Gradient Methods for Solving Stackelberg Games

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, inter-

vening 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 gener-

ally 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.