Distributionally Robust Optimization with Principal Component Analysis

Distributionally robust optimization (DRO) is widely used, because it offers a way to overcome the conservativeness of robust optimization without requiring the specificity of stochastic optimization. On the computational side, many practical DRO instances can be equivalently (or approximately) formulated as semidefinite programming (SDP) problems via conic duality of the moment problem. However, despite being … Read more

Adaptive Distributionally Robust Optimization

We develop a modular and tractable framework for solving an adaptive distributionally robust linear opti- mization problem, where we minimize the worst-case expected cost over an ambiguity set of probability dis- tributions. The adaptive distrbutaionally robust optimization framework caters for dynamic decision making, where decisions can adapt to the uncertain outcomes as they unfold in … Read more

Phi-Divergence Constrained Ambiguous Stochastic Programs for Data-Driven Optimization

This paper investigates the use of phi-divergences in ambiguous (or distributionally robust) two-stage stochastic programs. Classical stochastic programming assumes the distribution of uncertain parameters are known. However, the true distribution is unknown in many applications. Especially in cases where there is little data or not much trust in the data, an ambiguity set of distributions … Read more

Data-Driven Inverse Optimization with Imperfect Information

In data-driven inverse optimization an observer aims to learn the preferences of an agent who solves a parametric optimization problem depending on an exogenous signal. Thus, the observer seeks the agent’s objective function that best explains a historical sequence of signals and corresponding optimal actions. We focus here on situations where the observer has imperfect … Read more

Distributionally robust inventory control when demand is a martingale

Demand forecasting plays an important role in many inventory control problems. To mitigate the potential harms of model misspecification in this context, various forms of distributionally robust optimization have been applied. Although many of these methodologies suffer from the problem of time-inconsistency, the work of Klabjan, Simchi-Levi and Song [85] established a general time-consistent framework … Read more

Ambiguous Joint Chance Constraints under Mean and Dispersion Information

We study joint chance constraints where the distribution of the uncertain parameters is only known to belong to an ambiguity set characterized by the mean and support of the uncertainties and by an upper bound on their dispersion. This setting gives rise to pessimistic (optimistic) ambiguous chance constraints, which require the corresponding classical chance constraints … Read more

Distributionally Robust Logistic Regression

This paper proposes a distributionally robust approach to logistic regression. We use the Wasserstein distance to construct a ball in the space of probability distributions centered at the uniform distribution on the training samples. If the radius of this ball is chosen judiciously, we can guarantee that it contains the unknown data-generating distribution with high … Read more

Distributionally robust chance-constrained games: Existence and characterization of Nash equilibrium

We consider an n-player finite strategic game. The payoff vector of each player is a random vector whose distribution is not completely known. We assume that the distribution of a random payoff vector of each player belongs to a distributional uncertainty set. We define a distributionally robust chance-constrained game using worst-case chance constraint. We consider … Read more

Stability Analysis for Mathematical Programs with Distributionally Robust Chance Constraint

Stability analysis for optimization problems with chance constraints concerns impact of variation of probability measure in the chance constraints on the optimal value and optimal solutions and research on the topic has been well documented in the literature of stochastic programming. In this paper, we extend such analysis to optimization problems with distributionally robust chance … Read more

Quantitative Stability Analysis for Distributionally Robust Optimization With Moment Constraints

In this paper we consider a broad class of distributionally robust optimization (DRO for short) problems where the probability of the underlying random variables depends on the decision variables and the ambiguity set is de ned through parametric moment conditions with generic cone constraints. Under some moderate conditions including Slater type conditions of cone constrained moment … Read more