Related papers: Strong Convexity in Stochastic Programs with Devia…

This paper studies a structured compound stochastic program (SP) involving multiple expectations coupled by nonconvex and nonsmooth functions. We present a successive convex-programming based sampling algorithm and establish its…

The paper introduces the first formulation of convex Q-learning for Markov decision processes with function approximation. The algorithms and theory rest on a relaxation of a dual of Manne's celebrated linear programming characterization of…

The family of admissible positions in a transaction costs model is a random closed set, which is convex in case of proportional transaction costs. However, the convexity fails, e.g. in case of fixed transaction costs or when only a finite…

A classical result in risk measure theory states that every coherent risk measure has a dual representation as the supremum of certain expected value over a risk envelope. We study this topic in more detail. The related issues include: 1.…

We prove novel convergence results for a stochastic proximal gradient algorithm suitable for solving a large class of convex optimization problems, where a convex objective function is given by the sum of a smooth and a possibly non-smooth…

We study randomized variants of two classical algorithms: coordinate descent for systems of linear equations and iterated projections for systems of linear inequalities. Expanding on a recent randomized iterated projection algorithm of…

This paper conducts sensitivity analysis of random constraint and variational systems related to stochastic optimization and variational inequalities. We establish efficient conditions for well-posedness, in the sense of robust Lipschitzian…

This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…

In this paper, we establish the convergence of the stochastic Heavy Ball (SHB) algorithm under more general conditions than in the current literature. Specifically, (i) The stochastic gradient is permitted to be biased, and also, to have…

Stochastic gradient methods are among the most important algorithms in training machine learning problems. While classical assumptions such as strong convexity allow a simple analysis they are rarely satisfied in applications. In recent…

Model predictive control solves a constrained optimization problem online in order to compute an implicit closed-loop control policy. Recursive feasibility -- guaranteeing that the optimal control problem will have a solution at every time…

In this paper monetary risk measures that are positively superhomogeneous, called star-shaped risk measures, are characterized and their properties studied. The measures in this class, which arise when the controversial subadditivity…

In performative prediction, predictions guide decision-making and hence can influence the distribution of future data. To date, work on performative prediction has focused on finding performatively stable models, which are the fixed points…

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Single-level reformulations of (non-convex) distributionally robust optimization (DRO) problems are often intractable, as they contain semiinfinite dual constraints. Based on such a semiinfinite reformulation, we present a safe…

Stochastic dominance of a random variable by a convex combination of its independent copies has recently been shown to hold within the relatively narrow class of distributions with concave odds function, and later extended to broader…

To model combinatorial decision problems involving uncertainty and probability, we introduce stochastic constraint programming. Stochastic constraint programs contain both decision variables (which we can set) and stochastic variables…

This paper deals with multidimensional dynamic risk measures induced by conditional $g$-expectations. A notion of multidimensional $g$-expectation is proposed to provide a multidimensional version of nonlinear expectations. By a technical…

Adaptive experiment designs can dramatically improve statistical efficiency in randomized trials, but they also complicate statistical inference. For example, it is now well known that the sample mean is biased in adaptive trials.…

In this article we present a general framework for non-concave robust stochastic control problems under model uncertainty in a discrete time finite horizon setting. Our framework allows to consider a variety of different path-dependent…