840 research outputs found
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
Accelerated /Push-Pull Methods for Distributed Optimization over Time-Varying Directed Networks
This paper investigates a novel approach for solving the distributed
optimization problem in which multiple agents collaborate to find the global
decision that minimizes the sum of their individual cost functions. First, the
/Push-Pull gradient-based algorithm is considered, which employs row- and
column-stochastic weights simultaneously to track the optimal decision and the
gradient of the global cost function, ensuring consensus on the optimal
decision. Building on this algorithm, we then develop a general algorithm that
incorporates acceleration techniques, such as heavy-ball momentum and Nesterov
momentum, as well as their combination with non-identical momentum parameters.
Previous literature has established the effectiveness of acceleration methods
for various gradient-based distributed algorithms and demonstrated linear
convergence for static directed communication networks. In contrast, we focus
on time-varying directed communication networks and establish linear
convergence of the methods to the optimal solution, when the agents' cost
functions are smooth and strongly convex. Additionally, we provide explicit
bounds for the step-size value and momentum parameters, based on the properties
of the cost functions, the mixing matrices, and the graph connectivity
structures. Our numerical results illustrate the benefits of the proposed
acceleration techniques on the /Push-Pull algorithm
Distributed Stochastic Optimization with Gradient Tracking over Time-Varying Directed Networks
We study a distributed method called SAB-TV, which employs gradient tracking
to collaboratively minimize the sum of smooth and strongly-convex local cost
functions for networked agents communicating over a time-varying directed
graph. Each agent, assumed to have access to a stochastic first-order oracle
for obtaining an unbiased estimate of the gradient of its local cost function,
maintains an auxiliary variable to asymptotically track the stochastic gradient
of the global cost. The optimal decision and gradient tracking are updated over
time through limited information exchange with local neighbors using row- and
column-stochastic weights, guaranteeing both consensus and optimality. With a
sufficiently small constant step-size, we demonstrate that, in expectation,
SAB-TV converges linearly to a neighborhood of the optimal solution. Numerical
simulations illustrate the effectiveness of the proposed algorithm
Quantum-based Distributed Algorithms for Edge Node Placement and Workload Allocation
Edge computing is a promising technology that offers a superior user
experience and enables various innovative Internet of Things applications. In
this paper, we present a mixed-integer linear programming (MILP) model for
optimal edge server placement and workload allocation, which is known to be
NP-hard. To this end, we explore the possibility of addressing this
computationally challenging problem using quantum computing. However, existing
quantum solvers are limited to solving unconstrained binary programming
problems. To overcome this obstacle, we propose a hybrid quantum-classical
solution that decomposes the original problem into a quadratic unconstrained
binary optimization (QUBO) problem and a linear program (LP) subproblem. The
QUBO problem can be solved by a quantum solver, while the LP subproblem can be
solved using traditional LP solvers. Our numerical experiments demonstrate the
practicality of leveraging quantum supremacy to solve complex optimization
problems in edge computing
Optimal Workload Allocation for Distributed Edge Clouds With Renewable Energy and Battery Storage
This paper studies an optimal workload allocation problem for a network of
renewable energy-powered edge clouds that serve users located across various
geographical areas. Specifically, each edge cloud is furnished with both an
on-site renewable energy generation unit and a battery storage unit. Due to the
discrepancy in electricity pricing and the diverse temporal-spatial
characteristics of renewable energy generation, how to optimally allocate
workload to different edge clouds to minimize the total operating cost while
maximizing renewable energy utilization is a crucial and challenging problem.
To this end, we introduce and formulate an optimization-based framework
designed for Edge Service Providers (ESPs) with the overarching goal of
simultaneously reducing energy costs and environmental impacts through the
integration of renewable energy sources and battery storage systems, all while
maintaining essential quality-of-service standards. Numerical results
demonstrate the effectiveness of the proposed model and solution in maintaining
service quality as well as reducing operational costs and emissions.
Furthermore, the impacts of renewable energy generation and battery storage on
optimal system operations are rigorously analyzed
CrowdCache: A Decentralized Game-Theoretic Framework for Mobile Edge Content Sharing
Mobile edge computing (MEC) is a promising solution for enhancing the user
experience, minimizing content delivery expenses, and reducing backhaul
traffic. In this paper, we propose a novel privacy-preserving decentralized
game-theoretic framework for resource crowdsourcing in MEC. Our framework
models the interactions between a content provider (CP) and multiple mobile
edge device users (MEDs) as a non-cooperative game, in which MEDs offer idle
storage resources for content caching in exchange for rewards. We introduce
efficient decentralized gradient play algorithms for Nash equilibrium (NE)
computation by exchanging local information among neighboring MEDs only, thus
preventing attackers from learning users' private information. The key
challenge in designing such algorithms is that communication among MEDs is not
fixed and is facilitated by a sequence of undirected time-varying graphs. Our
approach achieves linear convergence to the NE without imposing any assumptions
on the values of parameters in the local objective functions, such as requiring
strong monotonicity to be stronger than its dependence on other MEDs' actions,
which is commonly required in existing literature when the graph is directed
time-varying. Extensive simulations demonstrate the effectiveness of our
approach in achieving efficient resource outsourcing decisions while preserving
the privacy of the edge devices
Nonlinear Control of Flexible Two-Dimensional Overhead Cranes
Considering gantry cable as an elastic string having a distributed mass, we constitute a dynamic model for coupled flexural overhead cranes by using the extended Hamilton principle. Two kinds of nonlinear controllers are proposed based on the Lyapunov stability and its improved version entitled barrier Lyapunov candidate to maintain payload motion in a certain defined range. With such a continuously distributed model, the finite difference method is utilized to numerically simulate the control system. The results show that the controllers work well and the crane system is stabilized
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
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