BIG Hype: Best Intervention in Games via Distributed Hypergradient Descent

TL;DR

This paper introduces a scalable, privacy-preserving hypergradient-based algorithm for hierarchical decision problems like Stackelberg games, with proven convergence and demonstrated efficiency on large-scale models.

Contribution

It develops a novel first-order hypergradient method with convergence guarantees for nonsmooth hierarchical problems, preserving structure for scalability and privacy.

Findings

Algorithm converges for nonsmooth hierarchical problems.

Efficient and scalable on large demand-response models.

Preserves hierarchical and distributed problem structure.

Abstract

Hierarchical decision making problems, such as bilevel programs and Stackelberg games, are attracting increasing interest in both the engineering and machine learning communities. Yet, existing solution methods lack either convergence guarantees or computational efficiency, due to the absence of smoothness and convexity. In this work, we bridge this gap by designing a first-order hypergradient-based algorithm for Stackelberg games and mathematically establishing its convergence using tools from nonsmooth analysis. To evaluate the \textit{hypergradient}, namely, the gradient of the upper-level objective, we develop an online scheme that simultaneously computes the lower-level equilibrium and its Jacobian. Crucially, this scheme exploits and preserves the original hierarchical and distributed structure of the problem, which renders it scalable and privacy-preserving. We numerically verify the computational efficiency and scalability of our algorithm on a large-scale hierarchical demand-response model.