Dynamics at the Frontiers of Optimization, Sampling, and Games

Dynamical systems have played an important role in the analysis and design of algorithms. Ideas ranging from variational methods, differential and symplectic geometry, numerical analysis, and control theory have paved the way for establishing non-asymptotic convergence guarantees in optimization, sampling, and equilibrium computation in games. Yet, the distinct mathematical backbone of these tools often creates barriers to entry for researchers and practitioners in machine learning. This workshop aims to lower that barrier by highlighting the unifying role of dynamical systems across these domains. We will convene optimization, sampling, and game theory experts to foster cross-disciplinary dialogue and collaboration. Emphasis will be placed on emerging applications in machine learning, such as diffusion models, distributed and adversarial training, and agentic AI, where dynamical systems perspectives are increasingly central. Through a combination of talks, posters, and open discussions, we hope to catalyze new collaborations and broaden the accessibility of these foundational methods.