Data-driven stochastic optimization for distributional ambiguity with integrated confidence region

Variational Theory for Optimization under Stochastic Ambiguity

Stochastic ambiguity provides a rich class of uncertainty models that includes those in stochastic, robust, risk-based, and semi-infinite optimization, and that accounts for both uncertainty about parameter values as well as incompleteness of the description of uncertainty. We provide a novel, unifying perspective on optimization under stochastic ambiguity that rests on two pillars. First, the ...

Data-Driven Risk-Averse Stochastic Optimization with Wasserstein Metric∗

The traditional two-stage stochastic programming approach is to minimize the total expected cost with the assumption that the distribution of the random parameters is known. However, in most practices, the actual distribution of the random parameters is not known, and instead, only a series of historical data are available. Thus, the solution obtained from the traditional twostage stochastic pr...

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

This paper investigates the use of φ-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 can be...

Subjective Risk, Confidence, and Ambiguity

The paper extends a dynamic version of the classical von NeumannMorgenstern setting to incorporate a degree of confidence in or subjectivity of probabilistic beliefs. It provides a simple axiomatic characterization of a new preference representation that addresses ambiguity from a simple perspective, employing only basic tools from risk analysis. Conceptually, the paper renders the concept of s...

A Stochastic Optimization Model for Groundwater Management