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A Lower Bound and a Near-Optimal Algorithm for Bilevel Empirical Risk Minimization
Mathieu Dagréou, Thomas Moreau, Samuel Vaiter +1
Bilevel optimization problems, which are problems where two optimization problems are nested, have more and more applications in machine learning. In many practical cases, the uppe…
A framework for bilevel optimization that enables stochastic and global variance reduction algorithms
Mathieu Dagréou, Pierre Ablin, Samuel Vaiter +1
Bilevel optimization, the problem of minimizing a value function which involves the arg-minimum of another function, appears in many areas of machine learning. In a large scale emp…
Infeasible Deterministic, Stochastic, and Variance-Reduction Algorithms for Optimization under Orthogonality Constraints
Pierre Ablin, Simon Vary, Bin Gao +1
Orthogonality constraints naturally appear in many machine learning problems, from principal component analysis to robust neural network training. They are usually solved using Rie…
Learning Elastic Costs to Shape Monge Displacements
Michal Klein, Aram-Alexandre Pooladian, Pierre Ablin +3
Given a source and a target probability measure supported on , the Monge problem asks to find the most efficient way to map one distribution to the other. This effici…