3,529 research outputs found
Towards time-varying proximal dynamics in Multi-Agent Network Games
Distributed decision making in multi-agent networks has recently attracted
significant research attention thanks to its wide applicability, e.g. in the
management and optimization of computer networks, power systems, robotic teams,
sensor networks and consumer markets. Distributed decision-making problems can
be modeled as inter-dependent optimization problems, i.e., multi-agent
game-equilibrium seeking problems, where noncooperative agents seek an
equilibrium by communicating over a network. To achieve a network equilibrium,
the agents may decide to update their decision variables via proximal dynamics,
driven by the decision variables of the neighboring agents. In this paper, we
provide an operator-theoretic characterization of convergence with a
time-invariant communication network. For the time-varying case, we consider
adjacency matrices that may switch subject to a dwell time. We illustrate our
investigations using a distributed robotic exploration example.Comment: 6 pages, 3 figure
Linear convergence in time-varying generalized Nash equilibrium problems
We study generalized games with full row rank equality constraints and we
provide a strikingly simple proof of strong monotonicity of the associated KKT
operator. This allows us to show linear convergence to a variational
equilibrium of the resulting primal-dual pseudo-gradient dynamics. Then, we
propose a fully-distributed algorithm with linear convergence guarantee for
aggregative games under partial-decision information. Based on these results,
we establish stability properties for online GNE seeking in games with
time-varying cost functions and constraints. Finally, we illustrate our
findings numerically on an economic dispatch problem for peer-to-peer energy
markets
Geometric Convergence of Distributed Heavy-Ball Nash Equilibrium Algorithm over Time-Varying Digraphs with Unconstrained Actions
We propose a new distributed algorithm that combines heavy-ball momentum and
a consensus-based gradient method to find a Nash equilibrium (NE) in a class of
non-cooperative convex games with unconstrained action sets. In this approach,
each agent in the game has access to its own smooth local cost function and can
exchange information with its neighbors over a communication network. The
proposed method is designed to work on a general sequence of time-varying
directed graphs and allows for non-identical step-sizes and momentum
parameters. Our work is the first to incorporate heavy-ball momentum in the
context of non-cooperative games, and we provide a rigorous proof of its
geometric convergence to the NE under the common assumptions of strong
convexity and Lipschitz continuity of the agents' cost functions. Moreover, we
establish explicit bounds for the step-size values and momentum parameters
based on the characteristics of the cost functions, mixing matrices, and graph
connectivity structures. To showcase the efficacy of our proposed method, we
perform numerical simulations on a Nash-Cournot game to demonstrate its
accelerated convergence compared to existing methods
Nash equilibrium seeking over digraphs with row-stochastic matrices and network-independent step-sizes
In this paper, we address the challenge of Nash equilibrium (NE) seeking in
non-cooperative convex games with partial-decision information. We propose a
distributed algorithm, where each agent refines its strategy through
projected-gradient steps and an averaging procedure. Each agent uses estimates
of competitors' actions obtained solely from local neighbor interactions, in a
directed communication network. Unlike previous approaches that rely on
(strong) monotonicity assumptions, this work establishes the convergence
towards a NE under a diagonal dominance property of the pseudo-gradient
mapping, that can be checked locally by the agents. Further, this condition is
physically interpretable and of relevance for many applications, as it suggests
that an agent's objective function is primarily influenced by its individual
strategic decisions, rather than by the actions of its competitors. In virtue
of a novel block-infinity norm convergence argument, we provide explicit bounds
for constant step-size that are independent of the communication structure, and
can be computed in a totally decentralized way. Numerical simulations on an
optical network's power control problem validate the algorithm's effectiveness
Distributed dynamics for aggregative games:Robustness and privacy guarantees
This paper considers the problem of Nash equilibrium (NE) seeking in aggregative games, where the cost function of each player depends on an aggregate of all players' actions. We present a distributed continuous-time algorithm such that the actions of the players converge to NE by communicating to each other through a connected network. As agents may deviate from their optimal strategies dictated by the NE seeking protocol, we investigate robustness of the proposed algorithm against time-varying disturbances. In particular, we provide rigorous robustness guarantees by proving input-to-state stability (ISS) and (Formula presented.) -stability properties of the NE seeking dynamics. A major concern in communicative schemes among strategic agents is that their private information may be revealed to other agents or to a curious third party who can eavesdrop the communications. Motivated by this, we investigate privacy properties of the algorithm and identify to what extent privacy is preserved when all communicated variables are compromised. Finally, we demonstrate practical applications of our theoretical findings on two case studies; namely, on an energy consumption game and a coordinated charging of electric vehicles
Distributed equilibrium seeking in aggregative games: linear convergence under singular perturbations lens
We present a fully-distributed algorithm for Nash equilibrium seeking in aggregative games over networks. The proposed scheme endows each agent with a gradient-based scheme equipped with a tracking mechanism to locally reconstruct the aggregative variable, which is not available to the agents. We show that our method falls into the framework of singularly perturbed systems, as it involves the interconnection between a fast subsystem – the global information reconstruction dynamics – with a slow one concerning the optimization of the local strategies. This perspective plays a key role in analyzing the scheme with a constant stepsize, and in proving its linear convergence to the Nash equilibrium in strongly monotone games with local constraints. By exploiting the flexibility of our aggregative variable definition (not necessarily the arithmetic average of the agents’ strategy), we show the efficacy of our algorithm on a realistic voltage support case study for the smart grid
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