Low-Complexity Algorithm for Stackelberg Prediction Games with Global Optimality

TL;DR

This paper introduces a simple, efficient ADMM-based algorithm for solving Stackelberg prediction games in the least-squares setting, achieving global optimality with reduced computational complexity.

Contribution

It develops a novel ADMM solver for the spherically constrained least-squares reformulation of SPGs, enabling scalable and fast solutions with closed-form updates.

Findings

The proposed ADMM method attains competitive solution quality.

It significantly improves computational efficiency over existing solvers.

The method performs well in sparse and high-dimensional scenarios.

Abstract

Stackelberg prediction games (SPGs) model strategic data manipulation in adversarial learning via a leader--follower interaction between a learner and a self-interested data provider, leading to challenging bilevel optimization problems. Focusing on the least-squares setting (SPG-LS), recent work shows that the bilevel program admits an equivalent spherically constrained least-squares (SCLS) reformulation, which avoids costly conic programming and enables scalable algorithms. In this paper, we develop a simple and efficient alternating direction method of multiplier (ADMM) based solver for the SCLS problem. By introducing a consensus splitting that separates the quadratic objective from the spherical constraint, we obtain an augmented Lagrangian formulation with closed-form updates: the primal quadratic step reduces to solving a fixed shifted linear system, the constraint step is a projection onto the unit sphere, and the dual step is a lightweight scaled ascent. The resulting method has low per-iteration complexity and allows pre-factorization of the constant system matrix for substantial speedups. Experiments demonstrate that the proposed ADMM approach achieves competitive solution quality with significantly improved computational efficiency compared with existing global solvers for SCLS, particularly in sparse and high-dimensional regimes.