Provably Efficient UCB-type Algorithms For Learning Predictive State Representations
Ruiquan Huang, Yingbin Liang, Jing Yang
TL;DR
This work develops provably efficient UCB-type algorithms for learning Predictive State Representations (PSRs) in low-rank sequential decision problems, addressing both online and offline settings. The online PSR-UCB algorithm integrates a stable maximum-likelihood estimation step with a novel total-variation-based UCB bonus, enabling last-iterate guarantees and near-optimal policies with polynomial sample complexity in rank, horizon, and feature dimensions. The offline PSR-LCB extension provides a principled pessimistic bound that scales as $\tilde{O}\left( \left(\sqrt{r} + \frac{Q_A\sqrt{H}}{\gamma}\right) \frac{C_{\pi^b,\infty}^{\pi} Q_A H^2}{\iota \gamma^2} \sqrt{\frac{r d \hat{\beta}}{K}} \right)$, ensuring competitive performance with finite coverage. Together, these results demonstrate computationally tractable planning in PSRs, guarantee model accuracy in online settings, and establish the first sample complexity results for offline PSRs, advancing scalable learning under partial observability.
Abstract
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.