We look at stochastic optimization problems through the lens of statistical decision theory. In particular, we address admissibility, in the statistical decision theory sense, of the natural sample average estimator for a stochastic optimization problem (which is also known as the empirical risk minimization (ERM) rule in learning literature). It is well known that for … Read more
In this paper, we propose and analyze zeroth-order stochastic approximation algorithms for nonconvex and convex optimization, with a focus on addressing constrained optimization, high-dimensional setting, and saddle-point avoiding. To handle constrained optimization, we first propose generalizations of the conditional gradient algorithm achieving rates similar to the standard stochastic gradient algorithm using only zeroth-order information. To … Read more
This paper studies the class of two-stage stochastic programs (SP) with a linearly bi-parameterized recourse function defined by a convex quadratic program. A distinguishing feature of this new class of stochastic programs is that the objective function in the second stage is linearly parameterized by the first-stage decision variable, in addition to the standard linear … Read more
Distributionally robust optimization (DRO) has been introduced for solving stochastic programs where the distribution of the random parameters is unknown and must be estimated by samples from that distribution. A key element of DRO is the construction of the ambiguity set, which is a set of distributions that covers the true distribution with a high … Read more
We study constrained nested stochastic optimization problems in which the objective function is a composition of two smooth functions whose exact values and derivatives are not available. We propose a single time-scale stochastic approximation algorithm, which we call the Nested Averaged Stochastic Approximation (NASA), to find an approximate stationary point of the problem. The algorithm … Read more
The most common approaches for solving stochastic resource allocation problems in the research literature is to either use value functions (“dynamic programming”) or scenario trees (“stochastic programming”) to approximate the impact of a decision now on the future. By contrast, common industry practice is to use a deterministic approximation of the future which is easier … Read more
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 efficient frontier of optimal objective value versus risk of constraint violation. To this end, we construct a reformulated problem whose objective is to minimize … Read more
Influence maximization aims at identifying a limited set of key individuals in a (social) network which spreads information based on some propagation model and maximizes the number of individuals reached. We show that influence maximization based on the probabilistic independent cascade model can be modeled as a stochastic maximal covering location problem. A reformulation based … Read more
We consider chance-constrained problems with discrete random distribution. We aim for problems with a large number of scenarios. We propose a novel method based on the stochastic gradient descent method which performs updates of the decision variable based only on looking at a few scenarios. We modify it to handle the non-separable objective. A complexity … Read more
Decomposition methods have been well studied for solving two-stage and multi-stage stochastic programming problems, see [29, 32, 33]. In this paper, we propose an algorithmic framework based on the fundamental ideas of the methods for solving two-stage minimax distributionally robust optimization (DRO) problems where the underlying random variables take a finite number of distinct values. … Read more