Frequentist Regret Bounds for Randomized Least-Squares Value Iteration

• URL: http://arxiv.org/abs/1911.00567v7
• Date: Fri, 8 Sep 2023 16:34:55 GMT
• Title: Frequentist Regret Bounds for Randomized Least-Squares Value Iteration
• Authors: Andrea Zanette, David Brandfonbrener, Emma Brunskill, Matteo Pirotta, Alessandro Lazaric
• Abstract summary: We consider the exploration-exploitation dilemma in finite-horizon reinforcement learning (RL) In this paper, we introduce an optimistically-perturbed variant of the popular randomized least-squares value (RLSVI) 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 $widetilde O(d2 H2 sqrtT)$ where $ d $ are the feature dimension, $ H $ is the horizon, and $ T $ is the total number of
• Score: 94.47472987987805
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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