  In real-world multi-agent reinforcement learning (MARL) applications, agents
may not have perfect state information (e.g., due to inaccurate measurement or
malicious attacks), which challenges the robustness of agents' policies. Though
robustness is getting important in MARL deployment, little prior work has
studied state uncertainties in MARL, neither in problem formulation nor
algorithm design. Motivated by this robustness issue and the lack of
corresponding studies, we study the problem of MARL with state uncertainty in
this work. We provide the first attempt to the theoretical and empirical
analysis of this challenging problem. We first model the problem as a Markov
Game with state perturbation adversaries (MG-SPA) by introducing a set of state
perturbation adversaries into a Markov Game. We then introduce robust
equilibrium (RE) as the solution concept of an MG-SPA. We conduct a fundamental
analysis regarding MG-SPA such as giving conditions under which such a robust
equilibrium exists. Then we propose a robust multi-agent Q-learning (RMAQ)
algorithm to find such an equilibrium, with convergence guarantees. To handle
high-dimensional state-action space, we design a robust multi-agent
actor-critic (RMAAC) algorithm based on an analytical expression of the policy
gradient derived in the paper. Our experiments show that the proposed RMAQ
algorithm converges to the optimal value function; our RMAAC algorithm
outperforms several MARL and robust MARL methods in multiple multi-agent
environments when state uncertainty is present. The source code is public on
\url{https://github.com/sihongho/robust_marl_with_state_uncertainty}.

Machine Learning;Artificial Intelligence;Computer Science and Game Theory;Multiagent Systems;Systems and Control;Systems and Control