  We study decentralized policy learning in Markov games where we control a
single agent to play with nonstationary and possibly adversarial opponents. Our
goal is to develop a no-regret online learning algorithm that (i) takes actions
based on the local information observed by the agent and (ii) is able to find
the best policy in hindsight. For such a problem, the nonstationary state
transitions due to the varying opponent pose a significant challenge. In light
of a recent hardness result \citep{liu2022learning}, we focus on the setting
where the opponent's previous policies are revealed to the agent for decision
making. With such an information structure, we propose a new algorithm,
\underline{D}ecentralized \underline{O}ptimistic hype\underline{R}policy
m\underline{I}rror de\underline{S}cent (DORIS), which achieves
$\sqrt{K}$-regret in the context of general function approximation, where $K$
is the number of episodes. Moreover, when all the agents adopt DORIS, we prove
that their mixture policy constitutes an approximate coarse correlated
equilibrium. In particular, DORIS maintains a \textit{hyperpolicy} which is a
distribution over the policy space. The hyperpolicy is updated via mirror
descent, where the update direction is obtained by an optimistic variant of
least-squares policy evaluation. Furthermore, to illustrate the power of our
method, we apply DORIS to constrained and vector-valued MDPs, which can be
formulated as zero-sum Markov games with a fictitious opponent.

Machine Learning;Machine Learning