$K$-Sparse Wasserstein Distributionally Robust Value Factorization for Cooperative MARL

Robust value factorization for MARL under concurrent actuator faults is combinatorial: allowing up to $K$ failures among $N$ agents creates ${\sum }_{k=1}^K\left(\genfrac{}{}{0ex}{}{N}{k}\right)$ fault patterns per Bellman backup. We introduce $K$-Sparse Wasserstein Distributionally Robust MARL (KW-DRO), which limits each fault realization to $K$ agents and uses a Wasserstein radius $\rho$ to control the expected fault count. For the standard single-hidden-layer QMIX mixer, we show that learner-side fault damage is monotone submodular under convex activation and nonnegative utility drops. KW-DRO therefore constructs candidates in $O(NK)$ time with a $(1-1/e)$ per-cardinality guarantee, exactly for VDN, and solves probability allocation by an exact lower-convex-hull computation. The solver agrees with reference linear programs, and greedy search matches exhaustive selection on all $1,536$ tested QMIX states. On RWARE, nominal VDN exhibits late policy collapse in long training runs; KW-DRO at $\rho =0.5$ keeps all $20/20$ runs alive, compared with $14/20$ under the nominal backup. Matched controls attribute this stabilization to moderate pessimism rather than Wasserstein geometry alone. Anonymous code available: https://anonymous.4open.science/r/kw-dro.