Title: A Diffusion Homotopy Algorithm for Nash Equilibria

Date: Wednesday, May 20th, 2026

Time: 1pm - 2pm ET

Location: MRDC 3515 (https://teams.microsoft.com/meet/225122560859133?p=BordRn7dHFBulSff2T)

Seth Golembeski

Robotics Ph.D. Student

Guggenheim School of Aerospace Engineering

Georgia Institute of Technology

Committee:

Dr Anirban Mazumdar (Advisor): School of Mechanical Engineering

Dr Shreyas Kousik: School of Mechanical Engineering

Dr Jonathan Rogers: School of Aerospace Engineering

Dr Kyriakos Vamvoudakis: School of Aerospace Engineering

Dr Scott Nivison: Air Force Research Lab

Abstract:

Many robotics problems involve multiple interacting agents, often with conflicting objectives. Robust control addresses problems involving systems that reject external disturbances, such as wind, uneven terrain, or mechanical vibrations. Adversarial settings consider agents that are in opposition, such as combat, markets, or navigating a crowd.

These seemingly disparate problems are connected by Nash equilibria: the combination of all agents’ actions from which no agent can unilaterally deviate to improve its reward. These solutions are not always globally optimal, but each agent can guarantee that it is locally optimal with respect to unilateral deviations by others. Computing Nash equilibria and optimal control solutions are exceptionally difficult. Most existing methods assume monotonicity and continuity to guarantee convergence – conditions rarely met in robotics systems, which are often complex, discontinuous, and operate in high-dimensional spaces.

Model-Based Diffusion alleviates the above problems, but is restricted to single-agent, non-game-theoretic problems, lacks formal convergence analysis, and requires large numbers of samples. To this end, this work proposes 1) MBD efficiency improvements via adaptive importance sampling 2) a decentralized, latency-robust, multi-agent diffusion algorithm for cooperative (potential) games and 3) a fully game-theoretic version of MBD for adversarial games and robust control, with convergence analysis.