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We study distributionally robust online learning, where a risk-averse learner updates decisions sequentially to guard against worst-case distributions drawn from a Wasserstein ambiguity set centered at past observations. While this paradigm…
Stochastic optimization is a widely used approach for optimization under uncertainty, where uncertain input parameters are modeled by random variables. Exact or approximation algorithms have been obtained for several fundamental problems in…
This paper proposes an analytical framework for modelling resource contention in multi-robot systems, where the travel times and task durations are uncertain. It uses several approximation methods to quickly and accurately calculate the…
This paper focuses on investigating an inexact stochastic model-based optimization algorithm that integrates preconditioning techniques for solving stochastic composite optimization problems. The proposed framework unifies and extends the…
This paper builds Wasserstein ambiguity sets for the unknown probability distribution of dynamic random variables leveraging noisy partial-state observations. The constructed ambiguity sets contain the true distribution of the data with…
Recently there has been a surge of interest in operations research (OR) and the machine learning (ML) community in combining prediction algorithms and optimization techniques to solve decision-making problems in the face of uncertainty.…
Within the framework of complex system design, it is often necessary to solve mixed variable optimization problems, in which the objective and constraint functions can depend simultaneously on continuous and discrete variables.…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
The efficacy of robust optimization spans a variety of settings with uncertainties bounded in predetermined sets. In many applications, uncertainties are affected by decisions and cannot be modeled with current frameworks. This paper takes…
In this article, we derive first-order necessary optimality conditions for a constrained optimal control problem formulated in the Wasserstein space of probability measures. To this end, we introduce a new notion of localised metric…
This article presents a constrained policy optimization approach for the optimal control of systems under nonstationary uncertainties. We introduce an assumption that we call Markov embeddability that allows us to cast the stochastic…
Incorporating side observations in decision making can reduce uncertainty and boost performance, but it also requires we tackle a potentially complex predictive relationship. While one may use off-the-shelf machine learning methods to…
Distributionally robust stochastic optimization (DRSO) is a framework for decision-making problems under certainty, which finds solutions that perform well for a chosen set of probability distributions. Many different approaches for…
Reinforcement learning can provide effective reasoning for sequential decision-making problems with variable dynamics. Such reasoning in practical implementation, however, poses a persistent challenge in interpreting the reward function and…
We study a variety of Wasserstein distributionally robust optimization (WDRO) problems where the distributions in the ambiguity set are chosen by constraining their Wasserstein discrepancies to the empirical distribution. Using the notion…
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…
This brief note aims to introduce the recent paradigm of distributional robustness in the field of shape and topology optimization. Acknowledging that the probability law of uncertain physical data is rarely known beyond a rough…
In this paper we consider multiple constrained resource allocation problems, where the constraints can be specified by formulating activity dependency restrictions or by using game-theoretic models. All the problems are focused on generic…
Long-term reservoir management often uses bounds on the reservoir level, between which the operator can work. However, these bounds are not always kept up-to-date with the latest knowledge about the reservoir drainage area, and thus become…
In this paper, we describe a representation for spatial information, called the stochastic map, and associated procedures for building it, reading information from it, and revising it incrementally as new information is obtained. The map…