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arXiv 2202.06385cs.LGcs.AIstat.ML
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切换代价为loglog(T)的样本有效强化学习

Sample-Efficient Reinforcement Learning with loglog(T) Switching Cost

UC Santa Barbara(加州大学圣巴巴拉分校)

Dan Qiao, Ming Yin, Ming Min, Yu-Xiang Wang

摘要:

我们研究了低(政策)切换成本的强化学习(RL)问题-现实生活中的RL应用程序,其中部署新的政策是昂贵的,政策更新的数量必须很低的问题。在本文中,我们提出了一种新的算法,基于阶段明智的探索和自适应的政策消除,实现了遗憾的$\widetilde{O}(\sqrt{H^4S^2AT})$,而需要的切换成本$O(HSA \log\log T)$。这是一个指数级的改善,在现有的方法与$\widetilde{O}(\mathrm{poly}(H,S,A)\sqrt{T})$遗憾的最著名的切换成本$O(H^2SA\log T)$。在上文中,$S,A$表示具有未知转移的$H$-水平情景马尔可夫决策过程模型中的状态和动作的数量,并且$T$是步骤的数量。作为我们的新技术的副产品,我们还得到了一个无奖励的探索算法的切换成本为$O(HSA)$。此外,我们证明了一对信息理论的下界说:(1)任何无遗憾算法必须有一个$Ω(HSA)$的切换成本;(2)任何$\widetilde{O}(\sqrt{T})$遗憾算法必须招致的切换成本$Ω(HSA\log\log T)$。因此,我们的算法是最佳的切换成本。

英文摘要:

We study the problem of reinforcement learning (RL) with low (policy) switching cost - a problem well-motivated by real-life RL applications in which deployments of new policies are costly and the number of policy updates must be low. In this paper, we propose a new algorithm based on stage-wise exploration and adaptive policy elimination that achieves a regret of $\widetilde{O}(\sqrt{H^4S^2AT})$ while requiring a switching cost of $O(HSA \log\log T)$. This is an exponential improvement over the best-known switching cost $O(H^2SA\log T)$ among existing methods with $\widetilde{O}(\mathrm{poly}(H,S,A)\sqrt{T})$ regret. In the above, $S,A$ denotes the number of states and actions in an $H$-horizon episodic Markov Decision Process model with unknown transitions, and $T$ is the number of steps. As a byproduct of our new techniques, we also derive a reward-free exploration algorithm with a switching cost of $O(HSA)$. Furthermore, we prove a pair of information-theoretical lower bounds which say that (1) Any no-regret algorithm must have a switching cost of $Ω(HSA)$; (2) Any $\widetilde{O}(\sqrt{T})$ regret algorithm must incur a switching cost of $Ω(HSA\log\log T)$. Both our algorithms are thus optimal in their switching costs.

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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