, rather than mixing the outputs of multiple experts. This appears to be an oversimplification of the MoE paradigm, making it more of a \"hard switch\" than a \"mixture.\" Why not use $k=2$? Using $k=1$ might lead to increased variance in routing decisions and forfeits the advantage of MoE's ability to combine experts.\n\n5. **Lack of Hyperparameter Sensitivity Analysis:** The MoE architecture introduces new hyperparameters, particularly the number of experts and the choice of $\\gamma$ values for pre-training. The paper uses 4 experts but does not discuss why these 4 specific $\\gamma$ values were chosen. How would performance change if the number of experts was increased or decreased, or if their specialized $\\gamma$ values were different? This is crucial for the method's robustness and practicality.\n\n6. The core contribution of this paper is applying the MoE architecture to a DRL scheduler. However, MoE itself is a mature technique and has already been explored in the DRL field for solving combinatorial optimization and VRP problems. This paper's problem is analogous to a special case of these.\n\n7. The paper emphasizes \"Mixture-of-Experts\" in its title and abstract, but admits in Appendix F that its experimental setup uses $k=1$. This implies that DEFT in practice is not a \"mixture\" model but a \"Switch-of-Experts\" model—selecting only one expert at each decision point. This somewhat undermines the core advantage of MoE (i.e., achieving smoother, more robust decisions by combining outputs from multiple experts). The authors do not provide experimental results for $k>1$ (e.g., $k=2$), and if they did not, an explanation for choosing a single expert per decision point is warranted.", "quality": null, "clarity": null, "significance": null, "originality": null, "strengths_and_weaknesses": "", "was_revised": false, "final_justification": "", "rebuttal": "", "claims_and_evidence": "", "methods_and_evaluation_criteria": "", "theoretical_claims": "", "experimental_designs_or_analyses": "", "relation_to_broader_scientific_literature": "", "essential_references_not_discussed": "", "other_strengths_and_weaknesses": "", "other_comments_or_suggestions": "", "questions_for_authors": "", "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:

Decision: Accept (Poster)