424 research outputs found
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.Comment: arXiv admin note: text overlap with arXiv:1803.1044
Nash and Wardrop equilibria in aggregative games with coupling constraints
We consider the framework of aggregative games, in which the cost function of
each agent depends on his own strategy and on the average population strategy.
As first contribution, we investigate the relations between the concepts of
Nash and Wardrop equilibrium. By exploiting a characterization of the two
equilibria as solutions of variational inequalities, we bound their distance
with a decreasing function of the population size. As second contribution, we
propose two decentralized algorithms that converge to such equilibria and are
capable of coping with constraints coupling the strategies of different agents.
Finally, we study the applications of charging of electric vehicles and of
route choice on a road network.Comment: IEEE Trans. on Automatic Control (Accepted without changes). The
first three authors contributed equall
Continuous-time integral dynamics for Aggregative Game equilibrium seeking
In this paper, we consider continuous-time semi-decentralized dynamics for
the equilibrium computation in a class of aggregative games. Specifically, we
propose a scheme where decentralized projected-gradient dynamics are driven by
an integral control law. To prove global exponential convergence of the
proposed dynamics to an aggregative equilibrium, we adopt a quadratic Lyapunov
function argument. We derive a sufficient condition for global convergence that
we position within the recent literature on aggregative games, and in
particular we show that it improves on established results
Probably Approximately Correct Nash Equilibrium Learning
We consider a multi-agent noncooperative game with agents' objective
functions being affected by uncertainty. Following a data driven paradigm, we
represent uncertainty by means of scenarios and seek a robust Nash equilibrium
solution. We treat the Nash equilibrium computation problem within the realm of
probably approximately correct (PAC) learning. Building upon recent
developments in scenario-based optimization, we accompany the computed Nash
equilibrium with a priori and a posteriori probabilistic robustness
certificates, providing confidence that the computed equilibrium remains
unaffected (in probabilistic terms) when a new uncertainty realization is
encountered. For a wide class of games, we also show that the computation of
the so called compression set - a key concept in scenario-based optimization -
can be directly obtained as a byproduct of the proposed solution methodology.
Finally, we illustrate how to overcome differentiability issues, arising due to
the introduction of scenarios, and compute a Nash equilibrium solution in a
decentralized manner. We demonstrate the efficacy of the proposed approach on
an electric vehicle charging control problem.Comment: Preprint submitted to IEEE Transactions on Automatic Contro
Single-timescale distributed GNE seeking for aggregative games over networks via forward-backward operator splitting
We consider aggregative games with affine coupling constraints, where agents
have partial information on the aggregate value and can only communicate with
neighbouring agents. We propose a single-layer distributed algorithm that
reaches a variational generalized Nash equilibrium, under constant step sizes.
The algorithm works on a single timescale, i.e., does not require multiple
communication rounds between agents before updating their action. The
convergence proof leverages an invariance property of the aggregate estimates
and relies on a forward-backward splitting for two preconditioned operators and
their restricted (strong) monotonicity properties on the consensus subspace.Comment: 8 pages, 8 figures, submitted to TA
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