Related papers: Approximation Algorithms for Distributionally Robu…
The EM (Expectation-Maximization) algorithm is regarded as an MM (Majorization-Minimization) algorithm for maximum likelihood estimation of statistical models. Expanding this view, this paper demonstrates that by choosing an appropriate…
Chance constraints are frequently used to limit the probability of constraint violations in real-world optimization problems where the constraints involve stochastic components. We study chance-constrained submodular optimization problems,…
Asset management attempts to keep the power system in working conditions. It requires much coordination between multiple entities and long term planning often months in advance. In this work we introduce a mid-term asset management…
Empirical risk minimization (ERM) and distributionally robust optimization (DRO) are popular approaches for solving stochastic optimization problems that appear in operations management and machine learning. Existing generalization error…
In this work we study binary two-stage robust optimization problems with objective uncertainty. We present an algorithm to calculate efficiently lower bounds for the binary two-stage robust problem by solving alternately the underlying…
In many contemporary optimization problems such as those arising in machine learning, it can be computationally challenging or even infeasible to evaluate an entire function or its derivatives. This motivates the use of stochastic…
This paper develops a unified methodology for probabilistic analysis and optimal control design for jump diffusion processes defined by polynomials. For such systems, the evolution of the moments of the state can be described via a system…
Designing controllers for systems affected by model uncertainty can prove to be a challenge, especially when seeking the optimal compromise between the conflicting goals of identification and control. This trade-off is explicitly taken into…
We consider an online two-stage stochastic optimization with long-term constraints over a finite horizon of $T$ periods. At each period, we take the first-stage action, observe a model parameter realization and then take the second-stage…
A large class of stochastic programs involve optimizing an expectation taken with respect to an underlying distribution that is unknown in practice. One popular approach to addressing the distributional uncertainty, known as the…
The cross-dock door design problem consists of deciding the strip and stack doors and nominal capacity of an entity under uncertainty. Inbound commodity flow from origin nodes is assigned to the strip doors, it is consolidated in the…
We introduce the class of multistage stochastic optimization problems with a random number of stages. For such problems, we show how to write dynamic programming equations and detail the Stochastic Dual Dynamic Programming algorithm to…
We study a statistical method to estimate the optimal value, and the optimality gap of a given solution for stochastic optimization as an assessment of the solution quality. Our approach is based on bootstrap aggregating, or bagging,…
Stochastic approximation algorithm is a useful technique which has been exploited successfully in probability theory and statistics for a long time. The step sizes used in stochastic approximation are generally taken to be deterministic and…
An algorithm is proposed, analyzed, and tested experimentally for solving stochastic optimization problems in which the decision variables are constrained to satisfy equations defined by deterministic, smooth, and nonlinear functions. It is…
Two-stage stochastic programs (2SPs) are important tools for making decisions under uncertainty. Decision-makers use contextual information to generate a set of scenarios to represent the true conditional distribution. However, the number…
Topology optimization under uncertainty (TOuU) often defines objectives and constraints by statistical moments of geometric and physical quantities of interest. Most traditional TOuU methods use gradient-based optimization algorithms and…
Chance constrained program is computationally intractable due to the existence of chance constraints, which are randomly disturbed and should be satisfied with a probability. This paper proposes a two-layer randomized algorithm to address…
To integrate strategic, tactical and operational decisions, the two-stage optimization has been widely used to guide dynamic decision making. In this paper, we study the two-stage stochastic programming for complex systems with unknown…
Covariate shift occurs when the distribution of input features differs between the training and testing phases. In covariate shift, estimating an unknown function's moment is a classical problem that remains under-explored, despite its…