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

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Byzantine tolerant gradient descent for distributed machine learning with adversaries

Rachid Guerraoui, El Mahdi El Mhamdi, Julien Michel Stainer, Peva François Blanchard

The present application concerns a computer-implemented method for training a machine learning model in a distributed fashion, using Stochastic Gradient Descent, SGD, wherein the method is performed by a first computer in a distributed computing environmen ...

2019

We propose a non-parametric regression method that does not rely on the structure of the ground-truth, but only on its regularity properties. The methodology can be readily used for learning surrogate models of nonlinear dynamical systems from data, while ...

2019

We consider an optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. The control function is a deterministic, distributed forcing term that minimizes an expected quadratic regularized loss functional. We cons ...

2018

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We consider the numerical approximation of a risk-averse optimal control problem for an elliptic partial differential equation (PDE) with random coefficients. Specifically, the control function is a deterministic, dis- tributed forcing term that minimizes ...

MATHICSE2018

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Aerodynamic shape optimization has many industrial applications. Existing methods, however, are so computationally demanding that typical engineering practices are to either simply try a limited number of hand-designed shapes or restrict oneself to shapes ...

2018

Uncertainty Quantification of geochemical and mechanical compaction in layered sedimentary basins

Fabio Nobile, Lorenzo Tamellini, Anna Scotti

In this work we propose an Uncertainty Quantification methodology for sedimentary basins evolution under mechanical and geochemical compaction processes, which we model as a coupled, time-dependent, non-linear, monodimensional (depth-only) system of PDEs w ...

Elsevier2018

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We propose a stochastic optimization method for the minimization of the sum of three convex functions, one of which has Lipschitz continuous gradient as well as restricted strong convexity. Our approach is most suitable in the setting where it is computati ...

2016

On the influence of momentum acceleration on online learning

Ali H. Sayed, Bicheng Ying, Kun Yuan

This paper examines the convergence rate and mean-square-error performance of momentum stochastic gradient methods in the constant step-size and slow adaptation regime. The results establish that momentum methods are equivalent to the standard stochastic g ...

IEEE2016

Multi-index Monte Carlo: when sparsity meets sampling

Fabio Nobile

We propose and analyze a novel Multi Index Monte Carlo (MIMC) method for weak approximation of stochastic models that are described in terms of differential equations either driven by random measures or with random coefficients. The MIMC method is both a s ...

2016

Expected Loss Analysis for Authentication in Constrained Channels

Serge Vaudenay, Christos Dimitrakakis, Aikaterini Mitrokotsa

We derive bounds on the expected loss for authentication protocols in channels which are constrained due to noisy conditions and communication costs. This is motivated by a number of authentication protocols, where at least some part of the authentication ...

IOS Press2015