Reachability-Certified Subteam Decomposition for Locally Interacting Multi-Agent MDPs

Abstract

Persistent communication limits force a multi-agent system to decide which agents may coordinate throughout a rollout. Current proximity alone is insufficient: separated agents may interact later, whereas a large pair reward may remain unreachable until it is heavily discounted. We introduce Reachability-Certified Subteam Decomposition (RCSD) for finite multi-agent Markov decision processes with factorized physical dynamics, finite-range ordered pair rewards, and almost-sure motion bounds. RCSD combines a speed-limit lower bound on pairwise contact time with a reward envelope to form a current-state affinity. For any capacity-valid persistent partition, the sum of cut affinities bounds the reward-deletion error of every unchanged stationary Markov state-feedback policy. A product of team-optimal policies for the resulting cut MDP incurs at most twice this certificate in regret against the centralized optimum. Both bounds are worst-case tight. On a controlled five-agent family, RCSD-Exact reduces aggregate normalized execution regret by 56.0%, 28.8%, and 25.3% relative to uniform, distance-only, and envelope-only partitions. A separate stochastic two-dimensional study finds no bound violation over 384 exact-partition and 1,440 restricted-controller evaluations. Exact four-agent evidence favors RCSD over uniform and distance-only grouping; raw evidence for current contact is borderline and envelope-only is unresolved. Across balanced 8-20-agent strata, controller-library utility is mixed: pointwise paired intervals favor RCSD over distance and current contact, include zero for uniform, and favor envelope-only and Value-MIP over RCSD. Partition construction remains subsecond in median up to 100 agents; this last result does not include affinity formation or MDP planning.