Prediction models are often employed in estimating parameters of optimization models. Despite the fact that in an \emph{end-to-end} view, the real goal is to achieve good optimization performance, the prediction performance is measured on its own. While it is usually believed that good prediction performance in estimating the parameters will result in good subsequent optimization … Read more
Security of cyber networks is crucial; recent severe cyber-attacks have had a devastating effect on many large organizations. The attack graph, which maps the potential attack paths of a cyber network, is a popular tool for analyzing cyber system vulnerability. In this study, we propose a bi-level stochastic network interdiction model on an attack graph … Read more
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to some useful property on its variance. We limit our consideration to a hybrid SARAH-SGD for nonconvex expectation problems. However, our idea … Read more
Empirical risk minimization is an important class of optimization problems with many popular machine learning applications, and stochastic variance reduction methods are popular choices for solving them. Among these methods, SVRG and Katyusha X (a Nesterov accelerated SVRG) achieve fast convergence without substantial memory requirement. In this paper, we propose to accelerate these two algorithms … Read more
Published in Journal of Global Optimization. https://doi.org/10.1007/s10898-021-01041-y We develop a stochastic optimization model for scheduling a hybrid solar-battery storage system. Solar power in excess of the promise can be used to charge the battery, while power short of the promise is met by discharging the battery. We ensure reliable operations by using a joint chance … Read more
Most state-of-the-art algorithms for the Vehicle Routing Problem, such as Branch-and- Price algorithms or meta heuristics, rely on a fast feasibility test for a given route. We devise the fi rst approach to approximately check feasibility in the Stochastic Vehicle Routing Problem with time windows, where travel times are correlated and depend on the time of … Read more
We aim to solve a structured convex optimization problem, where a nonsmooth function is composed with a linear operator. When opting for full splitting schemes, usually, primal-dual type methods are employed as they are effective and also well studied. However, under the additional assumption of Lipschitz continuity of the nonsmooth function which is composed with … Read more
We introduce a new method for solving nonlinear continuous optimization problems with chance constraints. Our method is based on a reformulation of the probabilistic constraint as a quantile function. The quantile function is approximated via a differentiable sample average approximation. We provide theoretical statistical guarantees of the approximation, and illustrate empirically that the reformulation can … Read more
We study data-driven decision-making problems in a parametrized Bayesian framework. We adopt a risk-sensitive approach to modeling the interplay between statistical estimation of parameters and optimization, by computing a risk measure over a loss/disutility function with respect to the posterior distribution over the parameters. While this forms the standard Bayesian decision-theoretic approach, we focus on … Read more
We address a stochastic variant of the Vehicle Routing Problem with Roaming Delivery Locations. In this model, direct-to-consumer deliveries can be made in the trunk of the customer’s car, while the vehicle is parked at a location along the customer’s itinerary. The stochasticity arises from the uncertainty in travel times and the problem is formulated … Read more