arXiv subjects

Kiran Rokade

Publications and source records attributed to Kiran Rokade.

6 recordsLinked to original sources

arXiv2025

Asymmetric Network Games: $α$-Potential Function and Learning

In a network game, players interact over a network and the utility of each player depends on his own action and on an aggregate of his neighbours' actions. Many real world networks of interest are asymmetric and involve a large number of heterogeneous players. This paper analyzes static network games using the framework of $α$-potential games. Under mild assumptions on the action sets (compact intervals) and the utility functions (twice continuously differentiable) of the players, we derive an expression for an inexact potential function of the game, called the $α$-potential function. Using such a function, we show that modified versions of the sequential best-response algorithm and the simultaneous gradient play algorithm achieve convergence of players' actions to a $2α$-Nash equilibrium. For linear-quadratic network games, we show that $α$ depends on the maximum asymmetry in the network and is well-behaved for a wide range of networks of practical interest. Further, we derive bounds on the social welfare of the $α$-Nash equilibrium corresponding to the maximum of the $α$-potential function, under suitable assumptions. We numerically illustrate the convergence of the proposed algorithms and properties of the learned $2α$-Nash equilibria.

cs.GT↗

arXiv2024

Learning in Time-Varying Monotone Network Games with Dynamic Populations

In this paper, we present a framework for multi-agent learning in a nonstationary dynamic network environment. More specifically, we examine projected gradient play in smooth monotone repeated network games in which the agents' participation and connectivity vary over time. We model this changing system with a stochastic network which takes a new independent realization at each repetition. We show that the strategy profile learned by the agents through projected gradient dynamics over the sequence of network realizations converges to a Nash equilibrium of the game in which players minimize their expected cost, almost surely and in the mean-square sense. We then show that the learned strategy profile is an almost Nash equilibrium of the game played by the agents at each stage of the repeated game with high probability. Using these two results, we derive non-asymptotic bounds on the regret incurred by the agents.

cs.GT↗

arXiv2023

Gradient Dynamics in Linear Quadratic Network Games with Time-Varying Connectivity and Population Fluctuation

In this paper, we consider a learning problem among non-cooperative agents interacting in a time-varying system. Specifically, we focus on repeated linear quadratic network games, in which the network of interactions changes with time and agents may not be present at each iteration. To get tractability, we assume that at each iteration, the network of interactions is sampled from an underlying random network model and agents participate at random with a given probability. Under these assumptions, we consider a gradient-based learning algorithm and establish almost sure convergence of the agents' strategies to the Nash equilibrium of the game played over the expected network. Additionally, we prove, in the large population regime, that the learned strategy is an $ε$-Nash equilibrium for each stage game with high probability. We validate our results over an online market application.

cs.GT↗

arXiv2023

Distributed ADMM with linear updates over directed networks

We propose a distributed version of the Alternating Direction Method of Multipliers (ADMM) with linear updates for directed networks. We show that if the objective function of the minimization problem is smooth and strongly convex, our distributed ADMM algorithm achieves a geometric rate of convergence to the optimal point. Our algorithm exploits the robustness inherent to ADMM by not enforcing accurate consensus, thereby significantly improving the convergence rate. We illustrate this by numerical examples, where we compare the performance of our algorithm with that of state-of-the-art ADMM methods over directed graphs.

math.OC↗

arXiv2023

Distributed Estimation over Directed Graphs Resilient to Sensor Spoofing

This paper addresses the problem of distributed estimation of an unknown dynamic parameter by a multi-agent system over a directed communication network in the presence of an adversarial attack on the agents' sensors. The mode of attack of the adversaries is to corrupt the sensor measurements of some of the agents, while the communication and information processing capabilities of those agents remain unaffected. To ensure that all the agents, both normal as well as those under attack, are able to correctly estimate the parameter value, the Resilient Estimation through Weight Balancing (REWB) algorithm is introduced. The only condition required for the REWB algorithm to guarantee resilient estimation is that at any given point in time, less than half of the total number of agents are under attack. The paper discusses the development of the REWB algorithm using the concepts of weight balancing of directed graphs, and the consensus+innovations approach for linear estimation. Numerical simulations are presented to illustrate the performance of our algorithm over directed graphs under different conditions of adversarial attacks.

eess.SY↗

arXiv2021

Distributed computation of fast consensus weights using ADMM

We consider the problem of achieving average consensus among multiple agents, where the inter-agent communication network is depicted by a graph. We consider the discrete-time consensus protocol where each agent updates its value as a weighted average of its own value and those of its neighbours. Given a graph, it is known that there exists a set of 'optimal weights' such that the agents reach average consensus asymptotically with an optimal rate of convergence. However, existing methods require the knowledge of the entire graph to compute these optimal weights. We propose a method for each agent to compute its set of optimal weights locally, i.e., each agent only has to know who are its neighbours. The method is derived by solving a matrix norm minimization problem subject to linear constraints in a distributed manner using the Alternating Direction Method of Multipliers (ADMM). We illustrate our results using numerical examples and compare our method with an existing method called the Metropolis weights, which are also computed locally.

eess.SY↗