Stochastic optimization of forward recursive functions

Stochastic Recursive Gradient Algorithm for Nonconvex Optimization

In this paper, we study and analyze the mini-batch version of StochAstic Recursive grAdient algoritHm (SARAH), a method employing the stochastic recursive gradient, for solving empirical loss minimization for the case of nonconvex losses. We provide a sublinear convergence rate (to stationary points) for general nonconvex functions and a linear convergence rate for gradient dominated functions,...

Stochastic global maximum principle for optimization with recursive utilities

In this paper, we study the recursive stochastic optimal control problems. The control domain does not need to be convex, and the generator of the backward stochastic differential equation can contain z. We obtain the variational equations for backward stochastic differential equations, and then obtain the maximum principle which solves completely Peng’s open problem.

Recursive Direct Optimization and Successive Refinement in Multistage Stochastic Programs

The paper presents a new algorithmic approach for multistage stochastic programs which are seen as discrete optimal control problems with a characteristic dynamic structure induced by the scenario tree. To exploit that structure, we propose a highly eecient dynamic programming recursion for the computationally intensive task of KKT systems solution within a primal-dual interior point method. Co...

Risk-Constrained Forward Trading Optimization by Stochastic Approximate Dynamic Programming

Real Recursive Functions and Real Extensions of Recursive Functions

Recently, functions over the reals that extend elementarily computable functions over the integers have been proved to correspond to the smallest class of real functions containing some basic functions and closed by composition and linear integration. We extend this result to all computable functions: functions over the reals that extend total recursive functions over the integers are proved to...