相关论文: Batch Sample-wise Stochastic Optimal Control via S…

We present a neural network approach for approximating the value function of high-dimensional stochastic control problems. Our training process simultaneously updates our value function estimate and identifies the part of the state space…

Many practical applications of control require that constraints on the inputs and states of the system be respected, while optimizing some performance criterion. In the presence of model uncertainties or disturbances, for many control…

We consider the utility maximization problem under convex constraints with regard to theoretical results which allow the formulation of algorithmic solvers which make use of deep learning techniques. In particular for the case of random…

Stochastic gradient descent is a canonical tool for addressing stochastic optimization problems, and forms the bedrock of modern machine learning and statistics. In this work, we seek to balance the fact that attenuating step-size is…

The paper addresses a continuous-time continuous-space chance-constrained stochastic optimal control (SOC) problem where the probability of failure to satisfy given state constraints is explicitly bounded. We leverage the notion of exit…

In this paper we study mean-field type control problems with risk-sensitive performance functionals. We establish a stochastic maximum principle (SMP) for optimal control of stochastic differential equations (SDEs) of mean-field type, in…

We propose a new stochastic optimization framework for empirical risk minimization problems such as those that arise in machine learning. The traditional approaches, such as (mini-batch) stochastic gradient descent (SGD), utilize an…

In this paper, we investigate an optimal control problem with terminal stochastic linear complementarity constraints (SLCC), and its discrete approximation using the relaxation, the sample average approximation (SAA) and the implicit Euler…

We study the Stochastic Gradient Descent (SGD) method in nonconvex optimization problems from the point of view of approximating diffusion processes. We prove rigorously that the diffusion process can approximate the SGD algorithm weakly…

We analyze a batched variant of Stochastic Gradient Descent (SGD) with weighted sampling distribution for smooth and non-smooth objective functions. We show that by distributing the batches computationally, a significant speedup in the…

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

In this work, we introduce a stochastic maximum principle (SMP) approach for solving the reinforcement learning problem with the assumption that the unknowns in the environment can be parameterized based on physics knowledge. For the…

In this paper, we study the optimal control of a discrete-time stochastic differential equation (SDE) of mean-field type, where the coefficients can depend on both a function of the law and the state of the process. We establish a new…

In this report, we study decentralized stochastic optimization to minimize a sum of smooth and strongly convex cost functions when the functions are distributed over a directed network of nodes. In contrast to the existing work, we use…

This paper investigates group distributionally robust optimization (GDRO) with the goal of learning a model that performs well over $m$ different distributions. First, we formulate GDRO as a stochastic convex-concave saddle-point problem,…

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Approximate methods to solve stochastic optimal control (SOC) problems have received significant interest from researchers in the past decade. Probabilistic inference approaches to SOC have been developed to solve nonlinear quadratic…

Stochastically controlled stochastic gradient (SCSG) methods have been proved to converge efficiently to first-order stationary points which, however, can be saddle points in nonconvex optimization. It has been observed that a stochastic…

Based on the stochastic maximum principle for the partially coupled forward-backward stochastic control system (FBSCS for short), a modified method of successive approximations (MSA for short) is established for stochastic recursive optimal…

We propose a sampling-based trajectory optimization methodology for constrained problems. We extend recent works on stochastic search to deal with box control constraints,as well as nonlinear state constraints for discrete dynamical…