Publications by Peyman Mohajerin Esfahani

Bridging Bayesian and Minimax Mean Square Error Estimation via Wasserstein Distributionally Robust Optimization

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

We introduce a distributionally robust minimium mean square error estimation model with a Wasserstein ambiguity set to recover an unknown signal from a noisy observation. The proposed model can be viewed as a zero-sum game between a statistician choosing a ...

2023

Distributionally Robust Inverse Covariance Estimation: The Wasserstein Shrinkage Estimator

Daniel Kuhn, Viet Anh Nguyen, Peyman Mohajerin Esfahani

We introduce a distributionally robust maximum likelihood estimation model with a Wasserstein ambiguity set to infer the inverse covariance matrix of a p-dimensional Gaussian random vector from n independent samples. The proposed model minimizes the worst ...

2022

From Data to Decisions: Distributionally Robust Optimization is Optimal

Daniel Kuhn, Peyman Mohajerin Esfahani

We study stochastic programs where the decision-maker cannot observe the distribution of the exogenous uncertainties but has access to a finite set of independent samples from this distribution. In this setting, the goal is to find a procedure that transfo ...

2021

Regularization via Mass Transportation

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, ...

2019

Generalized maximum entropy estimation

Peyman Mohajerin Esfahani, John Lygeros, Tobias Sutter

We consider the problem of estimating a probability distribution that maximizes the entropy while satisfying a finite number of moment constraints, possibly corrupted by noise. Based on duality of convex programming, we present a novel approximation scheme ...

2019

Wasserstein Distributionally Robust Optimization: Theory and Applications in Machine Learning

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

Many decision problems in science, engineering and economics are affected by uncertain parameters whose distribution is only indirectly observable through samples. The goal of data-driven decision-making is to learn a decision from finitely many training s ...

2019

Wasserstein Distributionally Robust Kalman Filtering

Daniel Kuhn, Viet Anh Nguyen, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani

We study a distributionally robust mean square error estimation problem over a nonconvex Wasserstein ambiguity set containing only normal distributions. We show that the optimal estimator and the least favorable distribution form a Nash equilibrium. Despit ...

2018

From Infinite to Finite Programs: Explicit Error Bounds with Applications to Approximate Dynamic Programming

Daniel Kuhn, Peyman Mohajerin Esfahani, John Lygeros, Tobias Sutter

We consider linear programming (LP) problems in infinite dimensional spaces that are in general computationally intractable. Under suitable assumptions, we develop an approximation bridge from the infinite-dimensional LP to tractable finite convex programs ...

2018

Data-Driven Distributionally Robust Optimization Using the Wasserstein Metric: Performance Guarantees and Tractable Reformulations

Daniel Kuhn, Peyman Mohajerin Esfahani

We consider stochastic programs where the distribution of the uncertain parameters is only observable through a finite training dataset. Using the Wasserstein metric, we construct a ball in the space of (multivariate and non-discrete) probability distribut ...

2018

Data-Driven Inverse Optimization with Incomplete Information

Daniel Kuhn, Soroosh Shafieezadeh Abadeh, Peyman Mohajerin Esfahani, Grani Adiwena Hanasusanto

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 ...

2018