Publications related to Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions 2: Numerical integrators

Localization errors of the stochastic heat equation

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

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Nicolas Boumal, Christopher Arnold Criscitiello

We describe the first gradient methods on Riemannian manifolds to achieve accelerated rates in the non-convex case. Under Lipschitz assumptions on the Riemannian gradient and Hessian of the cost function, these methods find approximate first-order critical ...

SPRINGER2022

AKSEL: Fast Byzantine SGD

Rachid Guerraoui, El Mahdi El Mhamdi, Alexandre David Olivier Maurer, Sébastien Louis Alexandre Rouault

Modern machine learning architectures distinguish servers and workers. Typically, a d-dimensional model is hosted by a server and trained by n workers, using a distributed stochastic gradient descent (SGD) optimization scheme. At each SGD step, the goal is ...

Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik2021

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Fabio Nobile, Sebastian Krumscheid, Matthieu Claude Martin

We consider the numerical approximation of an optimal control problem for an elliptic Partial Differential Equation (PDE) with random coefficients. Specifically, the control function is a deterministic, distributed forcing term that minimizes the expected ...

2021

Learning Generalized Nash Equilibria in a Class of Convex Games

Maryam Kamgarpour

We consider multiagent decision making where each agent optimizes its convex cost function subject to individual and coupling constraints. The constraint sets are compact convex subsets of a Euclidean space. To learn Nash equilibria, we propose a novel dis ...

2019

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Sebastian Urban Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...

2018

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Sebastian Urban Stich

We present the first accelerated randomized algorithm for solving linear systems in Euclidean spaces. One essential problem of this type is the matrix inversion problem. In particular, our algorithm can be specialized to invert positive definite matrices i ...

NEURAL INFORMATION PROCESSING SYSTEMS (NIPS)2018

Improved stability of optimal traffic paths

Maria Colombo

Models involving branched structures are employed to describe several supply-demand systems such as the structure of the nerves of a leaf, the system of roots of a tree, and the nervous or cardiovascular systems. Given a flow (traffic path) that transports ...

2018

Testing Graph Clusterability: Algorithms and Lower Bounds

Mikhail Kapralov, Aidasadat Mousavifar, Ashish Hari Chiplunkar

We consider the problem of testing graph cluster structure: given access to a graph G = (V, E), can we quickly determine whether the graph can be partitioned into a few clusters with good inner conductance, or is far from any such graph? This is a generali ...

IEEE COMPUTER SOC2018

Design and Performance Evaluation of an Infotaxis-Based Three-Dimensional Algorithm for Odor Source Localization

Alcherio Martinoli, Ali Marjovi, Faezeh Rahbar, Julian Ruddick

In this paper we tackle the problem of finding the source of a gaseous leak with a robot in a three-dimensional (3-D) physical space. The proposed method extends the operational range of the probabilistic Infotaxis algorithm [1] into 3-D and makes multiple ...

IEEE2018

Mixing of Hamiltonian Monte Carlo on strongly log-concave distributions 2: Numerical integrators

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Localization errors of the stochastic heat equation

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

AKSEL: Fast Byzantine SGD

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Learning Generalized Nash Equilibria in a Class of Convex Games

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

Improved stability of optimal traffic paths

Testing Graph Clusterability: Algorithms and Lower Bounds

Design and Performance Evaluation of an Infotaxis-Based Three-Dimensional Algorithm for Odor Source Localization

Localization errors of the stochastic heat equation

Testing Graph Clusterability: Algorithms and Lower Bounds

Learning Generalized Nash Equilibria in a Class of Convex Games

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization

AKSEL: Fast Byzantine SGD

Complexity analysis of stochastic gradient methods for PDE-constrained optimal control problems with uncertain parameters

Improved stability of optimal traffic paths

Design and Performance Evaluation of an Infotaxis-Based Three-Dimensional Algorithm for Odor Source Localization

An Accelerated First-Order Method for Non-convex Optimization on Manifolds

Accelerated Stochastic Matrix Inversion: General Theory and Speeding up BFGS Rules for Faster Second-Order Optimization