Sparse optimal stochastic control

Mean-field sparse optimal control.

We introduce the rigorous limit process connecting finite dimensional sparse optimal control problems with ODE constraints, modelling parsimonious interventions on the dynamics of a moving population divided into leaders and followers, to an infinite dimensional optimal control problem with a constraint given by a system of ODE for the leaders coupled with a PDE of Vlasov-type, governing the dy...

Stochastic optimal control theory

Control theory is a mathematical description of how to act optimally to gain future rewards. In this paper I give an introduction to deterministic and stochastic control theory; partial observability, learning and the combined problem of inference and control. Subsequently, I discuss a class of non-linear stochastic control problems that can be efficiently solved using a path integral. In this ...

Infinite Horizon Sparse Optimal Control

A class of infinite horizon optimal control problems involving Lp-type cost functionals with 0 < p ≤ 1 is discussed. The existence of optimal controls is studied for both the convex case with p = 1 and the nonconvex case with 0 < p < 1, and the sparsity structure of the optimal controls promoted by the Lp-type penalties is analyzed. A dynamic programming approach is proposed to numerically appr...

Pathwise Stochastic Optimal Control

This paper approaches optimal control problems for discrete-time controlled Markov processes by representing the value of the problem in a dual Lagrangian form; the value is expressed as an infimum over a family of Lagrangian martingales of an expectation of a pathwise supremum of the objective adjusted by the Lagrangian martingale term. This representation opens up the possibility of numerical...

Quantitative Determination Of Optimal Fiscal And Monetary Policies: A Stochastic Optimal Control Analysis For Iran