Deep Forward-Backward SDEs for Min-max Control

Wang, Ziyi; Lee, Keuntaek; Pereira, Marcus A.; Theodorou, Evangelos A.

doi:10.48550/arxiv.1906.04771

Cited by 1 publication

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“…Of these, the algorithms based on FBSDEs are the most general in the sense that they neither require assumptions to simplify the HJB Partial Differential Equation (PDE) nor do they require Taylor's approximations of the dynamics and value function [8]. More recently, with the introduction of deep learning methods to solve high-dimensional parabolic PDEs [11], deep learning based solutions of the HJB PDE using so called Deep FBSDE controllers have emerged [12,13,14]. These algorithms leverage importance sampling using Girsanov's theorem of change of measure [15,Chapter 5] for FBSDEs within deep learning models for sufficient exploration of the solution space.…”

Section: Introductionmentioning

confidence: 99%

Safe Optimal Control Using Stochastic Barrier Functions and Deep Forward-Backward SDEs

Pereira¹,

Wang²,

Theodorou³

2020

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This paper introduces a new formulation for stochastic optimal control and stochastic dynamic optimization that ensures safety with respect to state and control constraints. The proposed methodology brings together concepts such as Forward-Backward Stochastic Differential Equations, Stochastic Barrier Functions, Differentiable Convex Optimization and Deep Learning. Using the aforementioned concepts, a Neural Network architecture is designed for safe trajectory optimization in which learning can be performed in an end-to-end fashion. Simulations are performed on three systems to show the efficacy of the proposed methodology.

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