Resilient and Distributed Discrete Optimal Transport with Deceptive Adversary: A Game-Theoretic Approach

TL;DR

This paper introduces a game-theoretic framework for resilient optimal transport that accounts for malicious adversaries, providing a distributed algorithm to compute strategies resilient to stealthy attacks, with proven convergence and demonstrated effectiveness.

Contribution

It develops a novel game-theoretic model for resilient optimal transport under adversarial attacks and proposes a distributed algorithm with convergence guarantees.

Findings

The algorithm converges to a saddle-point equilibrium.

The framework effectively models strategic interactions between planner and attacker.

Case studies validate the resilience and effectiveness of the approach.

Abstract

Optimal transport (OT) is a framework that can be used to guide the optimal allocation of a limited amount of resources. The classical OT paradigm does not consider malicious attacks in its formulation and thus the designed transport plan lacks resiliency to an adversary. To address this concern, we establish an OT framework that explicitly accounts for the adversarial and stealthy manipulation of participating nodes in the network during the transport strategy design. Specifically, we propose a game-theoretic approach to capture the strategic interactions between the transport planner and the deceptive attacker. We analyze the properties of the established two-person zero-sum game thoroughly. We further develop a fully distributed algorithm to compute the optimal resilient transport strategies, and show the convergence of the algorithm to a saddle-point equilibrium. Finally, we demonstrate the effectiveness of the designed algorithm using case studies.