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arXiv 2501.04879cs.LG
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强化学习中策略梯度方法的多线性张量低秩近似

Multilinear Tensor Low-Rank Approximation for Policy-Gradient Methods in Reinforcement Learning

King Juan Carlos University(胡安·卡洛斯国王大学);The Chinese University of Hong Kong(香港中文大学)

Sergio Rozada, Hoi-To Wai, Antonio G. Marques

AI总结:

针对神经网络策略的收敛、架构选择及状态-动作冗余利用不足等问题,本文利用PARAFAC分解构建张量低秩RL策略,给出理论保证并实验证明其可降低计算与样本复杂度且奖励相近。

摘要:

强化学习(RL)旨在根据给定的(时变)状态估计要采取的动作,其目标是最大化累积奖励函数。总体而言,求解RL问题主要有两类算法:基于价值的方法和基于策略的方法,后者旨在学习一种从状态到动作的概率参数化策略。大多数当代方法使用神经网络(NN)实现该策略。然而,NN通常面临与收敛性、架构适用性、超参数选择以及状态-动作表示冗余(例如局部相似状态)利用不足相关的问题。本文提出使用多线性映射来高效估计RL策略的参数。更具体地说,我们利用PARAFAC分解来设计张量低秩策略。其核心思想是将策略参数汇集到一个张量中,并利用张量补全技术来强制实现低秩。我们为所提出方法在多种策略类别上建立了理论保证,并通过数值实验验证了其有效性。具体而言,我们证明了与NN模型相比,张量低秩策略模型降低了计算复杂度和样本复杂度,同时取得了相近的奖励。

英文摘要:

Reinforcement learning (RL) aims to estimate the action to take given a (time-varying) state, with the goal of maximizing a cumulative reward function. Predominantly, there are two families of algorithms to solve RL problems: value-based and policy-based methods, with the latter designed to learn a probabilistic parametric policy from states to actions. Most contemporary approaches implement this policy using a neural network (NN). However, NNs usually face issues related to convergence, architectural suitability, hyper-parameter selection, and underutilization of the redundancies of the state-action representations (e.g. locally similar states). This paper postulates multi-linear mappings to efficiently estimate the parameters of the RL policy. More precisely, we leverage the PARAFAC decomposition to design tensor low-rank policies. The key idea involves collecting the policy parameters into a tensor and leveraging tensor-completion techniques to enforce low rank. We establish theoretical guarantees of the proposed methods for various policy classes and validate their efficacy through numerical experiments. Specifically, we demonstrate that tensor low-rank policy models reduce computational and sample complexities in comparison to NN models while achieving similar rewards.

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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