{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T22:03:19Z","timestamp":1765231399974,"version":"3.46.0"},"reference-count":47,"publisher":"World Scientific Pub Co Pte Ltd","issue":"06","funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"crossref","award":["72201006","72192843"],"award-info":[{"award-number":["72201006","72192843"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Asia Pac. J. Oper. Res."],"published-print":{"date-parts":[[2025,12]]},"abstract":"<jats:p>In this work, we study stochastic non-cooperative games, where only noisy black-box function evaluations are available to estimate the cost function for each player. Since each player\u2019s cost function depends on both its own decision variables and its rivals\u2019 decision variables, local information needs to be exchanged through a center\/network in most existing work for seeking the Nash equilibrium (NE). We propose a new stochastic distributed learning algorithm that does not require communications among players. The proposed algorithm uses simultaneous perturbation method to estimate the gradient of each cost function, and uses mirror descent method to search for the NE. We provide asymptotic analysis for the bias and variance of gradient estimates, and show the proposed algorithm converges to the NE in mean square for the class of strictly monotone games at the optimal rate. The effectiveness of the proposed method is buttressed in a numerical experiment.<\/jats:p>","DOI":"10.1142\/s0217595925400123","type":"journal-article","created":{"date-parts":[[2025,9,21]],"date-time":"2025-09-21T15:37:37Z","timestamp":1758469057000},"source":"Crossref","is-referenced-by-count":1,"title":["Efficient Distributed Learning in Stochastic Non-Cooperative Games Without Information Exchange"],"prefix":"10.1142","volume":"42","author":[{"ORCID":"https:\/\/orcid.org\/0009-0006-6314-9111","authenticated-orcid":false,"given":"Zihan","family":"He","sequence":"first","affiliation":[{"name":"School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9939-7164","authenticated-orcid":false,"given":"Haidong","family":"Li","sequence":"additional","affiliation":[{"name":"School of Economics and Management, University of Chinese Academy of Sciences, Beijing 100190, P. R. China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"219","published-online":{"date-parts":[[2025,10,14]]},"reference":[{"key":"S0217595925400123BIB001","first-page":"28","volume-title":"Conf. Learning Theory COLT","author":"Agarwal A","year":"2010"},{"key":"S0217595925400123BIB002","doi-asserted-by":"publisher","DOI":"10.1109\/CDC.2002.1184680"},{"key":"S0217595925400123BIB003","doi-asserted-by":"publisher","DOI":"10.24193\/fpt-ro.2023.2.03"},{"key":"S0217595925400123BIB004","series-title":"Proceedings of Machine Learning Research","first-page":"383","volume-title":"Int. Conf. Machine Learning ICML","volume":"139","author":"Asi H","year":"2021"},{"key":"S0217595925400123BIB005","doi-asserted-by":"publisher","DOI":"10.1016\/j.sigpro.2023.109089"},{"key":"S0217595925400123BIB006","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2021.3135360"},{"key":"S0217595925400123BIB007","doi-asserted-by":"publisher","DOI":"10.1287\/mnsc.2018.3061"},{"key":"S0217595925400123BIB008","first-page":"5661","volume-title":"Advances in Neural Information Processing Systems","volume":"31","author":"Bravo M","year":"2018"},{"issue":"1","key":"S0217595925400123BIB009","first-page":"1","volume":"5","author":"Bubeck S","year":"2012","journal-title":"Machine Learning"},{"key":"S0217595925400123BIB010","doi-asserted-by":"publisher","DOI":"10.1137\/0803026"},{"key":"S0217595925400123BIB011","first-page":"10934","volume-title":"Advances in Neural Information Processing Systems","volume":"32","author":"Cheng S","year":"2019"},{"key":"S0217595925400123BIB012","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177728716"},{"key":"S0217595925400123BIB013","doi-asserted-by":"publisher","DOI":"10.1109\/TWC.2015.2456063"},{"volume-title":"Finite-dimensional Variational Inequalities and Complementarity Problems","year":"2007","author":"Facchinei F","key":"S0217595925400123BIB014"},{"key":"S0217595925400123BIB015","first-page":"831","volume-title":"Conf. Learning Theory","author":"Flammarion N","year":"2017"},{"key":"S0217595925400123BIB016","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2018.2833140"},{"key":"S0217595925400123BIB017","doi-asserted-by":"publisher","DOI":"10.1137\/120880811"},{"key":"S0217595925400123BIB018","doi-asserted-by":"publisher","DOI":"10.1080\/02331934.2020.1836634"},{"key":"S0217595925400123BIB019","doi-asserted-by":"publisher","DOI":"10.23919\/CCC52363.2021.9550749"},{"key":"S0217595925400123BIB020","series-title":"Proceedings