Provably Efficient UCB-type Algorithms For Learning Predictive State Representations
This work addresses the challenge of efficient learning in PSRs, which generalizes MDPs and POMDPs, offering a computationally tractable solution for researchers and practitioners in reinforcement learning.
The paper tackles the computational intractability of learning predictive state representations (PSRs) in sequential decision-making by proposing the first UCB-type algorithms, achieving sample complexity bounds for both online and offline settings with guaranteed near-optimal policies and model accuracy.
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.