Related papers: First order asymptotics of the sample average appr…
We study statistical properties of the optimal value of the Sample Average Approximation. The focus is on the tail function of the absolute error induced by the Sample Average Approximation, deriving upper estimates of its outcomes…
This paper is a study on solutions of the Sample Average Approximation Method to solve compound stochastic programs. We derive nonasymptotic upper estimates for probabilities of the approximation errors. The results depend on the sample…
We study statistical properties of the optimal value and optimal solutions of the Sample Average Approximation of risk averse stochastic problems. Central Limit Theorem type results are derived for the optimal value and optimal solutions…
We revisit the sample average approximation (SAA) approach for non-convex stochastic programming. We show that applying the SAA approach to problems with expected value equality constraints does not necessarily result in asymptotic…
Trajectory optimization under uncertainty underpins a wide range of applications in robotics. However, existing methods are limited in terms of reasoning about sources of epistemic and aleatoric uncertainty, space and time correlations,…
We establish central limit theorems for the Sample Average Approximation (SAA) method in discrete-time, finite-horizon stochastic optimal control. Our analysis is based on an abstract limit theorem for stochastic backward recursions, which…
Sample average approximation (SAA) replaces an intractable expected objective by an empirical average and is a basic device of modern stochastic optimization. We develop a rate theory for optimal values and empirical…
We propose a stochastic approximation method for approximating the efficient frontier of chance-constrained nonlinear programs. Our approach is based on a bi-objective viewpoint of chance-constrained programs that seeks solutions on the…
We consider a single stage stochastic program without recourse with a strictly convex loss function. We assume a compact decision space and grid it with a finite set of points. In addition, we assume that the decision maker can generate…
Sample average approximation (SAA), a popular method for tractably solving stochastic optimization problems, enjoys strong asymptotic performance guarantees in settings with independent training samples. However, these guarantees are not…
We develop a stochastic approximation-type algorithm to solve finite state/action, infinite-horizon, risk-aware Markov decision processes. Our algorithm has two loops. The inner loop computes the risk by solving a stochastic saddle-point…
We provide a general framework to study stochastic sequences related to individual learning in economics, learning automata in computer sciences, social learning in marketing, and other applications. More precisely, we study the asymptotic…
We discuss a general approach to building non-asymptotic confidence bounds for stochastic optimization problems. Our principal contribution is the observation that a Sample Average Approximation of a problem supplies upper and lower bounds…
This article deals with stochastic processes endowed with the Markov (memoryless) property and evolving over general (uncountable) state spaces. The models further depend on a non-deterministic quantity in the form of a control input, which…
We investigate sample average approximation (SAA) for two-stage stochastic programs without relatively complete recourse, i.e., for problems in which there are first-stage feasible solutions that are not guaranteed to have a feasible…
Large sectors of the recent optimization literature focused in the last decade on the development of optimal stochastic first order schemes for constrained convex models under progressively relaxed assumptions. Stochastic proximal point is…
Chance constrained programming (CCP) refers to a type of optimization problem with uncertain constraints that are satisfied with at least a prescribed probability level. In this work, we study the sample average approximation (SAA) of…
Optimal values and solutions of empirical approximations of stochastic optimization problems can be viewed as statistical estimators of their true values. From this perspective, it is important to understand the asymptotic behavior of these…
We consider constrained optimization problems with a nonsmooth objective function in the form of mathematical expectation. The Sample Average Approximation (SAA) is used to estimate the objective function and variable sample size strategy…
Stochastic gradient algorithms are more and more studied since they can deal efficiently and online with large samples in high dimensional spaces. In this paper, we first establish a Central Limit Theorem for these estimates as well as for…