A Douglas-Rachford Splitting for Semi-decentralized Equilibrium Seeking in Generalized Aggregative Games

We address the generalized aggregative equilibrium seeking problem for noncooperative agents playing average aggregative games with affine coupling constraints. First, we use operator theory to characterize the generalized aggregative equilibria of the game as the zeros of a monotone set-valued operator. Then, we massage the Douglas-Rachford splitting to solve the monotone inclusion problem and derive a single layer, semi-decentralized algorithm whose global convergence is guaranteed under mild assumptions. The potential of the proposed Douglas-Rachford algorithm is shown on a simplified resource allocation game, where we observe faster convergence with respect to forward-backward algorithms.

[1]  Francesca Parise,et al.  Mean field constrained charging policy for large populations of Plug-in Electric Vehicles , 2014, 53rd IEEE Conference on Decision and Control.

[2]  Jorge Barrera,et al.  Dynamic Incentives for Congestion Control , 2015, IEEE Transactions on Automatic Control.

[3]  Nikolai S. Kukushkin,et al.  Best response dynamics in finite games with additive aggregation , 2004, Games Econ. Behav..

[4]  Angelia Nedic,et al.  Distributed Algorithms for Aggregative Games on Graphs , 2016, Oper. Res..

[5]  Sergio Grammatico,et al.  Proximal Dynamics in Multiagent Network Games , 2018, IEEE Transactions on Control of Network Systems.

[6]  Munther A. Dahleh,et al.  Demand Response Using Linear Supply Function Bidding , 2015, IEEE Transactions on Smart Grid.

[7]  Farzad Salehisadaghiani,et al.  Distributed Nash Equilibrium Seeking via the Alternating Direction Method of Multipliers , 2016, ArXiv.

[8]  Francesca Parise,et al.  Decentralized Convergence to Nash Equilibria in Constrained Deterministic Mean Field Control , 2014, IEEE Transactions on Automatic Control.

[9]  Heinz H. Bauschke,et al.  Convex Analysis and Monotone Operator Theory in Hilbert Spaces , 2011, CMS Books in Mathematics.

[10]  Marc Teboulle,et al.  Lagrangian Duality and Related Multiplier Methods for Variational Inequality Problems , 1999, SIAM J. Optim..

[11]  Walid Saad,et al.  Game Theoretic Methods for the Smart Grid , 2012, ArXiv.

[12]  Uday V. Shanbhag,et al.  Distributed Computation of Equilibria in Monotone Nash Games via Iterative Regularization Techniques , 2012, SIAM J. Optim..

[13]  Francisco Facchinei,et al.  Generalized Nash Equilibrium Problems , 2010, Ann. Oper. Res..

[14]  Francesca Parise,et al.  Nash and Wardrop Equilibria in Aggregative Games With Coupling Constraints , 2017, IEEE Transactions on Automatic Control.

[15]  Ian A. Hiskens,et al.  Decentralized charging control for large populations of plug-in electric vehicles , 2010, 49th IEEE Conference on Decision and Control (CDC).

[16]  Ming Cao,et al.  Asynchronous proximal dynamics in multi-agent network games , 2018 .

[17]  Francesca Parise,et al.  Distributed computation of generalized Nash equilibria in quadratic aggregative games with affine coupling constraints , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[18]  Shu Liang,et al.  Distributed Nash equilibrium seeking for aggregative games with coupled constraints , 2016, Autom..

[19]  Sergio Grammatico,et al.  Projected-gradient algorithms for Generalized Equilibrium seeking in Aggregative Games arepreconditioned Forward-Backward methods , 2018, 2018 European Control Conference (ECC).

[20]  Sergio Grammatico,et al.  Semi-Decentralized Nash Equilibrium Seeking in Aggregative Games With Separable Coupling Constraints and Non-Differentiable Cost Functions , 2017, IEEE Control Systems Letters.

[21]  Sergio Grammatico.  Dynamic Control of Agents Playing Aggregative Games With Coupling Constraints , 2016, IEEE Transactions on Automatic Control.

[22]  Ian A. Hiskens,et al.  Efficient decentralized coordination of large-scale plug-in electric vehicle charging , 2016, Autom..

[23]  F. Facchinei,et al.  Finite-Dimensional Variational Inequalities and Complementarity Problems , 2003 .

[24]  Lacra Pavel,et al.  A distributed primal-dual algorithm for computation of generalized Nash equilibria via operator splitting methods , 2017, 2017 IEEE 56th Annual Conference on Decision and Control (CDC).

[25]  Sergio Grammatico,et al.  Exponentially convergent decentralized charging control for large populations of plug-in electric vehicles , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[26]  Convex Optimization in Signal Processing and Communications , 2010 .

[27]  M. K. Jensen.  Aggregative games and best-reply potentials , 2010 .

[28]  Lacra Pavel,et al.  Distributed Generalized Nash Equilibria Computation of Monotone Games via Double-Layer Preconditioned Proximal-Point Algorithms , 2019, IEEE Transactions on Control of Network Systems.

[29]  Sergio Grammatico,et al.  On convexity and monotonicity in generalized aggregative games , 2017 .