Tractable and Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation

• URL: http://arxiv.org/abs/2407.21260v1
• Date: Wed, 31 Jul 2024 00:43:51 GMT
• Title: Tractable and Provably Efficient Distributional Reinforcement Learning with General Value Function Approximation
• Authors: Taehyun Cho, Seungyub Han, Kyungjae Lee, Seokhun Ju, Dohyeong Kim, Jungwoo Lee,
• Abstract summary: We present a regret analysis for distributional reinforcement learning with general value function approximation. Our theoretical results show that approximating the infinite-dimensional return distribution with a finite number of moment functionals is the only method to learn the statistical information unbiasedly.
• Score: 8.378137704007038
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Distributional reinforcement learning improves performance by effectively capturing environmental stochasticity, but a comprehensive theoretical understanding of its effectiveness remains elusive. In this paper, we present a regret analysis for distributional reinforcement learning with general value function approximation in a finite episodic Markov decision process setting. We first introduce a key notion of Bellman unbiasedness for a tractable and exactly learnable update via statistical functional dynamic programming. Our theoretical results show that approximating the infinite-dimensional return distribution with a finite number of moment functionals is the only method to learn the statistical information unbiasedly, including nonlinear statistical functionals. Second, we propose a provably efficient algorithm, $\texttt{SF-LSVI}$, achieving a 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.

Related papers

• Online non-parametric likelihood-ratio estimation by Pearson-divergence functional minimization [55.98760097296213]
  We introduce a new framework for online non-parametric LRE (OLRE) for the setting where pairs of iid observations $(x_t sim p, x'_t sim q)$ are observed over time. We provide theoretical guarantees for the performance of the OLRE method along with empirical validation in synthetic experiments.
  arXiv  Detail & Related papers  (2023-11-03T13:20:11Z)
• Online Statistical Inference for Nonlinear Stochastic Approximation with Markovian Data [22.59079286063505]
  We study the statistical inference of nonlinear approximation algorithms utilizing a single trajectory of Markovian data. Our methodology has practical applications in various scenarios, such as Gradient Descent (SGD) on autoregressive data and asynchronous Q-Learning.
  arXiv  Detail & Related papers  (2023-02-15T14:31:11Z)
• Nearly Minimax Optimal Reinforcement Learning for Linear Markov Decision Processes [80.89852729380425]
  We propose the first computationally efficient algorithm that achieves the nearly minimax optimal regret $tilde O(dsqrtH3K)$. Our work provides a complete answer to optimal RL with linear MDPs, and the developed algorithm and theoretical tools may be of independent interest.
  arXiv  Detail & Related papers  (2022-12-12T18:58:59Z)
• Offline Reinforcement Learning with Differentiable Function Approximation is Provably Efficient [65.08966446962845]
  offline reinforcement learning, which aims at optimizing decision-making strategies with historical data, has been extensively applied in real-life applications. We take a step by considering offline reinforcement learning with differentiable function class approximation (DFA) Most importantly, we show offline differentiable function approximation is provably efficient by analyzing the pessimistic fitted Q-learning algorithm.
  arXiv  Detail & Related papers  (2022-10-03T07:59:42Z)
• Provable General Function Class Representation Learning in Multitask Bandits and MDPs [58.624124220900306]
  multitask representation learning is a popular approach in reinforcement learning to boost the sample efficiency. In this work, we extend the analysis to general function class representations. We theoretically validate the benefit of multitask representation learning within general function class for bandits and linear MDP.
  arXiv  Detail & Related papers  (2022-05-31T11:36:42Z)
• A Generalized Bootstrap Target for Value-Learning, Efficiently Combining Value and Feature Predictions [39.17511693008055]
  Estimating value functions is a core component of reinforcement learning algorithms. We focus on bootstrapping targets used when estimating value functions. We propose a new backup target, the $eta$-return mixture.
  arXiv  Detail & Related papers  (2022-01-05T21:54:55Z)
• Nearly Optimal Regret for Learning Adversarial MDPs with Linear Function Approximation [92.3161051419884]
  We study the reinforcement learning for finite-horizon episodic Markov decision processes with adversarial reward and full information feedback. We show that it can achieve $tildeO(dHsqrtT)$ regret, where $H$ is the length of the episode. We also prove a matching lower bound of $tildeOmega(dHsqrtT)$ up to logarithmic factors.
  arXiv  Detail & Related papers  (2021-02-17T18:54:08Z)
• Reinforcement Learning with General Value Function Approximation: Provably Efficient Approach via Bounded Eluder Dimension [124.7752517531109]
  We establish a provably efficient reinforcement learning algorithm with general value function approximation. We show that our algorithm achieves a regret bound of $widetildeO(mathrmpoly(dH)sqrtT)$ where $d$ is a complexity measure. Our theory generalizes recent progress on RL with linear value function approximation and does not make explicit assumptions on the model of the environment.
  arXiv  Detail & Related papers  (2020-05-21T17:36:09Z)
• Adaptive Approximate Policy Iteration [22.915651391812187]
  We present a learning scheme which enjoys a $tildeO(T2/3)$ regret bound for undiscounted, continuing learning in uniformly ergodic MDPs. This is an improvement over the best existing bound of $tildeO(T3/4)$ for the average-reward case with function approximation.
  arXiv  Detail & Related papers  (2020-02-08T02:27:03Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.