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 not computationally efficient. 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 efficiency, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.

翻译：一般序贯决策问题以马尔可夫决策过程（MDPs）和部分可观测MDPs（POMDPs）为特例，旨在通过基于历史观测和行动序列随时间做出决策来最大化累积奖励。近期研究表明，若该序贯决策问题具备由预测状态表示（PSRs）建模的低秩结构，则具有统计可学习性。尽管取得这些进展，现有方法通常涉及计算效率低下的预言机或步骤。另一方面，基于上置信界（UCB）的方法在赌博机和MDPs中已被成功验证为高效计算手段，但由于在这些更具挑战性的场景中乐观奖励设计的困难，其尚未被推广至更一般的PSRs。本文首次提出针对PSRs的UCB类型方法，其核心创新在于引入一个能对估计模型与真实模型之间的总变差距离进行上界约束的新型奖励项。我们进一步刻画了所设计的在线和离线PSRs UCB类型算法的样本复杂度界。与现有PSRs方法相比，我们的UCB类型算法具有计算高效性、终次迭代保证的近最优策略以及模型精度保证。