Frequentist Regret Bounds for Randomized Least-Squares Value Iteration
This provides the first frequentist regret analysis for randomized exploration with function approximation, addressing a key theoretical gap in RL for researchers.
The paper tackles the exploration-exploitation dilemma in reinforcement learning with large state spaces by introducing an optimistically-initialized variant of randomized least-squares value iteration (RLSVI), proving a frequentist regret bound of O~(d^2 H^2 √T) under low-rank transition dynamics.
We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL). When the state space is large or continuous, traditional tabular approaches are unfeasible and some form of function approximation is mandatory. In this paper, we introduce an optimistically-initialized variant of the popular randomized least-squares value iteration (RLSVI), a model-free algorithm where exploration is induced by perturbing the least-squares approximation of the action-value function. Under the assumption that the Markov decision process has low-rank transition dynamics, we prove that the frequentist regret of RLSVI is upper-bounded by $\widetilde O(d^2 H^2 \sqrt{T})$ where $ d $ are the feature dimension, $ H $ is the horizon, and $ T $ is the total number of steps. To the best of our knowledge, this is the first frequentist regret analysis for randomized exploration with function approximation.