  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.
