Gradient Methods for Solving Stackelberg Games

TL;DR

This paper explores gradient-based algorithms for solving high-dimensional Stackelberg Games in adversarial machine learning, analyzing their scalability and applicability through theoretical discussion and an adversarial prediction case study.

Contribution

It introduces and compares two gradient methods for solving complex Stackelberg Games, addressing their scalability and practical use in adversarial ML scenarios.

Findings

Both methods are scalable in time and space.

Each method is suitable for different problem settings.

Illustrated effectiveness in an adversarial prediction task.

Abstract

Stackelberg Games are gaining importance in the last years due to the raise of Adversarial Machine Learning (AML). Within this context, a new paradigm must be faced: in classical game theory, intervening agents were humans whose decisions are generally discrete and low dimensional. In AML, decisions are made by algorithms and are usually continuous and high dimensional, e.g. choosing the weights of a neural network. As closed form solutions for Stackelberg games generally do not exist, it is mandatory to have efficient algorithms to search for numerical solutions. We study two different procedures for solving this type of games using gradient methods. We study time and space scalability of both approaches and discuss in which situation it is more appropriate to use each of them. Finally, we illustrate their use in an adversarial prediction problem.