19 research outputs found
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
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
Projected-gradient algorithms for generalized equilibrium seeking in Aggregative Games are preconditioned Forward-Backward methods
We show that projected-gradient methods for the distributed computation of
generalized Nash equilibria in aggregative games are preconditioned
forward-backward splitting methods applied to the KKT operator of the game.
Specifically, we adopt the preconditioned forward-backward design, recently
conceived by Yi and Pavel in the manuscript "A distributed primal-dual
algorithm for computation of generalized Nash equilibria via operator splitting
methods" for generalized Nash equilibrium seeking in aggregative games.
Consequently, we notice that two projected-gradient methods recently proposed
in the literature are preconditioned forward-backward methods. More generally,
we provide a unifying operator-theoretic ground to design projected-gradient
methods for generalized equilibrium seeking in aggregative games
Distributed Aggregative Optimization over Multi-Agent Networks
This paper proposes a new framework for distributed optimization, called
distributed aggregative optimization, which allows local objective functions to
be dependent not only on their own decision variables, but also on the average
of summable functions of decision variables of all other agents. To handle this
problem, a distributed algorithm, called distributed gradient tracking (DGT),
is proposed and analyzed, where the global objective function is strongly
convex, and the communication graph is balanced and strongly connected. It is
shown that the algorithm can converge to the optimal variable at a linear rate.
A numerical example is provided to corroborate the theoretical result
Distributed strategy-updating rules for aggregative games of multi-integrator systems with coupled constraints
In this paper, we explore aggregative games over networks of multi-integrator
agents with coupled constraints. To reach the general Nash equilibrium of an
aggregative game, a distributed strategy-updating rule is proposed by a
combination of the coordination of Lagrange multipliers and the estimation of
the aggregator. Each player has only access to partial-decision information and
communicates with his neighbors in a weight-balanced digraph which
characterizes players' preferences as to the values of information received
from neighbors. We first consider networks of double-integrator agents and then
focus on multi-integrator agents. The effectiveness of the proposed
strategy-updating rules is demonstrated by analyzing the convergence of
corresponding dynamical systems via the Lyapunov stability theory, singular
perturbation theory and passive theory. Numerical examples are given to
illustrate our results.Comment: 9 pages, 4 figure
Distributed Online Convex Optimization with an Aggregative Variable
This paper investigates distributed online convex optimization in the
presence of an aggregative variable without any global/central coordinators
over a multi-agent network, where each individual agent is only able to access
partial information of time-varying global loss functions, thus requiring local
information exchanges between neighboring agents. Motivated by many
applications in reality, the considered local loss functions depend not only on
their own decision variables, but also on an aggregative variable, such as the
average of all decision variables. To handle this problem, an Online
Distributed Gradient Tracking algorithm (O-DGT) is proposed with exact gradient
information and it is shown that the dynamic regret is upper bounded by three
terms: a sublinear term, a path variation term, and a gradient variation term.
Meanwhile, the O-DGT algorithm is also analyzed with stochastic/noisy
gradients, showing that the expected dynamic regret has the same upper bound as
the exact gradient case. To our best knowledge, this paper is the first to
study online convex optimization in the presence of an aggregative variable,
which enjoys new characteristics in comparison with the conventional scenario
without the aggregative variable. Finally, a numerical experiment is provided
to corroborate the obtained theoretical results
Distributed Generalized Nash Equilibrium Seeking for Energy Sharing Games
With the proliferation of distributed generators and energy storage systems,
traditional passive consumers in power systems have been gradually evolving
into the so-called "prosumers", i.e., proactive consumers, which can both
produce and consume power. To encourage energy exchange among prosumers, energy
sharing is increasingly adopted, which is usually formulated as a generalized
Nash game (GNG). In this paper, a distributed approach is proposed to seek the
Generalized Nash equilibrium (GNE) of the energy sharing game. To this end, we
convert the GNG into an equivalent optimization problem. A
Krasnosel'ski{\v{i}}-Mann iteration type algorithm is thereby devised to solve
the problem and consequently find the GNE in a distributed manner. The
convergence of the proposed algorithm is proved rigorously based on the
nonexpansive operator theory. The performance of the algorithm is validated by
experiments with three prosumers, and the scalability is tested by simulations
using 123 prosumers