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Hierarchical decision making problems, such as bilevel programs andStackelberg games, are attracting increasing interest in both the engineeringand machine learning communities. Yet, existing solution methods lack eitherconvergence guarantees or computational efficiency, due to the absence ofsmoothness and convexity. In this work, we bridge this gap by designing afirst-order hypergradient-based algorithm for single-leader multi-followerStackelberg games and mathematically establishing its convergence usingtechnical tools from nonsmooth analysis. To evaluate the hypergradient, namely,the gradient of the upper-level objective, we develop an online scheme thatsimultaneously computes the lower-level equilibrium and its Jacobian.Crucially, this scheme exploits and preserves the original hierarchical anddistributed structure of the problem, which renders it scalable andprivacy-preserving. We numerically verify the computational efficiency andscalability of our algorithm on a large-scale hierarchical demand-responsemodel.

BIG Hype: Best Intervention in Games via Distributed Hypergradient Descent