Go to ICLR 2025 Conference homepageRiemannian Manifold Learning for Stackelberg Games with Neural Flow Representations
We present a novel framework for online learning in Stackelberg general-sum games, where two agents, the leader and follower, engage in sequential turn-based interactions. At the core of this approach is a learned diffeomorphism that maps the joint action space to a smooth Riemannian manifold, referred to as the $\textit{Stackelberg manifold}$. This mapping, facilitated by neural normalizing flows, ensures the formation of tractable isoplanar subspaces, enabling efficient techniques for online learning. By assuming linearity between the agents' reward functions on the $\textit{Stackelberg manifold}$, our construct allows the application of standard bandit algorithms. We then provide a rigorous theoretical basis for regret minimization on convex manifolds and establish finite-time bounds on simple regret for learning Stackelberg equilibria. This integration of manifold learning into game theory uncovers a previously unrecognized potential for neural normalizing flows as an effective tool for multi-agent learning. We present empirical results demonstrating the effectiveness of our approach compared to standard baselines, with applications spanning domains such as cybersecurity and economic supply chain optimization.