  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.
