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arXiv 2602.09300cs.LG
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基于期望值、短期风险和优化确定等价风险的风险敏感强化学习

Reinforcement learning with an expectile-based objective

Indian Institute of Technology Madras(印度理工学院马德拉斯学院);TCS Research, India(印度塔塔咨询服务研究所)

Shrey Rakeshkumar Patel, Sumedh Gupte, Soumen Pachal, Prashanth L. A., Sanjay P. Bhat

AI总结:

本文提出三种风险度量的风险敏感强化学习算法,推导策略梯度定理并建立收敛性界,通过实验验证理论成果。

摘要:

我们提出了三种风险度量(期望值、基于效用的短期风险和优化确定等价风险)的 risk-sensitive reinforcement learning 算法。对于每种风险度量,在有限时间马尔可夫决策过程中,我们首先推导出策略梯度定理。其次,我们为上述每种风险度量提出风险敏感策略梯度的估计器,并为这些估计器建立 $\mathcal{O}\left(1/m\right)$ 的均方误差界,其中 $m$ 是轨迹的数量。进一步,在标准的策略梯度型算法假设下,我们建立了风险敏感目标的光滑性,从而推导出我们提出的整体风险敏感策略梯度算法的 stationary 收敛率界。最后,我们通过数值实验在流行的 RL 基准上验证了理论发现。

英文摘要:

We consider the policy evaluation and control in a finite horizon reinforcement learning (RL) setting under an expectile-based objective. First, we derive the mean-squared error (MSE) and concentration bounds for the classic estimator of expectiles based on independent and identically distributed (i.i.d.) samples. To the best of our knowledge, expectiles have not been analyzed in the non-asymptotic regime and the bounds we derive may be of independent interest. Next, we analyze a Monte Carlo type estimator of expectile of the Markov chain underlying a given policy. We derive upper bounds that hold in expectation as well as with high probability for this estimator. Further, we show the order-optimality of our estimator by deriving a lower bound on expectile-based policy evaluation. For the problem of control, we adopt a policy gradient approach and derive a policy gradient theorem for expectiles. Using this result, we propose a gradient estimator with a $O\left(1/m\right)$ mean-squared error bounds, where $m$ is the number of trajectories. Further, under standard assumptions for policy gradient-type algorithms, we establish smoothness of the expectile-sensitive objective, in turn leading to stationary convergence rate bounds for the overall risk-sensitive policy gradient algorithm that we propose. Finally, we conduct numerical experiments to show the utility of expectiles on popular RL benchmarks.

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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