arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2011.07738cs.LGcs.SYeess.SY
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强化学习中的奖励偏置最大似然估计

Reward Biased Maximum Likelihood Estimation for Reinforcement Learning

Texas A&M University(得克萨斯农工大学);Indian Institute of Science(印度科学学院)

Akshay Mete, Rahul Singh, Xi Liu, P. R. Kumar

摘要:

为了克服自适应控制的基本“闭可辨识性问题”、“对偶控制问题”或“探索与利用问题”的中心障碍,提出了马尔可夫链自适应控制的有偏最大似然估计(RBMLE).它利用了一个关键的观察,即由于最大似然参数估计可以在确定性等价方法下渐近地识别闭转移概率,因此限制参数估计必须具有小于真实但未知系统可获得的最优奖励的最优奖励。因此,它提出了一个抵消反向偏置,有利于具有更大的最佳回报的参数,提供了一个解决方案,上面提到的基本问题。因此,它提出了一种支持具有更大最优回报的参数的乐观方法,现在被称为“面对不确定性的乐观”。RBMLE方法已被证明是在各种情况下的长期平均奖励最优。然而,现代人的注意力集中在“后悔”或有限时间表现的更精细的概念上。最近对多武器随机土匪和线性背景土匪的RBMLE分析表明,它不仅具有最先进的遗憾,而且还表现出与当前最佳竞争者相当或更好的经验表现,并导致惊人的简单指数政策。出于这一动机,我们研究的有限时间性能的RBMLE的强化学习任务,涉及一般问题的最优控制未知马尔可夫决策过程。我们表明,它有一个遗憾的$\mathcal{O}( \log T)$在一个时间范围内的$T$步骤,类似于国家的最先进的算法。仿真研究表明,RBMLE优于其他算法,如UCRL 2和汤普森采样。

英文摘要:

The Reward-Biased Maximum Likelihood Estimate (RBMLE) for adaptive control of Markov chains was proposed to overcome the central obstacle of what is variously called the fundamental "closed-identifiability problem" of adaptive control, the "dual control problem", or, contemporaneously, the "exploration vs. exploitation problem". It exploited the key observation that since the maximum likelihood parameter estimator can asymptotically identify the closed-transition probabilities under a certainty equivalent approach, the limiting parameter estimates must necessarily have an optimal reward that is less than the optimal reward attainable for the true but unknown system. Hence it proposed a counteracting reverse bias in favor of parameters with larger optimal rewards, providing a solution to the fundamental problem alluded to above. It thereby proposed an optimistic approach of favoring parameters with larger optimal rewards, now known as "optimism in the face of uncertainty". The RBMLE approach has been proved to be long-term average reward optimal in a variety of contexts. However, modern attention is focused on the much finer notion of "regret", or finite-time performance. Recent analysis of RBMLE for multi-armed stochastic bandits and linear contextual bandits has shown that it not only has state-of-the-art regret, but it also exhibits empirical performance comparable to or better than the best current contenders, and leads to strikingly simple index policies. Motivated by this, we examine the finite-time performance of RBMLE for reinforcement learning tasks that involve the general problem of optimal control of unknown Markov Decision Processes. We show that it has a regret of $\mathcal{O}( \log T)$ over a time horizon of $T$ steps, similar to state-of-the-art algorithms. Simulation studies show that RBMLE outperforms other algorithms such as UCRL2 and Thompson Sampling.

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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