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arXiv 2402.09113cs.LG
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你的RL智能体如何探索?基于占用测度轨迹的最优传输分析

How does Your RL Agent Explore? An Optimal Transport Analysis of Occupancy Measure Trajectories

The University of Sheffield(谢菲尔德大学);Univ. Lille(里尔大学);Inria(法国国家信息与自动化研究所);CNRS(法国国家科学研究中心);Centrale Lille(里尔中央理工学院);Centrum Wiskunde & Informatica(数学与计算机科学中心)

Reabetswe M. Nkhumise, Debabrota Basu, Tony J. Prescott, Aditya Gilra

AI总结:

本文将RL学习过程表示为占用测度流形上的策略轨迹,基于最优传输定义了序列学习努力(ESL)和最优移动比率(OMR)两个指标,用于量化算法探索路径长度与降低regret的有效性,并提供了有限样本下的近似保证。

摘要:

RL(强化学习)日益增长的成功,是通过结合巧妙的算法策略和深度架构来优化状态-动作空间上的回报与访问分布所推动的。目前缺乏一个定量框架来比较这些折衷RL算法的学习过程,但这在实际中是迫切需要的。我们通过将RL算法的学习过程表示为训练期间生成的一系列策略,然后研究在状态-动作占用测度流形上诱导的策略轨迹,从而填补了这一空白。使用基于最优传输的度量,我们测量RL算法生成的策略序列在初始策略和最终最优策略之间所诱导路径的长度。因此,我们首先定义了“序列学习努力”(ESL)。ESL量化了RL算法所行进的相对距离,即与从初始策略到最优策略的最短路径相比的相对距离。此外,我们通过定义“最优移动比率”(OMR),将占用测度空间中策略的动态与regret(用于理解RL算法次优性的另一度量)联系起来。OMR评估占用测度空间中有效减少regret类似物的移动比例。最后,我们推导出近似保证,以在有限样本且无法访问最优策略的情况下估计ESL和OMR。通过对各种环境和算法的实证分析,我们证明ESL和OMR为RL算法的探索过程以及离散和连续MDP中不同任务的难度提供了深刻见解。

英文摘要:

The rising successes of RL are propelled by combining smart algorithmic strategies and deep architectures to optimize the distribution of returns and visitations over the state-action space. A quantitative framework to compare the learning processes of these eclectic RL algorithms is currently absent but desired in practice. We address this gap by representing the learning process of an RL algorithm as a sequence of policies generated during training, and then studying the policy trajectory induced in the manifold of state-action occupancy measures. Using an optimal transport-based metric, we measure the length of the paths induced by the policy sequence yielded by an RL algorithm between an initial policy and a final optimal policy. Hence, we first define the 'Effort of Sequential Learning' (ESL). ESL quantifies the relative distance that an RL algorithm travels compared to the shortest path from the initial to the optimal policy. Further, we connect the dynamics of policies in the occupancy measure space and regret (another metric to understand the suboptimality of an RL algorithm), by defining the 'Optimal Movement Ratio' (OMR). OMR assesses the fraction of movements in the occupancy measure space that effectively reduce an analogue of regret. Finally, we derive approximation guarantees to estimate ESL and OMR with finite number of samples and without access to an optimal policy. Through empirical analyses across various environments and algorithms, we demonstrate that ESL and OMR provide insights into the exploration processes of RL algorithms and hardness of different tasks in discrete and continuous MDPs.

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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