We develop several new algorithms for learning Markov Decision Processes in
an infinite-horizon average-reward setting with linear function approximation.
Using the optimism principle and assuming that the MDP has a linear structure,
we first propose a computationally inefficient algorithm with optimal
$\widetilde{O}(\sqrt{T})$ regret and another computationally efficient variant
with $\widetilde{O}(T^{3/4})$ regret, where $T$ is the number of interactions.
Next, taking inspiration from adversarial linear bandits, we develop yet
another efficient algorithm with $\widetilde{O}(\sqrt{T})$ regret under a
different set of assumptions, improving the best existing result by Hao et al.
(2020) with $\widetilde{O}(T^{2/3})$ regret. Moreover, we draw a connection
between this algorithm and the Natural Policy Gradient algorithm proposed by
Kakade (2002), and show that our analysis improves the sample complexity bound
recently given by Agarwal et al. (2020).

开发多种学习用于 Markov Decision Processes 的无限时间平均奖励设置和线性函数逼近的算法，使用乐观原则和假设 MDP 具有线性结构，提出具有优化的计算效率的算法，并展开了详细的分析，改进了现有最佳结果。