Online Markov Decision Processes with Non-oblivious Strategic Adversary


We study a novel setting in Online Markov Decision Processes (OMDPs) where the loss function is chosen by a non-oblivious strategic adversary who follows a no-external regret algorithm. In this setting, we first demonstrate that MDP-Expert, an existing algorithm that works well with oblivious adversaries can still apply and achieve a policy regret bound of O(Tlog(L)−−−−−−−√+τ2Tlog(|A|)−−−−−−−−√) where L is the size of adversary’s pure strategy set and |A| denotes the size of agent’s action space.Considering real-world games where the support size of a NE is small, we further propose a new algorithm: MDP-Online Oracle Expert (MDP-OOE), that achieves a policy regret bound of O(Tlog(L)−−−−−−−√+τ2Tklog(k)−−−−−−−√) where k depends only on the support size of the NE. MDP-OOE leverages the key benefit of Double Oracle in game theory and thus can solve games with prohibitively large action space. Finally, to better understand the learning dynamics of no-regret methods, under the same setting of no-external regret adversary in OMDPs, we introduce an algorithm that achieves last-round convergence to a NE result. To our best knowledge, this is the first work leading to the last iteration result in OMDPs.

Autonomous Agents and Multi-Agent Systems (2023)