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In practical optimization problems, we typically model uncertainty as a random variable though its true probability distribution is unobservable to the decision maker. Historical data provides some information of this distribution that we…
We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…
We develop a Distributionally Robust Optimization (DRO) formulation for Multiclass Logistic Regression (MLR), which could tolerate data contaminated by outliers. The DRO framework uses a probabilistic ambiguity set defined as a ball of…
Noisy data are often viewed as a challenge for decision-making. This paper studies a distributionally robust optimization (DRO) that shows how such noise can be systematically incorporated. Rather than applying DRO to the noisy empirical…
Despite strong performance in numerous applications, the fragility of deep learning to input perturbations has raised serious questions about its use in safety-critical domains. While adversarial training can mitigate this issue in…
We study the distributionally robust optimization (DRO) in a dynamic context where the model uncertainty is captured by penalizing potential models in function of their adapted Wasserstein distance to a given reference model. We consider…
We propose a mathematically principled PDE gradient flow framework for distributionally robust optimization (DRO). Exploiting the recent advances in the intersection of Markov Chain Monte Carlo sampling and gradient flow theory, we show…
There is a recent surge of interest in nonconvex reformulations via low-rank factorization for stochastic convex semidefinite optimization problem in the purpose of efficiency and scalability. Compared with the original convex formulations,…
Distributionally robust optimization (DRO) has attracted attention in machine learning due to its connections to regularization, generalization, and robustness. Existing work has considered uncertainty sets based on phi-divergences and…
We consider the distributionally robust optimization (DRO) model of principal component analysis (PCA) to account for uncertainty in the underlying probability distribution. The resulting formulation leads to a nonsmooth constrained min-max…
This work studies the design of safe control policies for large-scale non-linear systems operating in uncertain environments. In such a case, the robust control framework is a principled approach to safety that aims to maximize the…
In reinforcement learning, robust policies for high-stakes decision-making problems with limited data are usually computed by optimizing the percentile criterion, which minimizes the probability of a catastrophic failure. Unfortunately,…
Safe and economic operation of networked systems is often challenging. Optimization-based schemes are frequently considered, since they achieve near-optimality while ensuring safety via the explicit consideration of constraints. In…
Statistical uncertainties complicate engineering design -- confounding regulated design approaches, and degrading the performance of reliability efforts. The simplest means to tackle this uncertainty is double loop simulation; a nested…
We investigate the use of distributionally robust optimization (DRO) as a tractable tool to recover the asymptotic statistical guarantees provided by the Central Limit Theorem, for maintaining the feasibility of an expected value constraint…
The non-convexity and intractability of distributionally robust chance constraints make them challenging to cope with. From a data-driven perspective, we propose formulating it as a robust optimization problem to ensure that the…
In this paper, we consider a network capacity expansion problem in the context of telecommunication networks, where there is uncertainty associated with the expected traffic demand. We employ a distributionally robust stochastic…
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…
Submodular functions have applications throughout machine learning, but in many settings, we do not have direct access to the underlying function $f$. We focus on stochastic functions that are given as an expectation of functions over a…
The Douglas-Rachford algorithm (DRA) is a powerful optimization method for minimizing the sum of two convex (not necessarily smooth) functions. The vast majority of previous research dealt with the case when the sum has at least one…