We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an adversary. We propose the \textsc{UCSG} algorithm that achieves a sublinear regret compared to the game value when competing with an arbitrary opponent. This result improves previous ones under the same setting. The regret bound has a dependency on the \textit{diameter}, which is an intrinsic value related to the mixing property of SGs.

We study online reinforcement learning in average-reward stochastic games (SGs). An SG models a two-player zero-sum game in a Markov environment, where state transitions and one-step payoffs are determined simultaneously by a learner and an adversary. We propose the \textsc{UCSG} algorithm that achieves a sublinear regret compared to the game value when competing with an arbitrary opponent. This result improves previous ones under the same setting. The regret bound has a dependency on the \textit{diameter}, which is an intrinsic value related to the mixing property of SGs. Slightly extended, \textsc{UCSG} finds an $\varepsilon$-maximin stationary policy with a sample complexity of $\tilde{\mathcal{O}}\left(\text{poly}(1/\varepsilon)\right)$, where $\varepsilon$ is the error parameter. To the best of our knowledge, this extended result is the first in the average-reward setting. In the analysis, we develop Markov chain's perturbation bounds for mean first passage times and techniques to deal with non-stationary opponents, which may be of interest in their own right.

We study the dynamic regret of multi-armed bandit and experts problem in non-stationary stochastic environments. We introduce a new parameter $\W$, which measures the total statistical variance of the loss distributions over $T$ rounds of the process, and study how this amount affects the regret. We investigate the interaction between $\W$ and $\Gamma$, which counts the number of times the distributions change, as well as $\W$ and $V$, which measures how far the distributions deviates over time. One striking result we find is that even when $\Gamma$, $V$, and $\Lambda$ are all restricted to constant, the regret lower bound in the bandit setting still grows with $T$. The other highlight is that in the full-information setting, a constant regret becomes achievable with constant $\Gamma$ and $\Lambda$, as it can be made independent of $T$, while with constant $V$ and $\Lambda$, the regret still has a $T^{1/3}$ dependency. We not only propose algorithms with upper bound guarantee, but prove their matching lower bounds as well.