of Machine Learning Research","first-page":"3142","volume-title":"Int. Conf. Artificial Intelligence and Statistics AISTATS","volume":"130","author":"Li H","year":"2021"},{"key":"S0217595925400123BIB021","first-page":"40238","volume-title":"Advances in Neural Information Processing Systems","volume":"36","author":"Li H","year":"2023"},{"key":"S0217595925400123BIB022","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.07.064"},{"key":"S0217595925400123BIB023","doi-asserted-by":"publisher","DOI":"10.1109\/TCYB.2018.2828118"},{"key":"S0217595925400123BIB024","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2020.3002592"},{"key":"S0217595925400123BIB025","doi-asserted-by":"publisher","DOI":"10.1287\/opre.1120.1137"},{"key":"S0217595925400123BIB026","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-018-1254-8"},{"key":"S0217595925400123BIB027","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.36.1.48"},{"volume-title":"Problem Complexity and Method Efficiency in Optimization","year":"1983","author":"Nemirovskij AS","key":"S0217595925400123BIB028"},{"key":"S0217595925400123BIB029","unstructured":"Neri, M, N Pischke and T Powell (2025). On the asymptotic behaviour of stochastic processes, with applications to supermartingale convergence, Dvoretzky\u2019s approximation theorem, and stochastic quasi-Fej\u00e9r monotonicity, arXiv:2504.12922."},{"key":"S0217595925400123BIB030","doi-asserted-by":"publisher","DOI":"10.1007\/s10107-007-0149-x"},{"key":"S0217595925400123BIB031","doi-asserted-by":"publisher","DOI":"10.1007\/s10208-015-9296-2"},{"key":"S0217595925400123BIB032","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2019.2922953"},{"key":"S0217595925400123BIB033","doi-asserted-by":"publisher","DOI":"10.1214\/aoms\/1177729586"},{"key":"S0217595925400123BIB034","doi-asserted-by":"publisher","DOI":"10.2307\/1911749"},{"key":"S0217595925400123BIB035","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2016.06.004"},{"key":"S0217595925400123BIB036","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2017.09.016"},{"key":"S0217595925400123BIB037","doi-asserted-by":"publisher","DOI":"10.1109\/MSP.2010.936021"},{"key":"S0217595925400123BIB038","doi-asserted-by":"publisher","DOI":"10.1561\/2200000018"},{"key":"S0217595925400123BIB039","first-page":"1265","volume-title":"Proc. 19th Int. Conf. Neural Information Processing Systems","author":"Shalev-Shwartz S","year":"2006"},{"key":"S0217595925400123BIB040","first-page":"3","volume-title":"Conference on Learning Theory","author":"Shamir O","year":"2013"},{"key":"S0217595925400123BIB041","doi-asserted-by":"publisher","DOI":"10.52202\/079017-1306"},{"key":"S0217595925400123BIB042","doi-asserted-by":"publisher","DOI":"10.1109\/9.119632"},{"key":"S0217595925400123BIB043","first-page":"2543","volume":"11","author":"Xiao L","year":"2010","journal-title":"Journal of Machine Learning Research"},{"key":"S0217595925400123BIB044","doi-asserted-by":"publisher","DOI":"10.1109\/TAC.2017.2688452"},{"key":"S0217595925400123BIB045","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2018.05.020"},{"key":"S0217595925400123BIB046","doi-asserted-by":"publisher","DOI":"10.1016\/j.automatica.2019.01.008"},{"key":"S0217595925400123BIB047","doi-asserted-by":"crossref","unstructured":"Yukawa, M and I Yamada (2024). Monotone Lipschitz-gradient denoiser: Explainability of operator regularization approaches and convergence to optimal point, arXiv:2406.04676.","DOI":"10.1109\/TSP.2025.3580667"}],"container-title":["Asia-Pacific Journal of Operational Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.worldscientific.com\/doi\/pdf\/10.1142\/S0217595925400123","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,12,8]],"date-time":"2025-12-08T09:11:16Z","timestamp":1765185076000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.worldscientific.com\/doi\/10.1142\/S0217595925400123"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,10,14]]},"references-count":47,"journal-issue":{"issue":"06","published-print":{"date-parts":[[2025,12]]}},"alternative-id":["10.1142\/S0217595925400123"],"URL":"https:\/\/doi.org\/10.1142\/s0217595925400123","relation":{},"ISSN":["0217-5959","1793-7019"],"issn-type":[{"type":"print","value":"0217-5959"},{"type":"electronic","value":"1793-7019"}],"subject":[],"published":{"date-parts":[[2025,10,14]]},"article-number":"2540012"}}