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Approximations of optimization problems arise in computational procedures and sensitivity analysis. The resulting effect on solutions can be significant, with even small approximations of components of a problem translating into large…
Decision-making problems are commonly formulated as optimization problems, which are then solved to make optimal decisions. In this work, we consider the inverse problem where we use prior decision data to uncover the underlying…
In this paper, we introduce an unbiased gradient simulation algorithms for solving convex optimization problem with stochastic function compositions. We show that the unbiased gradient generated from the algorithm has finite variance and…
Resource allocation is an essential aspect of successful Product Development (PD). In this paper, we formulate the dynamic resource allocation of the PD process as a convex optimization problem. Specially, we build and solve two variants of…
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonconvex part is smooth and the nonsmooth part is convex. Surprisingly, unlike the smooth case, our knowledge of this fundamental problem…
Approximations of functions with finite data often do not respect certain "structural" properties of the functions. For example, if a given function is non-negative, a polynomial approximation of the function is not necessarily also…
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more…
In this paper we analyze several new methods for solving nonconvex optimization problems with the objective function formed as a sum of two terms: one is nonconvex and smooth, and another is convex but simple and its structure is known.…
In this paper, we propose a new way to obtain optimal convergence rates for smooth stochastic (strong) convex optimization tasks. Our approach is based on results for optimization tasks where gradients have nonrandom noise. In contrast to…
We consider a discrete time stochastic queueing system where a controller makes a 2-stage decision every slot. The decision at the first stage reveals a hidden source of randomness with a control-dependent (but unknown) probability…
Consensus maximization is one of the most widely used robust fitting paradigms in computer vision, and the development of algorithms for consensus maximization is an active research topic. In this paper, we propose an efficient…
Min-max problems have broad applications in machine learning, including learning with non-decomposable loss and learning with robustness to data distribution. Convex-concave min-max problem is an active topic of research with efficient…
We apply a recently developed framework for analyzing the convergence of stochastic algorithms to the general problem of large-scale nonconvex composite optimization more generally, and nonconvex likelihood maximization in particular. Our…
Non-convex optimization plays a key role in a growing number of machine learning applications. This motivates the identification of specialized structure that enables sharper theoretical analysis. One such identified structure is…
This research considers the ranking and selection with input uncertainty. The objective is to maximize the posterior probability of correctly selecting the best alternative under a fixed simulation budget, where each alternative is measured…
Min-max optimization is emerging as a key framework for analyzing problems of robustness to strategically and adversarially generated data. We propose a random reshuffling-based gradient free Optimistic Gradient Descent-Ascent algorithm for…
Separable convex optimization problems with linear ascending inequality and equality constraints are addressed in this paper. Under an ordering condition on the slopes of the functions at the origin, an algorithm that determines the optimum…
It is classical that, when the small deformation is assumed, the incremental analysis problem of an elastoplastic structure with a piecewise-linear yield condition and a linear strain hardening model can be formulated as a convex quadratic…
We consider the framework of convex high dimensional stochastic control problems, in which the controls are aggregated in the cost function. As first contribution, we introduce a modified problem, whose optimal control is under some…
We provide a unifying approximate dynamic programming framework that applies to a broad variety of problems involving sequential estimation. We consider first the construction of surrogate cost functions for the purposes of optimization,…