Independent Learning in Performative Markov Potential Games

Rilind Sahitaj, Paulius Sasnauskas, Yiğit Yalın, Debmalya Mandal, Goran Radanovic
Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, PMLR 258:3304-3312, 2025.

Abstract

Performative Reinforcement Learning (PRL) refers to a scenario in which the deployed policy changes the reward and transition dynamics of the underlying environment. In this work, we study multi-agent PRL by incorporating performative effects into Markov Potential Games (MPGs). We introduce the notion of a performatively stable equilibrium (PSE) and show that it always exists under a reasonable sensitivity assumption. We then provide convergence results for state-of-the-art algorithms used to solve MPGs. Specifically, we show that independent policy gradient ascent (IPGA) and independent natural policy gradient (INPG) converge to an approximate PSE in the best-iterate sense, with an additional term that accounts for the performative effects. Furthermore, we show that INPG asymptotically converges to a PSE in the last-iterate sense. As the performative effects vanish, we recover the convergence rates from prior work. For a special case of our game, we provide finite-time last-iterate convergence results for a repeated retraining approach, in which agents independently optimize a surrogate objective. We conduct extensive experiments to validate our theoretical findings.

Cite this Paper

BibTeX
@InProceedings{pmlr-v258-sahitaj25a, title = {Independent Learning in Performative Markov Potential Games}, author = {Sahitaj, Rilind and Sasnauskas, Paulius and Yal{\i}n, Yi{\u{g}}it and Mandal, Debmalya and Radanovic, Goran}, booktitle = {Proceedings of The 28th International Conference on Artificial Intelligence and Statistics}, pages = {3304--3312}, year = {2025}, editor = {Li, Yingzhen and Mandt, Stephan and Agrawal, Shipra and Khan, Emtiyaz}, volume = {258}, series = {Proceedings of Machine Learning Research}, month = {03--05 May}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v258/main/assets/sahitaj25a/sahitaj25a.pdf}, url = {https://proceedings.mlr.press/v258/sahitaj25a.html}, abstract = {Performative Reinforcement Learning (PRL) refers to a scenario in which the deployed policy changes the reward and transition dynamics of the underlying environment. In this work, we study multi-agent PRL by incorporating performative effects into Markov Potential Games (MPGs). We introduce the notion of a performatively stable equilibrium (PSE) and show that it always exists under a reasonable sensitivity assumption. We then provide convergence results for state-of-the-art algorithms used to solve MPGs. Specifically, we show that independent policy gradient ascent (IPGA) and independent natural policy gradient (INPG) converge to an approximate PSE in the best-iterate sense, with an additional term that accounts for the performative effects. Furthermore, we show that INPG asymptotically converges to a PSE in the last-iterate sense. As the performative effects vanish, we recover the convergence rates from prior work. For a special case of our game, we provide finite-time last-iterate convergence results for a repeated retraining approach, in which agents independently optimize a surrogate objective. We conduct extensive experiments to validate our theoretical findings.} }
Endnote
%0 Conference Paper %T Independent Learning in Performative Markov Potential Games %A Rilind Sahitaj %A Paulius Sasnauskas %A Yiğit Yalın %A Debmalya Mandal %A Goran Radanovic %B Proceedings of The 28th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2025 %E Yingzhen Li %E Stephan Mandt %E Shipra Agrawal %E Emtiyaz Khan %F pmlr-v258-sahitaj25a %I PMLR %P 3304--3312 %U https://proceedings.mlr.press/v258/sahitaj25a.html %V 258 %X Performative Reinforcement Learning (PRL) refers to a scenario in which the deployed policy changes the reward and transition dynamics of the underlying environment. In this work, we study multi-agent PRL by incorporating performative effects into Markov Potential Games (MPGs). We introduce the notion of a performatively stable equilibrium (PSE) and show that it always exists under a reasonable sensitivity assumption. We then provide convergence results for state-of-the-art algorithms used to solve MPGs. Specifically, we show that independent policy gradient ascent (IPGA) and independent natural policy gradient (INPG) converge to an approximate PSE in the best-iterate sense, with an additional term that accounts for the performative effects. Furthermore, we show that INPG asymptotically converges to a PSE in the last-iterate sense. As the performative effects vanish, we recover the convergence rates from prior work. For a special case of our game, we provide finite-time last-iterate convergence results for a repeated retraining approach, in which agents independently optimize a surrogate objective. We conduct extensive experiments to validate our theoretical findings.
APA
Sahitaj, R., Sasnauskas, P., Yalın, Y., Mandal, D. & Radanovic, G.. (2025). Independent Learning in Performative Markov Potential Games. Proceedings of The 28th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 258:3304-3312 Available from https://proceedings.mlr.press/v258/sahitaj25a.html.

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