Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning

• URL: http://arxiv.org/abs/2405.16077v3
• Date: Fri, 20 Dec 2024 21:23:53 GMT
• Title: Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning
• Authors: Yudan Wang, Peiyao Xiao, Hao Ban, Kaiyi Ji, Shaofeng Zou,
• Abstract summary: We develop a novel dynamic weighting multi-task actor-critic algorithm (MTAC) under two options of sub-procedures named as CA and FC. MTAC-CA aims to find a conflict-avoidant (CA) update direction that maximizes the minimum value improvement among tasks, and MTAC-FC targets at a much faster convergence rate. Our experiments on MT10 demonstrate the improved performance of our algorithms over existing MTRL methods with fixed preference.
• Score: 21.288881065839007
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• Abstract: Multi-task reinforcement learning (MTRL) has shown great promise in many real-world applications. Existing MTRL algorithms often aim to learn a policy that optimizes individual objective functions simultaneously with a given prior preference (or weights) on different tasks. However, these methods often suffer from the issue of \textit{gradient conflict} such that the tasks with larger gradients dominate the update direction, resulting in a performance degeneration on other tasks. In this paper, we develop a novel dynamic weighting multi-task actor-critic algorithm (MTAC) under two options of sub-procedures named as CA and FC in task weight updates. MTAC-CA aims to find a conflict-avoidant (CA) update direction that maximizes the minimum value improvement among tasks, and MTAC-FC targets at a much faster convergence rate. We provide a comprehensive finite-time convergence analysis for both algorithms. We show that MTAC-CA can find a $\epsilon+\epsilon_{\text{app}}$-accurate Pareto stationary policy using $\mathcal{O}({\epsilon^{-5}})$ samples, while ensuring a small $\epsilon+\sqrt{\epsilon_{\text{app}}}$-level CA distance (defined as the distance to the CA direction), where $\epsilon_{\text{app}}$ is the function approximation error. The analysis also shows that MTAC-FC improves the sample complexity to $\mathcal{O}(\epsilon^{-3})$, but with a constant-level CA distance. Our experiments on MT10 demonstrate the improved performance of our algorithms over existing MTRL methods with fixed preference.

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