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arXiv 2109.04640cs.LGstat.ME
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离线强化学习的投影状态-动作平衡权

Projected State-action Balancing Weights for Offline Reinforcement Learning

Texas A&M University(德州农工大学);George Washington University(乔治华盛顿大学)

Jiayi Wang, Zhengling Qi, Raymond K. W. Wong

摘要:

离线策略评估(OPE)被认为是强化学习(RL)中的一个基本且具有挑战性的问题。本文重点研究了基于预先收集的数据的目标策略的价值估计,该数据是在无限时域马尔可夫决策过程的框架下从可能不同的策略中产生的。受RL中的边缘重要性采样方法和因果推理中协变量平衡思想的启发,我们提出了一种新的具有近似投影状态-动作平衡权重的策略值估计器。我们得到了这些权重的收敛速度,并证明了所提出的值估计是半参数有效的技术条件下。在渐近性方面,我们的结果与轨迹的数量和每个轨迹处的决策点的数量都成比例。因此,当决策点的数量出现分歧时,仍然可以用有限数量的受试者实现一致性。此外,我们开发了一个必要和充分条件,建立适定性的Bellman运营商在关闭的政策设置,其特点是困难的OPE,可能是独立的利益。数值实验表明,我们提出的估计有前途的性能。

英文摘要:

Offline policy evaluation (OPE) is considered a fundamental and challenging problem in reinforcement learning (RL). This paper focuses on the value estimation of a target policy based on pre-collected data generated from a possibly different policy, under the framework of infinite-horizon Markov decision processes. Motivated by the recently developed marginal importance sampling method in RL and the covariate balancing idea in causal inference, we propose a novel estimator with approximately projected state-action balancing weights for the policy value estimation. We obtain the convergence rate of these weights and show that the proposed value estimator is semi-parametric efficient under technical conditions. In terms of asymptotics, our results scale with both the number of trajectories and the number of decision points at each trajectory. As such, consistency can still be achieved with a limited number of subjects when the number of decision points diverges. In addition, we develop a necessary and sufficient condition for establishing the well-posedness of the Bellman operator in the off-policy setting, which characterizes the difficulty of OPE and may be of independent interest. Numerical experiments demonstrate the promising performance of our proposed estimator.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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