Related papers: Subdifferentials of Value Functions in Nonconvex D…
We develop a GPU-accelerated dynamic programming (DP) method for valuing, operating, and bidding energy storage under multistage stochastic electricity prices. Motivated by computational limitations in existing models, we formulate DP…
Stochastic gradient methods have been a popular and powerful choice of optimization methods, aimed at minimizing functions. Their advantage lies in the fact that that one approximates the gradient as opposed to using the full Jacobian…
This article characterizes conjugates and subdifferentials of convex integral functionals over the linear space $\mathcal N^\infty$ of stochastic processes of essentially bounded variation (BV) when $\mathcal N^\infty$ is identified with…
The stochastic subgradient method is a widely-used algorithm for solving large-scale optimization problems arising in machine learning. Often these problems are neither smooth nor convex. Recently, Davis et al. [1-2] characterized the…
The paper addresses the study and applications of a broad class of extended-real-valued functions, known as optimal value or marginal functions, which are frequently appeared in variational analysis, parametric optimization, and a variety…
This paper studies the asymptotic behavior of the constant step Stochastic Gradient Descent for the minimization of an unknown function F , defined as the expectation of a non convex, non smooth, locally Lipschitz random function. As the…
The purpose of this paper is to propose a time-step-robust cell-to-cell integration of particle trajectories in 3-D unstructured meshes in particle/mesh Lagrangian stochastic methods. The main idea is to dynamically update the mean fields…
Space-time regularity of linear stochastic partial differential equations is studied. The solution is defined in the mild sense in the state space $L^p$. The corresponding regularity is obtained by showing that the stochastic convolution…
Policy gradient methods are widely used in reinforcement learning. Yet, the nonconvexity of policy optimization poses significant challenges in understanding the global convergence of policy gradient methods. For a class of finite-horizon…
The present paper proposes new fully discrete schemes for long-time approximations of stochastic partial differential equations (SPDEs) with non-globally Lipschitz coefficients in a bounded domain $D \subset \R^d, d =1,2,3 $. A novel family…
We consider a broad class of dynamic programming (DP) problems that involve a partially linear structure and some positivity properties in their system equation and cost function. We address deterministic and stochastic problems, possibly…
Several non-linear operators in stochastic analysis, such as solution maps to stochastic differential equations, depend on a temporal structure which is not leveraged by contemporary neural operators designed to approximate general maps…
In this work, we study dynamic programming (DP) algorithms for partially observable Markov decision processes with jointly continuous and discrete state-spaces. We consider a class of stochastic systems which have coupled discrete and…
Probability functions figure prominently in optimization problems of engineering. They may be nonsmooth even if all input data are smooth.This fact motivates the consideration of subdifferentials for such typically just continuous…
Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…
In this paper we study the value function of Bolza problems governed by stochastic difference equations, with particular emphasis on the convex non-anticipative case. Our goal is to provide some insights on the structure of the…
A hypodifferential is a compact family of affine mappings that defines a local max-type approximation of a nonsmooth convex function. We present a general theory of hypodifferentials of nonsmooth convex functions defined on a Banach space.…
Stochastic gradient descent is an optimisation method that combines classical gradient descent with random subsampling within the target functional. In this work, we introduce the stochastic gradient process as a continuous-time…
This paper studies dynamic stochastic optimization problems parametrized by a random variable. Such problems arise in many applications in operations research and mathematical finance. We give sufficient conditions for the existence of…
This book is devoted to finite-dimensional problems of non-convex non-smooth optimization and numerical methods for their solution. The problem of nonconvexity is studied in the book on two main models of nonconvex dependencies: these are…