  This paper studies regret minimization with randomized value functions in
reinforcement learning. In tabular finite-horizon Markov Decision Processes, we
introduce a clipping variant of one classical Thompson Sampling (TS)-like
algorithm, randomized least-squares value iteration (RLSVI). Our
$\tilde{\mathrm{O}}(H^2S\sqrt{AT})$ high-probability worst-case regret bound
improves the previous sharpest worst-case regret bounds for RLSVI and matches
the existing state-of-the-art worst-case TS-based regret bounds.
