Abstract
In this paper, we consider the problem of learning a generalized Nash equilibrium (GNE) in strongly monotone games. First, we propose semi-decentralized and distributed continuous-time solution algorithms that use regular projections and first-order information to compute a GNE with and without a central coordinator. As the second main contribution, we design a data-driven variant of the former semi-decentralized algorithm where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values, as typical of extremum seeking control. Third, we generalize our setup and results for multi-agent systems with nonlinear dynamics. Finally, we apply our methods to connectivity control in robotic sensor networks and almost-decentralized wind farm optimization.
Highlights
Multi-agent optimization problems and games with selfinterested decision-makers or agents appear in many engineering applications, such as demand-side management in smart grids (Mohsenian-Rad, Wong, Jatskevich, Schober, & Leon-Garcia, 2010; Saad, Han, Poor, & Basar, 2012), charging/discharging coordination for plug-in electric vehicles (Ma, Callaway, & Hiskens, 2011), thermostatically controlled loads (Li, Zhang, Lian, & Kalsi, 2015a, 2015b) and robotic formation control (Lin, Qu, & Simaan, 2014)
We prove that, with a time-scale separation, our algorithm learns a generalized Nash equilibrium (GNE) in monotone games with nonlinear dynamical agents (Section 4)
Where ε > 0 is a time scale separation constant with the objective of reaching a neighborhood of a variational GNE (v-GNE), we propose the same control law as in (24), with the distinction that θis estimated by a parameter estimation scheme (19) – (23), where we collect the measurements of the output yi in (1b) instead of Ji(ui, u−i) directly
Summary
Multi-agent optimization problems and games with selfinterested decision-makers or agents appear in many engineering applications, such as demand-side management in smart grids (Mohsenian-Rad, Wong, Jatskevich, Schober, & Leon-Garcia, 2010; Saad, Han, Poor, & Basar, 2012), charging/discharging coordination for plug-in electric vehicles (Ma, Callaway, & Hiskens, 2011), thermostatically controlled loads (Li, Zhang, Lian, & Kalsi, 2015a, 2015b) and robotic formation control (Lin, Qu, & Simaan, 2014). In most of the literature and all of previously mentioned work, GNE seeking algorithms are designed in discrete-time and for static agents, i.e., where the agent costs instantaneously reflect the chosen decisions. In Bianchi and Grammatico (2021), the authors extend the convergence results to GNEPs for the first time via a preconditioning approach as in Yi and Pavel (2019) and the use of non-Lipschitz continuous projections onto tangents cones. In payoff-based algorithms, each agent can only measure the value of their cost function, but does not know its analytic form Many of such algorithms are designed for NEPs with static agents with finite action spaces, e.g. We design novel continuous-time GNE seeking algorithms (Section 3.1, Section 3.2), which use projections onto fixed convex sets instead of projections onto state-dependent tangent cones as in Bianchi and Grammatico (2021). For a set M := {1, . . . , M} and a vector-valued function φ := col ((φi(·))i∈M) : R → RM , we denote
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