Bellman Unbiasedness: Toward Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation

• URL: http://arxiv.org/abs/2407.21260v3
• Date: Tue, 13 May 2025 04:53:31 GMT
• Title: Bellman Unbiasedness: Toward Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation
• Authors: Taehyun Cho, Seungyub Han, Seokhun Ju, Dohyeong Kim, Kyungjae Lee, Jungwoo Lee,
• Abstract summary: We present a regret analysis of distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting.<n>We propose a provably efficient algorithm, $textttSF-LSVI$, that achieves a tight regret bound of $tildeO(d_E Hfrac32sqrtK)$ where $H$ is the horizon, $K$ is the number of episodes, and $d_E$ is the eluder dimension of a function class.
• Score: 8.378137704007038
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Distributional reinforcement learning improves performance by capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In addition, the intractable element of the infinite dimensionality of distributions has been overlooked. In this paper, we present a regret analysis of distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of $\textit{Bellman unbiasedness}$ which is essential for exactly learnable and provably efficient distributional updates in an online manner. Among all types of statistical functionals for representing infinite-dimensional return distributions, our theoretical results demonstrate that only moment functionals can exactly capture the statistical information. Secondly, we propose a provably efficient algorithm, $\texttt{SF-LSVI}$, that achieves a tight regret bound of $\tilde{O}(d_E H^{\frac{3}{2}}\sqrt{K})$ where $H$ is the horizon, $K$ is the number of episodes, and $d_E$ is the eluder dimension of a function class.

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