# Riemannian Manifold Learning for Stackelberg Games with Neural Flow Representations

arXiv: https://arxiv.org/abs/2502.05498 · HTML: https://mlsanity.com/paper/2502.05498/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 47 references that are in the map.
- First posted on arXiv 8 Feb 2025.

## Builds on (most cited first, 19 of 19)

- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Density estimation using Real NVP](https://mlsanity.com/paper/1605.08803/) (2016)
- [Normalizing Flows for Probabilistic Modeling and Inference](https://mlsanity.com/paper/1912.02762/) (2019)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications](https://mlsanity.com/paper/1705.06270/) (2017)
- [Flows for simultaneous manifold learning and density estimation](https://mlsanity.com/paper/2003.13913/) (2020)
- [Normalizing Flows on Tori and Spheres](https://mlsanity.com/paper/2002.02428/) (2020)
- [Normalizing Flows on Riemannian Manifolds](https://mlsanity.com/paper/1611.02304/) (2016)
- [Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond](https://mlsanity.com/paper/2110.00455/) (2021)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Enhanced Bilevel Optimization via Bregman Distance](https://mlsanity.com/paper/2107.12301/) (2021)
- [Design of Experiments for Stochastic Contextual Linear Bandits](https://mlsanity.com/paper/2107.09912/) (2021)
- [No-Regret Learning in Games with Noisy Feedback: Faster Rates and Adaptivity via Learning Rate Separation](https://mlsanity.com/paper/2206.06015/) (2022)
- [A Gradient Method for Multilevel Optimization](https://mlsanity.com/paper/2105.13954/) (2021)
- [Optimal Hessian/Jacobian-Free Nonconvex-PL Bilevel Optimization](https://mlsanity.com/paper/2407.17823/) (2024)
- [MAGICS: Adversarial RL with Minimax Actors Guided by Implicit Critic Stackelberg for Convergent Neural Synthesis of Robot Safety](https://mlsanity.com/paper/2409.13867/) (2024)
- [Feature and Parameter Selection in Stochastic Linear Bandits](https://mlsanity.com/paper/2106.05378/) (2021)
- [Gradient Methods for Solving Stackelberg Games](https://mlsanity.com/paper/1908.06901/) (2019)
- [No-Regret Learning for Stackelberg Equilibrium Computation in Newsvendor Pricing Games](https://mlsanity.com/paper/2404.00203/) (2024)

## Abstract (arXiv)

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 spherical Riemannian manifold, referred to as the Stackelberg manifold. This mapping, facilitated by neural normalizing flows, ensures the formation of tractable isoplanar subspaces, enabling efficient techniques for online learning. Leveraging the linearity of the agents' reward functions on the Stackelberg manifold, our construct allows the application of linear bandit algorithms. We then provide a rigorous theoretical basis for regret minimization on the learned manifold and establish bounds on the simple regret for learning Stackelberg equilibrium. 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.