# Logarithmic Regret for Reinforcement Learning with Linear Function Approximation

@article{He2020LogarithmicRF, title={Logarithmic Regret for Reinforcement Learning with Linear Function Approximation}, author={Jiafan He and Dongruo Zhou and Quanquan Gu}, journal={ArXiv}, year={2020}, volume={abs/2011.11566} }

Reinforcement learning (RL) with linear function approximation has received increasing attention recently. However, existing work has focused on obtaining $\sqrt{T}$-type regret bound, where $T$ is the number of steps. In this paper, we show that logarithmic regret is attainable under two recently proposed linear MDP assumptions provided that there exists a positive sub-optimality gap for the optimal action-value function. In specific, under the linear MDP assumption (Jin et al. 2019), the LSVI…

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