Publications related to Barycentric Bounds in Stochastic Programming: Theory and Application

Contextual Stochastic Bilevel Optimization

Daniel Kuhn, Andreas Krause, Yifan Hu, Jie Wang

We introduce contextual stochastic bilevel optimization (CSBO) -- a stochastic bilevel optimization framework with the lower-level problem minimizing an expectation conditioned on some contextual information and the upper-level decision variable. This fram ...

2023

Localization errors of the stochastic heat equation

David Jean-Michel Candil

In this thesis, we study the stochastic heat equation (SHE) on bounded domains and on the whole Euclidean space

\R^d.

We confirm the intuition that as the bounded domain increases to the whole space, both solutions become arbitrarily close to one another ...

EPFL2022

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Victor Panaretos, Julien René Pierre Fageot, Matthieu Martin Jean-André Simeoni, Alessia Caponera

We propose nonparametric estimators for the second-order central moments of possibly anisotropic spherical random fields, within a functional data analysis context. We consider a measurement framework where each random field among an identically distribute ...

2022

Preconditioners for robust optimal control problems under uncertainty

Fabio Nobile, Tommaso Vanzan

The discretization of robust quadratic optimal control problems under uncertainty using the finite element method and the stochastic collocation method leads to large saddle-point systems, which are fully coupled across the random realizations. Despite its ...

2022

Multi-armed Bandits in Action

Farnood Salehi

Making decisions is part and parcel of being human. Among a set of actions, we want to choose the one that has the highest reward. But the uncertainty of the outcome prevents us from always making the right decision. Making decisions under uncertainty can ...

EPFL2020

MATHICSE Technical Report : A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters

Fabio Nobile, Matthieu Claude Martin, Panagiotis Tsilifis

In this paper, we present a multilevel Monte Carlo (MLMC) version of the Stochastic Gradient (SG) method for optimization under uncertainty, in order to tackle Optimal Control Problems (OCP) where the constraints are described in the form of PDEs with rand ...

MATHICSE2020

The Decision Rule Approach to Optimisation under Uncertainty: Methodology and Applications

Daniel Kuhn, Wolfram Wiesemann

Dynamic decision-making under uncertainty has a long and distinguished history in operations research. Due to the curse of dimensionality, solution schemes that naively partition or discretize the support of the random problem parameters are limited to sma ...

2019

Scalable Convex Optimization Methods for Semidefinite Programming

Alp Yurtsever

With the ever-growing data sizes along with the increasing complexity of the modern problem formulations, contemporary applications in science and engineering impose heavy computational and storage burdens on the optimization algorithms. As a result, there ...

EPFL2019

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

Daniel Kuhn, John Lygeros, Peyman Mohajerin Esfahani, 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

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Fabio Nobile, Francesca Bonizzoni

The present work concerns the approximation of the solution map

S

associated to the parametric Helmholtz boundary value problem, i.e., the map which associates to each (real) wavenumber belonging to a given interval of interest the corresponding solution ...

2018

Barycentric Bounds in Stochastic Programming: Theory and Application

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Contextual Stochastic Bilevel Optimization

Localization errors of the stochastic heat equation

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Preconditioners for robust optimal control problems under uncertainty

Multi-armed Bandits in Action

MATHICSE Technical Report : A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters

The Decision Rule Approach to Optimisation under Uncertainty: Methodology and Applications

Scalable Convex Optimization Methods for Semidefinite Programming

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

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Contextual Stochastic Bilevel Optimization

Preconditioners for robust optimal control problems under uncertainty

Localization errors of the stochastic heat equation

Scalable Convex Optimization Methods for Semidefinite Programming

The Decision Rule Approach to Optimisation under Uncertainty: Methodology and Applications

Functional estimation of anisotropic covariance and autocovariance operators on the sphere

Convergence analysis of Padé approximations for Helmholtz frequency response problems

Multi-armed Bandits in Action

MATHICSE Technical Report : A Multilevel Stochastic Gradient method for PDE-constrained Optimal Control Problems with uncertain parameters

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