The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond

• URL: http://arxiv.org/abs/2305.10697v2
• Date: Tue, 12 Dec 2023 21:47:08 GMT
• Title: The Blessing of Heterogeneity in Federated Q-Learning: Linear Speedup and Beyond
• Authors: Jiin Woo, Gauri Joshi, Yuejie Chi
• Abstract summary: We consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. We provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. We propose a novel federated Q-learning algorithm with importance averaging, giving larger weights to more frequently visited state-action pairs.
• Score: 44.43850105124659
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: When the data used for reinforcement learning (RL) are collected by multiple agents in a distributed manner, federated versions of RL algorithms allow collaborative learning without the need for agents to share their local data. In this paper, we consider federated Q-learning, which aims to learn an optimal Q-function by periodically aggregating local Q-estimates trained on local data alone. Focusing on infinite-horizon tabular Markov decision processes, we provide sample complexity guarantees for both the synchronous and asynchronous variants of federated Q-learning. In both cases, our bounds exhibit a linear speedup with respect to the number of agents and near-optimal dependencies on other salient problem parameters. In the asynchronous setting, existing analyses of federated Q-learning, which adopt an equally weighted averaging of local Q-estimates, require that every agent covers the entire state-action space. In contrast, our improved sample complexity scales inverse proportionally to the minimum entry of the average stationary state-action occupancy distribution of all agents, thus only requiring the agents to collectively cover the entire state-action space, unveiling the blessing of heterogeneity in enabling collaborative learning by relaxing the coverage requirement of the single-agent case. However, its sample complexity still suffers when the local trajectories are highly heterogeneous. In response, we propose a novel federated Q-learning algorithm with importance averaging, giving larger weights to more frequently visited state-action pairs, which achieves a robust linear speedup as if all trajectories are centrally processed, regardless of the heterogeneity of local behavior policies.

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