Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2024
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| _version_ | 1866909437263872000 |
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| author | Wang, Yudan Xiao, Peiyao Ban, Hao Ji, Kaiyi Zou, Shaofeng |
| author_facet | Wang, Yudan Xiao, Peiyao Ban, Hao Ji, Kaiyi Zou, Shaofeng |
| contents | 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 $ε+ε_{\text{app}}$-accurate Pareto stationary policy using $\mathcal{O}({ε^{-5}})$ samples, while ensuring a small $ε+\sqrt{ε_{\text{app}}}$-level CA distance (defined as the distance to the CA direction), where $ε_{\text{app}}$ is the function approximation error. The analysis also shows that MTAC-FC improves the sample complexity to $\mathcal{O}(ε^{-3})$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_16077 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning Wang, Yudan Xiao, Peiyao Ban, Hao Ji, Kaiyi Zou, Shaofeng Machine Learning 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 $ε+ε_{\text{app}}$-accurate Pareto stationary policy using $\mathcal{O}({ε^{-5}})$ samples, while ensuring a small $ε+\sqrt{ε_{\text{app}}}$-level CA distance (defined as the distance to the CA direction), where $ε_{\text{app}}$ is the function approximation error. The analysis also shows that MTAC-FC improves the sample complexity to $\mathcal{O}(ε^{-3})$, 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. |
| title | Theoretical Study of Conflict-Avoidant Multi-Objective Reinforcement Learning |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2405.16077 |