Papers
Topics
Authors
Recent
2000 character limit reached

Personalized incentives as feedback design in generalized Nash equilibrium problems (2203.12948v3)

Published 24 Mar 2022 in math.OC, cs.GT, cs.LG, cs.SY, and eess.SY

Abstract: We investigate both stationary and time-varying, nonmonotone generalized Nash equilibrium problems that exhibit symmetric interactions among the agents, which are known to be potential. As may happen in practical cases, however, we envision a scenario in which the formal expression of the underlying potential function is not available, and we design a semi-decentralized Nash equilibrium seeking algorithm. In the proposed two-layer scheme, a coordinator iteratively integrates the (possibly noisy and sporadic) agents' feedback to learn the pseudo-gradients of the agents, and then design personalized incentives for them. On their side, the agents receive those personalized incentives, compute a solution to an extended game, and then return feedback measurements to the coordinator. In the stationary setting, our algorithm returns a Nash equilibrium in case the coordinator is endowed with standard learning policies, while it returns a Nash equilibrium up to a constant, yet adjustable, error in the time-varying case. As a motivating application, we consider the ridehailing service provided by several companies with mobility as a service orchestration, necessary to both handle competition among firms and avoid traffic congestion, which is also adopted to run numerical experiments verifying our results.

Definition Search Book Streamline Icon: https://streamlinehq.com
References (54)
  1. F. Facchinei and C. Kanzow, “Generalized Nash equilibrium problems,” 4OR, vol. 5, no. 3, pp. 173–210, 2007.
  2. F. Salehisadaghiani and L. Pavel, “Distributed Nash equilibrium seeking: A gossip-based algorithm,” Automatica, vol. 72, pp. 209–216, 2016.
  3. 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.
  4. M. Ye and G. Hu, “Distributed Nash equilibrium seeking by a consensus based approach,” IEEE Transactions on Automatic Control, vol. 62, no. 9, pp. 4811–4818, 2017.
  5. D. Gadjov and L. Pavel, “On the exact convergence to Nash equilibrium in hypomonotone regimes under full and partial-decision information,” IEEE Transactions on Automatic Control, pp. 1–15, 2022.
  6. A. Jadbabaie, A. Rakhlin, S. Shahrampour, and K. Sridharan, “Online optimization: Competing with dynamic comparators,” in Artificial Intelligence and Statistics.   PMLR, 2015, pp. 398–406.
  7. I. Bogunovic, J. Scarlett, and V. Cevher, “Time-varying Gaussian process bandit optimization,” in Artificial Intelligence and Statistics.   PMLR, 2016, pp. 314–323.
  8. S. Shahrampour and A. Jadbabaie, “Distributed online optimization in dynamic environments using mirror descent,” IEEE Transactions on Automatic Control, vol. 63, no. 3, pp. 714–725, 2017.
  9. D. Davis and D. Drusvyatskiy, “Stochastic model-based minimization of weakly convex functions,” SIAM Journal on Optimization, vol. 29, no. 1, pp. 207–239, 2019.
  10. R. Dixit, A. S. Bedi, R. Tripathi, and K. Rajawat, “Online learning with inexact proximal online gradient descent algorithms,” IEEE Transactions on Signal Processing, vol. 67, no. 5, pp. 1338–1352, 2019.
  11. A. Simonetto, E. Dall’Anese, J. Monteil, and A. Bernstein, “Personalized optimization with user’s feedback,” Automatica, vol. 131, p. 109767, 2021.
  12. E. Dall’Anese, A. Simonetto, S. Becker, and L. Madden, “Optimization and learning with information streams: Time-varying algorithms and applications,” IEEE Signal Processing Magazine, vol. 37, no. 3, pp. 71–83, 2020.
  13. T. Ui, “A Shapley value representation of potential games,” Games and Economic Behavior, vol. 31, no. 1, pp. 121–135, 2000.
  14. T. Heikkinen, “A potential game approach to distributed power control and scheduling,” Computer Networks, vol. 50, no. 13, pp. 2295–2311, 2006.
  15. F. Fabiani and S. Grammatico, “Multi-vehicle automated driving as a generalized mixed-integer potential game,” IEEE Transactions on Intelligent Transportation Systems, vol. 21, no. 3, pp. 1064–1073, 2019.
