Local Policies for Graph-Structured Markov Decision Processes

Fathima Zarin Faizal, Asuman E. Ozdaglar, Martin J Wainwright
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:28665-28689, 2026.

Abstract

We study a cooperative form of multi-agent reinforcement learning with state space dynamics and agent interaction controlled by an underlying graph. Each agent has a local state and action, the evolution of the local state depends only on the states and actions in the $1$-hop neighborhood defined by the graph. Structured dynamics of this type arise in various applications, including network resource allocation, co-operative games, epidemic control, and wireless scheduling. The global state-action space scales exponentially in the number of agents, so that computing global optimal policies is intractable in the worst-case. We study conditions under which it is possible to approximate the optimal policies by a local policy for each agent that depends only on states associated with nodes within its $m$-hop neighborhood. By controlling the propagation of influences via a Dobrushin-type stability matrix, we establish that globally optimal policies can be approximated by local policies with sub-optimality gap decaying exponentially in $m$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-faizal26a, title = {Local Policies for Graph-Structured {M}arkov Decision Processes}, author = {Faizal, Fathima Zarin and Ozdaglar, Asuman E. and Wainwright, Martin J}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {28665--28689}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/faizal26a/faizal26a.pdf}, url = {https://proceedings.mlr.press/v306/faizal26a.html}, abstract = {We study a cooperative form of multi-agent reinforcement learning with state space dynamics and agent interaction controlled by an underlying graph. Each agent has a local state and action, the evolution of the local state depends only on the states and actions in the $1$-hop neighborhood defined by the graph. Structured dynamics of this type arise in various applications, including network resource allocation, co-operative games, epidemic control, and wireless scheduling. The global state-action space scales exponentially in the number of agents, so that computing global optimal policies is intractable in the worst-case. We study conditions under which it is possible to approximate the optimal policies by a local policy for each agent that depends only on states associated with nodes within its $m$-hop neighborhood. By controlling the propagation of influences via a Dobrushin-type stability matrix, we establish that globally optimal policies can be approximated by local policies with sub-optimality gap decaying exponentially in $m$.} }
Endnote
%0 Conference Paper %T Local Policies for Graph-Structured Markov Decision Processes %A Fathima Zarin Faizal %A Asuman E. Ozdaglar %A Martin J Wainwright %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-faizal26a %I PMLR %P 28665--28689 %U https://proceedings.mlr.press/v306/faizal26a.html %V 306 %X We study a cooperative form of multi-agent reinforcement learning with state space dynamics and agent interaction controlled by an underlying graph. Each agent has a local state and action, the evolution of the local state depends only on the states and actions in the $1$-hop neighborhood defined by the graph. Structured dynamics of this type arise in various applications, including network resource allocation, co-operative games, epidemic control, and wireless scheduling. The global state-action space scales exponentially in the number of agents, so that computing global optimal policies is intractable in the worst-case. We study conditions under which it is possible to approximate the optimal policies by a local policy for each agent that depends only on states associated with nodes within its $m$-hop neighborhood. By controlling the propagation of influences via a Dobrushin-type stability matrix, we establish that globally optimal policies can be approximated by local policies with sub-optimality gap decaying exponentially in $m$.
APA
Faizal, F.Z., Ozdaglar, A.E. & Wainwright, M.J.. (2026). Local Policies for Graph-Structured Markov Decision Processes. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:28665-28689 Available from https://proceedings.mlr.press/v306/faizal26a.html.

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