Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
167 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
42 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Distributed Generalized Nash Equilibria Seeking Algorithms Involving Synchronous and Asynchronous Schemes (2402.03669v2)

Published 6 Feb 2024 in cs.GT and cs.MA

Abstract: This paper considers a class of noncooperative games in which the feasible decision sets of all players are coupled together by a coupled inequality constraint. Adopting the variational inequality formulation of the game, we first introduce a new local edge-based equilibrium condition and develop a distributed primal-dual proximal algorithm with full information. Considering challenges when communication delays occur, we devise an asynchronous distributed algorithm to seek a generalized Nash equilibrium. This asynchronous scheme arbitrarily activates one player to start new computations independently at different iteration instants, which means that the picked player can use the involved out-dated information from itself and its neighbors to perform new updates. A distinctive attribute is that the proposed algorithms enable the derivation of new distributed forward-backward-like extensions. In theoretical aspect, we provide explicit conditions on algorithm parameters, for instance, the step-sizes to establish a sublinear convergence rate for the proposed synchronous algorithm. Moreover, the asynchronous algorithm guarantees almost sure convergence in expectation under the same step-size conditions and some standard assumptions. An interesting observation is that our analysis approach improves the convergence rate of prior synchronous distributed forward-backward-based algorithms. Finally, the viability and performance of the proposed algorithms are demonstrated by numerical studies on the networked Cournot competition.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (41)
  1. R. Egging-Bratseth, T. Baltensperger, and A. Tomasgard, “Solving oligopolistic equilibrium problems with convex optimization,” European Journal of Operational Research, vol. 284, pp. 44–52, 2020.
  2. M. Ye and G. Hu, “Game design and analysis for price-based demand response: An aggregate game approach,” IEEE Transactions on Cybernetics, vol. 47, no. 3, pp. 720–730, 2017.
  3. Y. Liang, W. Wei, and C. Wang, “A generalized Nash equilibrium approach for autonomous energy management of residential energy hubs,” IEEE Transactions on Industrial Informatics, vol. 15, no. 11, pp. 5892–5905, 2019.
  4. A. A. Kulkarni and U. V. Shanbhag, “On the variational equilibrium as a refinement of the generalized Nash equilibrium,” Automatica, vol. 48, no. 1, pp. 45–55, 2012.
  5. P. T. Harker, “Generalized Nash games and quasi-variational inequalities,” European Journal of Operational Research, vol. 54, no. 1, pp. 81–94, 1991.
  6. F. Facchinei, A. Fischer, and V. Piccialli, “On generalized Nash games and variational inequalities,” Operations Research Letters, vol. 35, no. 2, pp. 159–164, 2007.
  7. M. Hintermüller, T. Surowiec, and A. Kämmler, “Generalized Nash equilibrium problems in Banach spaces: Theory, nikaido-isoda-based path-following methods, and applications,” SIAM Journal on Optimization, vol. 25, no. 3, pp. 1826–1856, 2015.
  8. G. A. Jason R. Marden and J. S. Shamma, “Joint strategy fictitious play with inertia for potential games,” IEEE Transactions on Automatic Control, vol. 54, no. 2, pp. 208–220, 2009.
  9. M. Bianchi, G. Belgioioso, and S. Grammatico, “A fully-distributed proximal-point algorithm for Nash equilibrium seeking with linear convergence rate,” in Proceedings of the IEEE Conference on Decision and Control, pp. 2303–2308, 2020.
  10. G. Belgioioso, A. Nedić, and S. Grammatico, “Distributed generalized Nash equilibrium seeking in aggregative games on time-varying networks,” IEEE Transactions on Automatic Control, vol. 66, no. 5, pp. 2061–2075, 2021.
  11. Y. Zhu, W. Yu, G. Wen, and G. Chen, “Distributed Nash equilibrium seeking in an aggregative game on a directed Graph,” IEEE Transactions on Automatic Control, vol. 66, no. 6, pp. 2746–2753, 2021.
  12. M. Ye, G. Hu, L. Xie, and S. Xu, “Differentially private distributed Nash equilibrium seeking for aggregative games,” IEEE Transactions on Automatic Control, vol. 67, no. 5, pp. 2451–2458, 2022.
  13. Y. Pang and G. Hu, “Distributed Nash equilibrium seeking with limited cost function knowledge via a consensus-based gradient-free method,” IEEE Transactions on Automatic Control, vol. 66, no. 4, pp. 1832–1839, 2021.
  14. F. Liu, Q. Wang, Y. Hua, X. Dong, and Z. Ren, “Distributed Nash equilibrium seeking for non-cooperative convex games with local constraints,” in 40th Chinese Control Conference (CCC), pp. 7480–7485, 2021.
  15. F. Salehisadaghiani, W. Shi, and L. Pavel, “Distributed Nash equilibrium seeking under partial-decision information via the alternating direction method of multipliers,” Automatica, vol. 103, pp. 27–35, 2019.
  16. K. Lu and Q. Zhu, “Nonsmooth continuous-time distributed algorithms for seeking generalized Nash equilibria of noncooperative games via digraphs,” IEEE Transactions on Cybernetics, 2021.
