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This research addresses the "tragedy of the commons" by introducing a Lagrangian framework for constrained multi-agent reinforcement learning, ensuring shared resources are preserved within specific depletion budgets. The authors provide theoretical guarantees for feasibility and optimality in reset episodes while validating their approach with experiments on fishery management using IPPO and MAPPO algorithms. This work advances AI safety and sustainability by formally integrating resource constraints into the reward-seeking behavior of autonomous agents.
Learning to Harvest Without Collapse in a Regenerative Commons: A Lagrangian Framework
arXiv:2609.36478v1 Announce Type: new Abstract: The tragedy of the commons poses a multi-agent safety problem: reward-seeking agents can deplete a shared resource, and cooperation among its users does not itself specify how much must be preserved. We make preservation an explicit requirement by formulating a regenerative commons as a constrained Markov game or a constrained multi-agent MDP with a designer-specified depletion budget. We develop a nonstationary Lagrangian framework that constructs a policy sequence from solutions of unconstrained games or cooperative control problems. Extending earlier time-average constructions, we introduce average-epoch solution concepts for reset episodes with discounted rewards and terminal costs. We prove a reward-independent feasibility certificate, cooperative feasibility and approximate optimality against feasible policy mixtures, and an extension to unbiased sampled costs. For self-interested agents, a constrained Nash certificate quantifies the price-dispersion term introduced by deviations that redistribute budget across epochs. Under the stated assumptions on solver accuracy and multiplier updates, these results give constrained policy-sequence guarantees using solutions of unconstrained problems. Experiments with constrained IPPO and MAPPO in a Gordon-Schaefer fishery examine how depletion budgets shape stock retention, harvest rewards, and price adaptation.
Abstract:The tragedy of the commons poses a multi-agent safety problem: reward-seeking agents can deplete a shared resource, and cooperation among its users does not itself specify how much must be preserved. We make preservation an explicit requirement by formulating a regenerative commons as a constrained Markov game or a constrained multi-agent MDP with a designer-specified depletion budget. We develop a nonstationary Lagrangian framework that constructs a policy sequence from solutions of unconstrained games or cooperative control problems. Extending earlier time-average constructions, we introduce average-epoch solution concepts for reset episodes with discounted rewards and terminal costs. We prove a reward-independent feasibility certificate, cooperative feasibility and approximate optimality against feasible policy mixtures, and an extension to unbiased sampled costs. For self-interested agents, a constrained Nash certificate quantifies the price-dispersion term introduced by deviations that redistribute budget across epochs. Under the stated assumptions on solver accuracy and multiplier updates, these results give constrained policy-sequence guarantees using solutions of unconstrained problems. Experiments with constrained IPPO and MAPPO in a Gordon-Schaefer fishery examine how depletion budgets shape stock retention, harvest rewards, and price adaptation.
Artificial Intelligence (cs.AI); Computer Science and Game Theory (cs.GT)
arXiv:2609.36478 [cs.AI]
(or arXiv:2609.36478v1 [cs.AI] for this version)
https://doi.org/10.48550/arXiv.2609.36478 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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