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arXiv 2302.04375cs.LGcs.AI
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瞬时硬约束下安全强化学习的近优算法

A Near-Optimal Algorithm for Safe Reinforcement Learning Under Instantaneous Hard Constraints

The Ohio State University(俄亥俄州立大学)

Ming Shi, Yingbin Liang, Ness Shroff

摘要:

在强化学习(RL)的许多应用中,算法的安全执行至关重要,以便在每一步都满足瞬时硬约束,避免不安全的状态和动作。然而,现有的“安全”RL算法通常是在要求期望累积成本有界或假设所有状态都是安全的约束下设计的。因此,这样的算法可能违反瞬时硬约束,并在实践中遍历不安全的状态(和动作)。因此,在本文中,我们开发了第一个接近最优的安全RL算法的情节马尔可夫决策过程的不安全状态和行动下的瞬时硬约束和线性混合模型。它不仅实现了一个遗憾$\tilde{O}(\frac{d H^3 \sqrt{dK}}{Δ_c})$,该遗憾与仅具有不安全动作的设置中的最新遗憾紧密匹配,并且几乎与无约束设置中的遗憾匹配,而且在每个步骤处都是安全的,其中$d$是特征映射维度,$K$是发作次数,$H$是每个发作中的步骤次数,并且$Δ_c$是安全相关参数。我们还提供了一个下限$\tildeΩ(\max\{dH \sqrt{K}, \frac{H}{Δ_c^2}\})$,这表明依赖于$Δ_c$是必要的。此外,我们的算法设计和遗憾分析涉及几个新的想法,这可能是独立的利益。

英文摘要:

In many applications of Reinforcement Learning (RL), it is critically important that the algorithm performs safely, such that instantaneous hard constraints are satisfied at each step, and unsafe states and actions are avoided. However, existing algorithms for ''safe'' RL are often designed under constraints that either require expected cumulative costs to be bounded or assume all states are safe. Thus, such algorithms could violate instantaneous hard constraints and traverse unsafe states (and actions) in practice. Therefore, in this paper, we develop the first near-optimal safe RL algorithm for episodic Markov Decision Processes with unsafe states and actions under instantaneous hard constraints and the linear mixture model. It not only achieves a regret $\tilde{O}(\frac{d H^3 \sqrt{dK}}{Δ_c})$ that tightly matches the state-of-the-art regret in the setting with only unsafe actions and nearly matches that in the unconstrained setting, but is also safe at each step, where $d$ is the feature-mapping dimension, $K$ is the number of episodes, $H$ is the number of steps in each episode, and $Δ_c$ is a safety-related parameter. We also provide a lower bound $\tildeΩ(\max\{dH \sqrt{K}, \frac{H}{Δ_c^2}\})$, which indicates that the dependency on $Δ_c$ is necessary. Further, both our algorithm design and regret analysis involve several novel ideas, which may be of independent interest.

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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