Francis Bach

Max-Plus Matching Pursuit for Deterministic Markov Decision Processes

2019 · arXiv (Cornell University)

We consider deterministic Markov decision processes (MDPs) and apply max-plus algebra tools to approximate the value iteration algorithm by a smaller-dimensional iteration based on a representation on dictionaries of value functions. The setup naturally leads …

Online Regularized Nonlinear Acceleration

2018 · arXiv (Cornell University)

Regularized nonlinear acceleration (RNA) estimates the minimum of a function by post-processing iterates from an algorithm such as the gradient method. It can be seen as a regularized version of Anderson acceleration, a classical acceleration …

Harder, Better, Faster, Stronger Convergence Rates for Least-Squares Regression

2016 · arXiv (Cornell University)

We consider the optimization of a quadratic objective function whose gradients are only accessible through a stochastic oracle that returns the gradient at any given point plus a zero-mean finite variance random error. We present …

Structured Prediction with Partial Labelling through the Infimum Loss

2020 · arXiv (Cornell University)

Annotating datasets is one of the main costs in nowadays supervised learning. The goal of weak supervision is to enable models to learn using only forms of labelling which are cheaper to collect, as partial …

Super fast rates in structured prediction

2021 · arXiv (Cornell University)

Discrete supervised learning problems such as classification are often tackled by introducing a continuous surrogate problem akin to regression. Bounding the original error, between estimate and solution, by the surrogate error endows discrete problems with …

Differentiable Clustering with Perturbed Spanning Forests

2023 · arXiv (Cornell University)

We introduce a differentiable clustering method based on stochastic perturbations of minimum-weight spanning forests. This allows us to include clustering in end-to-end trainable pipelines, with efficient gradients. We show that our method performs well even …

Physics-informed kernel learning

2024 · arXiv (Cornell University)

Physics-informed machine learning typically integrates physical priors into the learning process by minimizing a loss function that includes both a data-driven term and a partial differential equation (PDE) regularization. Building on the formulation of the …

Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model

2026 · HAL (Le Centre pour la Communication Scientifique Directe)

We study ridge-regularized log-density-ratio estimation in the Gaussian location model with a common covariance matrix. By affine invariance, the model is written as q $\sim$ N(0, I), p $\sim$ N($Δ$, I), with linear features, where …