可证明高效的UCB型算法用于学习预测状态表示
Provably Efficient UCB-type Algorithms For Learning Predictive State Representations
AI总结：
本文提出首个计算可处理的UCB型算法用于学习预测状态表示，通过新颖的奖励项上界模型间全变差距离，实现在线与离线场景下样本复杂度界及近最优策略保证。
摘要：
一般序贯决策问题，包括马尔可夫决策过程（MDPs）和部分可观测马尔可夫决策过程（POMDPs）作为特例，旨在通过基于历史观测和行动随时间做出的一系列决策来最大化累积奖励。近期研究表明，如果序贯决策问题具有由预测状态表示（PSRs）建模的低秩结构，则该问题在统计上是可学习的。尽管有这些进展，现有方法通常涉及计算上难以处理的预言机或步骤。另一方面，基于上置信界（UCB）的方法在赌博机和MDPs中已成功作为计算高效的方法，但由于在这些更具挑战性的设置中乐观奖励设计的困难，尚未被研究用于更一般的PSRs。本文提出了首个已知的用于PSRs的UCB型方法，其特点是一个新颖的奖励项，该奖励项上界了估计模型与真实模型之间的全变差距离。我们进一步刻画了我们设计的UCB型算法在在线和离线PSRs中的样本复杂度界。与现有的PSRs方法相比，我们的UCB型算法具有计算可处理性、保证近最优策略的最后迭代以及保证的模型准确性。
英文摘要：
The general sequential decision-making problem, which includes Markov decision processes (MDPs) and partially observable MDPs (POMDPs) as special cases, aims at maximizing a cumulative reward by making a sequence of decisions based on a history of observations and actions over time. Recent studies have shown that the sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs). Despite these advancements, existing approaches typically involve oracles or steps that are computationally intractable. On the other hand, the upper confidence bound (UCB) based approaches, which have served successfully as computationally efficient methods in bandits and MDPs, have not been investigated for more general PSRs, due to the difficulty of optimistic bonus design in these more challenging settings. This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. We further characterize the sample complexity bounds for our designed UCB-type algorithms for both online and offline PSRs. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.
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。
