Related papers: Distributionally-Robust Optimization with Noisy Da…
Distributionally robust optimization (DRO) is a powerful technique to train robust models against data distribution shift. This paper aims to solve regularized nonconvex DRO problems, where the uncertainty set is modeled by a so-called…
The problem of minimizing convex functionals of probability distributions is solved under the assumption that the density of every distribution is bounded from above and below. A system of sufficient and necessary first-order optimality…
This paper studies the problem of distributionally robust model predictive control (MPC) using total variation distance ambiguity sets. For a discrete-time linear system with additive disturbances, we provide a conditional value-at-risk…
This paper studies the problem of steering the distribution of a discrete-time dynamical system from an initial distribution to a target distribution in finite time. The formulation is fully nonlinear, allowing the use of general control…
A common theme in stochastic optimization problems is that, theoretically, stochastic algorithms need to "know" relatively rich information about the underlying distributions. This is at odds with most applications, where distributions are…
We study a stochastic program where the probability distribution of the uncertain problem parameters is unknown and only indirectly observed via finitely many correlated samples generated by an unknown Markov chain with $d$ states. We…
In this paper, we present approximation algorithms for combinatorial optimization problems under probabilistic constraints. Specifically, we focus on stochastic variants of two important combinatorial optimization problems: the k-center…
We consider data-driven approaches that integrate a machine learning prediction model within distributionally robust optimization (DRO) given limited joint observations of uncertain parameters and covariates. Our framework is flexible in…
Utility preference robust optimization (PRO) has recently been proposed to deal with optimal decision making problems where the decision maker's (DM) preference over gains and losses is ambiguous. In this paper, we take a step further to…
Recently, (Blanchet, Kang, and Murhy 2016, and Blanchet, and Kang 2017) showed that several machine learning algorithms, such as square-root Lasso, Support Vector Machines, and regularized logistic regression, among many others, can be…
In this paper, an optimization problem with uncertain constraint coefficients is considered. Possibility theory is used to model the uncertainty. Namely, a joint possibility distribution in constraint coefficient realizations, called…
Constructing uncertainty sets as unions of multiple subsets has emerged as an effective approach for creating compact and flexible uncertainty representations in data-driven robust optimization (RO). This paper focuses on two separate…
Stochastic optimization has found wide applications in minimizing objective functions in machine learning, which motivates a lot of theoretical studies to understand its practical success. Most of existing studies focus on the convergence…
Robust optimization is a popular paradigm for modeling and solving two- and multi-stage decision-making problems affected by uncertainty. In many real-world applications, the time of information discovery is decision-dependent and the…
Distributed abstract programs are a novel class of distributed optimization problems where (i) the number of variables is much smaller than the number of constraints and (ii) each constraint is associated to a network node. Abstract…
Stochastic Approximation has been a prominent set of tools for solving problems with noise and uncertainty. Increasingly, it becomes important to solve optimization problems wherein there is noise in both a set of constraints that a…
We consider a distributed stochastic optimization problem in networks with finite number of nodes. Each node adjusts its action to optimize the global utility of the network, which is defined as the sum of local utilities of all nodes.…
This paper is devoted to reduce the conservatism of distributionally robust optimization with moments information. Since the optimal solution of distributionally robust optimization is required to be feasible for all uncertain distributions…
Optimal-Transport Distributionally Robust Optimization (OT-DRO) robustifies data-driven decision-making under uncertainty by capturing the sampling-induced statistical error via optimal transport ambiguity sets. The standard OT-DRO pipeline…
In this paper, we develop a unified framework for studying constrained robust optimal control problems with adjustable uncertainty sets. In contrast to standard constrained robust optimal control problems with known uncertainty sets, we…