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（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）旨在基于随时间推移的观测和行动历史，通过做出序列决策来最大化累积奖励。近期研究表明，若序贯决策问题具备由预测状态表示（PSRs）建模的低秩结构，则其在统计上是可学习的。尽管取得了这些进展，现有方法通常依赖预言机或计算效率低下的步骤。另一方面，基于上置信界（UCB）的方法已在多臂赌博机和MDPs中成功实现高效计算，但由于在这些更具挑战性的设定中乐观奖励设计存在困难，尚未被应用于更一般的PSRs。本文提出了首个已知的PSRs的UCB类方法，其核心在于一个新颖的奖励项，该奖励项上界了估计模型与真实模型之间的全变差距离。我们进一步刻画了所设计的在线与离线PSRs的UCB类算法的样本复杂度界。与现有PSRs方法相比，我们的UCB类算法具备计算高效性、保证近最优策略的末次迭代收敛性以及模型精度保障性。