  17. K. Lu, G. Jing, and L. Wang, “Distributed algorithms for searching generalized Nash equilibrium of noncooperative games,” IEEE Transactions on Cybernetics, vol. 49, no. 6, pp. 2362–2371, 2019.
  18. S. Liang, P. Yi, and Y. Hong, “Distributed Nash equilibrium seeking for aggregative games with coupled constraints,” Automatica, vol. 85, pp. 179–185, 2017.
  19. P. Yi and L. Pavel, “An operator splitting approach for distributed generalized Nash equilibria computation,” Automatica, vol. 102, pp. 111–121, 2019.
  20. B. Franci and S. Grammatico, “A distributed forward-backward algorithm for stochastic generalized Nash equilibrium seeking,” IEEE Transactions on Automatic Control, vol. 66, no. 11, pp. 5467–5473, 2021.
  21. L. Pavel, “Distributed GNE seeking under partial-decision information over networks via a doubly-augmented operator splitting approach,” IEEE Transactions on Automatic Control, vol. 65, no. 4, pp. 1584–1597, 2020.
  22. Z. Wang, F. Liu, Z. Ma, Y. Chen, M. Jia, W. Wei, and Q. Wu, “Distributed generalized Nash equilibrium seeking for energy sharing games in prosumers,” IEEE Transactions on Power Systems, vol. 36, no. 5, pp. 3973–3986, 2021.
  23. Y. Tian, Y. Sun, and G. Scutari, “Achieving linear convergence in distributed asynchronous multiagent optimization,” IEEE Transactions on Automatic Control, vol. 65, no. 12, pp. 5264–5279, 2020.
  24. T. Wu, K. Yuan, Q. Ling, W. Yin, and A. H. Sayed, “Decentralized consensus optimization with asynchrony and delays,” IEEE Transactions on Signal and Information Processing over Networks, vol. 4, no. 2, pp. 293–307, 2018.
  25. J. Lei, U. Shanbhag, J.-S. Pang, and S. Sen, “On synchronous, asynchronous, and randomized best-response schemes for computing equilibria in stochastic Nash games,” Mathematics of Operations Research, 2017.
  26. P. Yi and L. Pavel, “Asynchronous distributed algorithms for seeking generalized Nash equilibria under full and partial-decision information,” IEEE Transactions on Cybernetics, vol. 50, no. 6, pp. 2514–2526, 2020.
  27. C. Cenedese, G. Belgioioso, S. Grammatico, and M. Cao, “An asynchronous, forward-backward, distributed generalized Nash equilibrium seeking algorithm,” in 2019 18th European Control Conference, ECC 2019, 2019.
  28. F. Facchinei and C. Kanzow, “Generalized Nash equilibrium problems,” Annals of Operations Research, vol. 175, pp. 177–211, 2010.
  29. G. Belgioioso and S. Grammatico, “Semi-decentralized Nash equilibrium seeking in aggregative games with separable coupling constraints and non-differentiable cost functions,” IEEE Control Systems Letters, vol. 1, no. 2, pp. 400–405, 2017.
  30. L. Zheng, H. Li, L. Ran, L. Gao, and D. Xia, “Distributed primal¨Cdual algorithms for stochastic generalized Nash equilibrium seeking under full and partial-decision information,” IEEE Transactions on Control of Network Systems, vol. 10, no. 2, pp. 718–730, 2023.
  31. A. Kannan and U. V. Shanbhag, “Distributed computation of equilibria in monotone Nash games via iterative regularization techniques,” SIAM Journal on Optimization, vol. 22, no. 3, pp. 1177–1205, 2012.
  32. G. Scutari, D. P. Palomar, F. Facchinei, and J.-s. Pang, “Convex optimization, game theory, and variational inequality theory,” IEEE Signal Processing Magazine, vol. 27, no. 3, pp. 35–49, 2010.
  33. F. Facchinei and J.-S. Pang, “Nash equilibria: The variational approach,” Convex Optimization in Signal Processing and Communications, pp. 443–493, 2009.
  34. H. H. Bauschke and P. L. Combettes, “Convex analysis and monotone operator theory in Hilbert spaces,” in Cham, Switzerland: Springer, 2011.
  35. G. Carnevale, F. Fabiani, F. Fele, K. Margellos, and G. Notarstefano, “Tracking-based distributed equilibrium seeking for aggregative games,” arXiv:2210.14547, 2022.
  36. M. Fatemeh and W. Ermin, “A fast distributed asynchronous newton-based optimization algorithm,” IEEE Transactions on Automatic Control, vol. 65, no. 7, pp. 2769–2784, 2020.
  37. Z. Peng, Y. Xu, M. Yan, and W. Yin, “ARock: An algorithmic framework for asynchronous parallel coordinate updates,” SIAM Journal on Scientific Computing, vol. 38, no. 5, pp. 2851–2879, 2016.
  38. P. Latafat and P. Patrinos, “Asymmetric forward-backward-adjoint splitting for solving monotone inclusions involving three operators,” Computational Optimization and Applications, vol. 68, pp. 57–93, 2017.
  39. M. Yan, “A new primal-dual algorithm for minimizing the sum of three functions with a linear operator,” Journal of Entific Computing, vol. 76, no. 3, pp. 1698–1717, 2018.
  40. Z. Opial, “Weak convergence of the sequence of successive approximations for nonexpansive mappings,” Bulletin of the American Mathematical Society, vol. 73, no. 4, pp. 591–597, 1967.
  41. G. Qu and N. Li, “Accelerated distributed Nesterov gradient descent,” IEEE Transactions on Automatic Control, vol. 65, no. 6, pp. 2566–2581, 2020.
Citations (1)
View on Semantic Scholar

Summary

We haven't generated a summary for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Summarize Now
X Twitter Logo Streamline Icon: https://streamlinehq.com

Tweets