VERA: Verifiable Feasibility Representations with Counterfactual Credit for Constrained Multi-Agent Control

Constrained Multi-agent reinforcement learning (CMARL) faces two intertwined challenges: the joint action space grows exponentially with the number of agents, and additional requirements couple agents in ways that reward structure alone does not capture. We introduce Coordination Graphs for Constrained Multi-Agent Reinforcement Learning (CG-CMARL), a framework that addresses both challenges by combining coordination graphs with Lagrangian duality. The system decomposes the joint problem into pairwise regions, each served by a set of shared Q-functions, one for the primary objective and one for each of the constraints, so that the number of learned models is independent of the number of agents. At execution time, Max-Sum message passing coordinates actions across the factor graph, while a Lagrangian multiplier controls the objective--constraint tradeoff, allowing a single trained model to trace a Pareto front without retraining. We provide convergence guarantees under mild conditions, together with a compositional error bound that decomposes into separate interpretable sources, each traceable to a specific design choice and independently controllable. Experiments on cooperative navigation tasks (where teams of up to 10 agents must coordinate to reach target positions while satisfying pairwise constraints) show that our method produces Pareto fronts dominating established baselines trained at fixed reward-shaping ratios, while scaling to team sizes where centralized approaches become intractable.

We present a distributed approach for constrained Multi-Agent Reinforcement Learning (MARL) that combines state-augmented policy learning with distributed consensus over dual variables. Our method targets systems where agents have separable dynamics but must coordinate to satisfy global resource constraints, a setting in which, as we demonstrate empirically, independent learning fails to produce feasible solutions because agents cannot determine appropriate individual contributions toward collective constraint satisfaction. The key technical contribution is showing that lightweight neighbor-to-neighbor consensus over Lagrange multipliers suffices for globally coordinated constraint enforcement while preserving the scalability of independent training. Each agent learns a single augmented policy offline, conditioned on both its local state and a dual variable encoding constraint feedback. During execution, agents reach agreement on this dual variable through local communication alone. We prove that under mild connectivity assumptions, the consensus error among agents' multipliers is bounded, and show that this translates to a bounded constraint violation that decreases with graph connectivity and the number of consensus rounds. Unlike centralized training with decentralized execution (CTDE) approaches, whose complexity grows at least quadratically with agent count, our method scales linearly in both training and execution. Experiments on smart grid demand response demonstrate that consensus coordination is \emph{essential for feasibility}: without it, agents satisfy grid capacity constraints only by indefinitely postponing demand, a degenerate non-solution. With consensus, agents converge to a shared dual variable and satisfy both grid constraints and demand fulfillment, scaling to thousands of agents while CTDE baselines are limited to dozens.

Modern agent frameworks compose planners, tool agents, remote services, and shared specialists into runtime delegation graphs, but their revocation APIs still resemble token or subtree invalidation. When one delegation is withdrawn, the runtime must know which agents lose authority while independently authorized agents keep working. We study this authority consistency problem and introduce VERA (Verifiable Edge Revocation for Agents), a verifier-checkable revocation contract and API emitted by agent-runtime adapters as signed evidence. Under disjunctive authority, revoking edge e invalidates exactly T_intent(e,G) = reach(G) \ reach(G \ {e}), the agents whose every authorizing root path used e. Used as a contract, this target exposes two runtime failures: tree cascades over-revoke shared agents, while deployer-scoped cascades under-revoke cross-domain descendants. In a LangGraph framework-replt cells repeated 20 times yield 500compiled-framework traces and 2,000 valid signed delegation decisions; 13/25 cells contain runtime multi-parsharing and 8/25 contain cross-deployer shies 500/500 target proofs, preserves all320 alternate-parent shared-agent cases that tree cascade revokes, and rejects unauthorized signers and omission attacks. Baseline replay over 1,9that holder/node and tree-style targetscannot express this behavior. We further validate schema portability on A2A, AutoGen, and CrewAI artifacts: nine traces, including five executable Cregned delegation events that pass schema and signature checks.