In this study, we explore the robustness of cooperative multi-agent
reinforcement learning (c-MARL) against Byzantine failures, where any agent can
enact arbitrary, worst-case actions due to malfunction or adversarial attack.
To address the uncertainty that any agent can be adversarial, we propose a
Bayesian Adversarial Robust Dec-POMDP (BARDec-POMDP) framework, which views
Byzantine adversaries as nature-dictated types, represented by a separate
transition. This allows agents to learn policies grounded on their posterior
beliefs about the type of other agents, fostering collaboration with identified
allies and minimizing vulnerability to adversarial manipulation. We define the
optimal solution to the BARDec-POMDP as an ex post robust Bayesian Markov
perfect equilibrium, which we proof to exist and weakly dominates the
equilibrium of previous robust MARL approaches. To realize this equilibrium, we
put forward a two-timescale actor-critic algorithm with almost sure convergence
under specific conditions. Experimentation on matrix games, level-based
foraging and StarCraft II indicate that, even under worst-case perturbations,
our method successfully acquires intricate micromanagement skills and
adaptively aligns with allies, demonstrating resilience against non-oblivious
adversaries, random allies, observation-based attacks, and transfer-based
attacks