  Model-free reinforcement learning is known to be memory and computation
efficient and more amendable to large scale problems. In this paper, two
model-free algorithms are introduced for learning infinite-horizon
average-reward Markov Decision Processes (MDPs). The first algorithm reduces
the problem to the discounted-reward version and achieves
$\mathcal{O}(T^{2/3})$ regret after $T$ steps, under the minimal assumption of
weakly communicating MDPs. To our knowledge, this is the first model-free
algorithm for general MDPs in this setting. The second algorithm makes use of
recent advances in adaptive algorithms for adversarial multi-armed bandits and
improves the regret to $\mathcal{O}(\sqrt{T})$, albeit with a stronger ergodic
assumption. This result significantly improves over the $\mathcal{O}(T^{3/4})$
regret achieved by the only existing model-free algorithm by Abbasi-Yadkori et
al. (2019a) for ergodic MDPs in the infinite-horizon average-reward setting.
