DeepAI AI Chat
Log In Sign Up

Global Convergence of Successive Approximations for Non-convex Stochastic Optimal Control Problems

by   Shaolin Ji, et al.
Shandong University

This paper focuses on finding approximate solutions to the stochastic optimal control problems where the state trajectory is subject to controlled stochastic differential equations permitting controls in the diffusion coefficients. An algorithm based on the method of successive approximations is described for finding a set of small measure, in which the control is varied finitely so as to reduce the value of the functional and, as the control domains are not necessarily convex, the second-order adjoint processes are introduced in each minimization step of the Hamiltonian. Under certain convexity conditions, we prove that the values of the cost functional descend to the global minimum as the number of iterations tends to infinity. In particular, a convergence rate for a class of linear-quadratic systems is available.


page 1

page 2

page 3

page 4


Optimal control for stochastic nonlinear Schrodinger equation on graph

We study the optimal control formulation for stochastic nonlinear Schrod...

On the numerical stability of discretised Optimal Control Problems

Optimal Control Problems consist on the optimisation of an objective fun...

Optimal Control via Combined Inference and Numerical Optimization

Derivative based optimization methods are efficient at solving optimal c...

Gradient Flows for Regularized Stochastic Control Problems

This work is motivated by a desire to extend the theoretical underpinnin...

Deep 2FBSDEs for Systems with Control Multiplicative Noise

We present a deep recurrent neural network architecture to solve a class...

Regularity and time discretization of extended mean field control problems: a McKean-Vlasov FBSDE approach

We analyze the solution regularity and discrete-time approximations of e...

A combination technique for optimal control problems constrained by random PDEs

We present a combination technique based on mixed differences of both sp...