# Large-Scale Multi-Agent Deep FBSDEs

arXiv: https://arxiv.org/abs/2011.10890 · HTML: https://mlsanity.com/paper/2011.10890/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Nov 2020.

## Built on by (most cited first, 5 of 5)

- [Deep Momentum Multi-Marginal Schr"odinger Bridge](https://mlsanity.com/paper/2303.01751/) (2023)
- [Recent Developments in Machine Learning Methods for Stochastic Control and Games](https://mlsanity.com/paper/2303.10257/) (2023)
- [Decentralized Safe Multi-agent Stochastic Optimal Control using Deep FBSDEs and ADMM](https://mlsanity.com/paper/2202.10658/) (2022)
- [Deep Graphic FBSDEs for Opinion Dynamics Stochastic Control](https://mlsanity.com/paper/2204.02506/) (2022)
- [DockGame: Cooperative Games for Multimeric Rigid Protein Docking](https://mlsanity.com/paper/2310.06177/) (2023)

## Abstract (arXiv)

In this paper we present a scalable deep learning framework for finding Markovian Nash Equilibria in multi-agent stochastic games using fictitious play. The motivation is inspired by theoretical analysis of Forward Backward Stochastic Differential Equations (FBSDE) and their implementation in a deep learning setting, which is the source of our algorithm's sample efficiency improvement. By taking advantage of the permutation-invariant property of agents in symmetric games, the scalability and performance is further enhanced significantly. We showcase superior performance of our framework over the state-of-the-art deep fictitious play algorithm on an inter-bank lending/borrowing problem in terms of multiple metrics. More importantly, our approach scales up to 3000 agents in simulation, a scale which, to the best of our knowledge, represents a new state-of-the-art. We also demonstrate the applicability of our framework in robotics on a belief space autonomous racing problem.