  16. C. Cenedese, F. Fabiani, M. Cucuzzella, J. M. Scherpen, M. Cao, and S. Grammatico, “Charging plug-in electric vehicles as a mixed-integer aggregative game,” in 2019 IEEE 58th Conference on Decision and Control (CDC).   IEEE, 2019, pp. 4904–4909.
  17. F. Fabiani, D. Fenucci, and A. Caiti, “A distributed passivity approach to AUV teams control in cooperating potential games,” Ocean Engineering, vol. 157, pp. 152–163, 2018.
  18. B. F. Hobbs and J.-S. Pang, “Nash-Cournot equilibria in electric power markets with piecewise linear demand functions and joint constraints,” Operations Research, vol. 55, no. 1, pp. 113–127, 2007.
  19. A. M. Ospina, A. Simonetto, and E. Dall’Anese, “Personalized demand response via shape-constrained online learning,” in Proceedings of the IEEE International Conference on Communications, Control, and Computing Technologies for Smart Grids (SmartGridComm), 2020.
  20. I. Notarnicola, A. Simonetto, F. Farina, and G. Notarstefano, “Distributed personalized gradient tracking with convex parametric models,” IEEE Transactions on Automatic Control, vol. 68, no. 1, pp. 588–595, 2023.
  21. A. M. Ospina, A. Simonetto, and E. Dall’Anese, “Time-varying optimization of networked systems with human preferences,” IEEE Transactions on Control of Network Systems, vol. 10, no. 1, pp. 503–515, 2023.
  22. E. Tampubolon and H. Boche, “Coordinated online learning for multiagent systems with coupled constraints and perturbed utility observations,” IEEE Transactions on Automatic Control, vol. 66, no. 11, pp. 5080–5095, 2021.
  23. ——, “On the convergence of online mirror ascent for aggregative games with approximated aggregates,” in 2019 IEEE 20th International Workshop on Signal Processing Advances in Wireless Communications (SPAWC).   IEEE, 2019, pp. 1–5.
  24. ——, “Robust pricing mechanism for resource sustainability under privacy constraint in competitive online learning multi-agent systems,” in ICASSP 2020-2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP).   IEEE, 2020, pp. 8733–8737.
  25. P. Mertikopoulos and Z. Zhou, “Learning in games with continuous action sets and unknown payoff functions,” Mathematical Programming, vol. 173, no. 1, pp. 465–507, 2019.
  26. Z. Zhou, P. Mertikopoulos, N. Bambos, P. Glynn, and C. Tomlin, “Multi-agent online learning with imperfect information,” 2018, (Under review).
  27. J. Cohen, A. Héliou, and P. Mertikopoulos, “Learning with bandit feedback in potential games,” in Proceedings of the 31st International Conference on Neural Information Processing Systems, 2017, pp. 6372–6381.
  28. A. R. Cardoso, J. Abernethy, H. Wang, and H. Xu, “Competing against Nash equilibria in adversarially changing zero-sum games,” in International Conference on Machine Learning.   PMLR, 2019, pp. 921–930.
  29. B. Duvocelle, P. Mertikopoulos, M. Staudigl, and D. Vermeulen, “Multiagent online learning in time-varying games,” Mathematics of Operations Research, 2022.
  30. F. Fabiani, A. Simonetto, and P. J. Goulart, “Learning equilibria with personalized incentives in a class of nonmonotone games,” in 2022 European Control Conference (ECC).   IEEE, 2022, pp. 2179–2184.
  31. N. Li and J. R. Marden, “Designing games for distributed optimization,” IEEE Journal of Selected Topics in Signal Processing, vol. 7, no. 2, pp. 230–242, 2013.
  32. J. R. Marden and J. S. Shamma, “Game theory and control,” Annual Review of Control, Robotics, and Autonomous Systems, vol. 1, pp. 105–134, 2018.
  33. D. Paccagnan, R. Chandan, and J. R. Marden, “Utility and mechanism design in multi-agent systems: An overview,” Annual Reviews in Control, 2022.
  34. A. A. Kulkarni and U. V. Shanbhag, “An existence result for hierarchical Stackelberg v/s Stackelberg games,” IEEE Transactions on Automatic Control, vol. 60, no. 12, pp. 3379–3384, 2015.
  35. F. Fabiani, M. A. Tajeddini, H. Kebriaei, and S. Grammatico, “Local Stackelberg equilibrium seeking in generalized aggregative games,” IEEE Transactions on Automatic Control, vol. 67, no. 2, pp. 965–970, 2022.
  36. NYC OpenData. (2021) For-hire vehicle base aggregate report. [Online] https://opendata.cityofnewyork.us/.
