Provably Efficient UCB-type Algorithms For Learning Predictive State Representations

TL;DR

This paper introduces the first computationally efficient UCB-type algorithms for predictive state representations, providing provable guarantees on sample complexity, model accuracy, and policy optimality in general sequential decision-making problems.

Contribution

It develops a novel UCB approach for PSRs with a new bonus term, enabling tractable learning with theoretical guarantees, unlike previous intractable methods.

Findings

First UCB-type algorithms for PSRs with sample complexity bounds

Guaranteed near-optimal policies and model accuracy

Computationally tractable approach for general PSRs

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.