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Hauptverfasser: Zhang, Haochen, Zheng, Zhong, Xue, Lingzhou
Format: Preprint
Veröffentlicht: 2025
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Online-Zugang:https://arxiv.org/abs/2502.02859
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author Zhang, Haochen
Zheng, Zhong
Xue, Lingzhou
author_facet Zhang, Haochen
Zheng, Zhong
Xue, Lingzhou
contents We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.
format Preprint
id arxiv_https___arxiv_org_abs_2502_02859
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Gap-Dependent Bounds for Federated $Q$-learning
Zhang, Haochen
Zheng, Zhong
Xue, Lingzhou
Machine Learning
We present the first gap-dependent analysis of regret and communication cost for on-policy federated $Q$-Learning in tabular episodic finite-horizon Markov decision processes (MDPs). Existing FRL methods focus on worst-case scenarios, leading to $\sqrt{T}$-type regret bounds and communication cost bounds with a $\log T$ term scaling with the number of agents $M$, states $S$, and actions $A$, where $T$ is the average total number of steps per agent. In contrast, our novel framework leverages the benign structures of MDPs, such as a strictly positive suboptimality gap, to achieve a $\log T$-type regret bound and a refined communication cost bound that disentangles exploration and exploitation. Our gap-dependent regret bound reveals a distinct multi-agent speedup pattern, and our gap-dependent communication cost bound removes the dependence on $MSA$ from the $\log T$ term. Notably, our gap-dependent communication cost bound also yields a better global switching cost when $M=1$, removing $SA$ from the $\log T$ term.
title Gap-Dependent Bounds for Federated $Q$-learning
topic Machine Learning
url https://arxiv.org/abs/2502.02859