  37. F. Facchinei, V. Piccialli, and M. Sciandrone, “Decomposition algorithms for generalized potential games,” Computational Optimization and Applications, vol. 50, no. 2, pp. 237–262, 2011.
  38. T. Roughgarden, “Algorithmic game theory,” Communications of the ACM, vol. 53, no. 7, p. 78–86, jul 2010.
  39. R. W. Rosenthal, “A class of games possessing pure-strategy Nash equilibria,” International Journal of Game Theory, vol. 2, no. 1, pp. 65–67, 1973.
  40. P. A. Kattuman, R. J. Green, and J. W. Bialek, “Allocating electricity transmission costs through tracing: A game-theoretic rationale,” Operations Research Letters, vol. 32, no. 2, pp. 114–120, 2004.
  41. Q. Zhu and T. Başar, “A multi-resolution large population game framework for smart grid demand response management,” in International Conference on NETwork Games, Control and Optimization (NetGCooP 2011).   IEEE, 2011, pp. 1–8.
  42. F. Zhang and N. E. Leonard, “Cooperative filters and control for cooperative exploration,” IEEE Transactions on Automatic Control, vol. 55, no. 3, pp. 650–663, 2010.
  43. E. Cavazzuti, M. Pappalardo, and M. Passacantando, “Nash equilibria, variational inequalities, and dynamical systems,” Journal of Optimization Theory and Applications, vol. 114, no. 3, pp. 491–506, 2002.
  44. G. Scutari, F. Facchinei, and L. Lampariello, “Parallel and distributed methods for constrained nonconvex optimization - Part I: Theory,” IEEE Transactions on Signal Processing, vol. 65, no. 8, pp. 1929–1944, 2017.
  45. C. Jin, R. Ge, P. Netrapalli, S. M. Kakade, and M. I. Jordan, “How to escape saddle points efficiently,” in Proceedings of the 34th International Conference on Machine Learning - Volume 70, 2017, pp. 1724–1732.
  46. A. Mokhtari, S. Shahrampour, A. Jadbabaie, and A. Ribeiro, “Online optimization in dynamic environments: Improved regret rates for strongly convex problems,” in IEEE Conference on Decision and Control, 2016, pp. 7195–7201.
  47. Y. Li, G. Qu, and N. Li, “Online optimization with predictions and switching costs: Fast algorithms and the fundamental limit,” IEEE Transactions on Automatic Control, vol. 66, no. 10, pp. 4761–4768, 2021.
  48. G. Mateos and G. B. Giannakis, “Distributed recursive least-squares for consensus-based in-network adaptive estimation,” IEEE Transactions on Signal Processing, pp. 4583–4588, 2009.
  49. V. Pandey, J. Monteil, C. Gambella, and A. Simonetto, “On the needs for MaaS platforms to handle competition in ridesharing mobility,” Transportation Research Part C: Emerging Technologies, vol. 108, pp. 269–288, 2019.
  50. M. Diao, H. Kong, and J. Zhao, “Impacts of transportation network companies on urban mobility,” Nature Sustainability, vol. 4, no. 6, pp. 494–500, 2021.
  51. F. Fabiani and B. Franci, “A stochastic generalized Nash equilibrium model for platforms competition in the ride-hail market,” in 2022 IEEE 61st Conference on Decision and Control (CDC), 2022, pp. 4455–4460.
  52. M. V. Solodov and P. Tseng, “Modified projection-type methods for monotone variational inequalities,” SIAM Journal on Control and Optimization, vol. 34, no. 5, pp. 1814–1830, 1996.
  53. V. Mai and M. Johansson, “Convergence of a stochastic gradient method with momentum for non-smooth non-convex optimization,” in International Conference on Machine Learning.   PMLR, 2020, pp. 6630–6639.
  54. D. P. Bertsekas, “Nonlinear programming,” Journal of the Operational Research Society, vol. 48, no. 3, pp. 334–334, 1997.
Citations (4)
View on Semantic Scholar

Summary

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

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

Whiteboard

Open Problems

We haven't generated a list of open problems mentioned in this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Continue Learning

We haven't generated follow-up questions for this paper yet.

Ai Sparkles Streamline Icon: https://streamlinehq.com Generate Now

Collections

Sign up for free to add this paper to one or more collections.

User Circle Single Streamline Icon: https://streamlinehq.com Sign Up