Population-Aware Primal--Dual Coordination for Large-Scale Multi-Agent Systems

In large-scale multi-agent systems with shared resource constraints, an upstream planner must iteratively evaluate candidate resource plans—assessing feasibility, aggregate response, and marginal cost—before committing to one. Lagrangian relaxation separates local decisions through a broadcast cost signal, but the planner still needs the induced cost-to-utilization response map, which depends on population composition that changes across planning cycles. We introduce planner-facing, population-aware primal–dual coordination interfaces: a forward map predicting aggregate resource use under candidate costs and an inverse-direction map producing costs for target resource levels, both conditioned on compact population summaries. By encoding response-relevant population structure, these interfaces generalize across evolving populations without per-cycle retraining and support coordination of large populations from compact cohorts. We train the interfaces on simulator rollouts spanning controlled shifts in population composition and resource targets. In a supply-chain capacity-control study, population-aware interfaces reduce forecast error by 16–19\% under population distribution shift and mean capacity violation by 20–51\% relative to baselines without explicit population conditioning; compact cohorts of roughly 20K agents support accurate prediction and control for target populations up to 500K agents.