Accelerated ABAB/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 $AB$/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 $AB$/Push-Pull algorithm

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

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

Distributed Nash Equilibrium Seeking over Time-Varying Directed Communication Networks

We study distributed algorithms for finding a Nash equilibrium (NE) in a class of non-cooperative convex games under partial information. Specifically, each agent has access only to its own smooth local cost function and can receive information from its neighbors in a time-varying directed communication network. To this end, we propose a distributed gradient play algorithm to compute a NE by utilizing local information exchange among the players. In this algorithm, every agent performs a gradient step to minimize its own cost function while sharing and retrieving information locally among its neighbors. The existing methods impose strong assumptions such as balancedness of the mixing matrices and global knowledge of the network communication structure, including Perron-Frobenius eigenvector of the adjacency matrix and other graph connectivity constants. In contrast, our approach relies only on a reasonable and widely-used assumption of row-stochasticity of the mixing matrices. We analyze the algorithm for time-varying directed graphs and prove its convergence to the NE, when the agents' cost functions are strongly convex and have Lipschitz continuous gradients. Numerical simulations are performed for a Nash-Cournot game to illustrate the efficacy of the proposed algorithm

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

Microsimulation of impacts of tax and transfer in Viet Nam: Feasibility study

This paper assesses the feasibility of simulating the distributional impacts produced by various tax and transfer instruments in Viet Nam. Viet Nam's system of tax and transfer policies underwent frequent changes, in terms of diversity and adjustment scope. The most important source of data is the Viet Nam Household Living Standards Survey. Investigation of the survey data shows the wide-ranging feasibility of simulating tax and benefit instruments, though more details are available for transfer instruments. The microsimulation should thus focus more on the transfer instruments, which invites interests from a range of government agencies, international organizations, and non-governmental organizations