Learning generalized Nash equilibria in monotone games
A hybrid adaptive extremum seeking control approach
Suad Krilašević (TU Delft - Team Sergio Grammatico)
Sergio Grammatico (TU Delft - Team Bart De Schutter, TU Delft - Team Sergio Grammatico)
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Abstract
In this paper, we solve the problem of learning a generalized Nash equilibrium (GNE) in merely monotone games. First, we propose a novel continuous semi-decentralized solution algorithm without projections that uses first-order information to compute a GNE with a central coordinator. As the second main contribution, we design a gain adaptation scheme for the previous algorithm in order to alleviate the problem of improper scaling of the cost functions versus the constraints. Third, we propose a data-driven variant of the former algorithm, where each agent estimates their individual pseudogradient via zeroth-order information, namely, measurements of their individual cost function values. Finally, we apply our method to a perturbation amplitude optimization problem in oil extraction engineering.
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