Eigensubspace of Temporal-Difference Dynamics and How It Improves Value Approximation in Reinforcement Learning

• URL: http://arxiv.org/abs/2306.16750v2
• Date: Wed, 8 Nov 2023 09:38:35 GMT
• Title: Eigensubspace of Temporal-Difference Dynamics and How It Improves Value Approximation in Reinforcement Learning
• Authors: Qiang He and Tianyi Zhou and Meng Fang and Setareh Maghsudi
• Abstract summary: Eigensubspace Regularized Critic (ERC) is motivated by an analysis of dynamics of Q-value approximation error. We show that ERC effectively reduces the variance of value functions. It shows significant advantages in Q-value approximation and variance reduction.
• Score: 44.663181739694664
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel value approximation method, namely Eigensubspace Regularized Critic (ERC) for deep reinforcement learning (RL). ERC is motivated by an analysis of the dynamics of Q-value approximation error in the Temporal-Difference (TD) method, which follows a path defined by the 1-eigensubspace of the transition kernel associated with the Markov Decision Process (MDP). It reveals a fundamental property of TD learning that has remained unused in previous deep RL approaches. In ERC, we propose a regularizer that guides the approximation error tending towards the 1-eigensubspace, resulting in a more efficient and stable path of value approximation. Moreover, we theoretically prove the convergence of the ERC method. Besides, theoretical analysis and experiments demonstrate that ERC effectively reduces the variance of value functions. Among 26 tasks in the DMControl benchmark, ERC outperforms state-of-the-art methods for 20. Besides, it shows significant advantages in Q-value approximation and variance reduction. Our code is available at https://sites.google.com/view/erc-ecml23/.

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