From the 1 of 224 linked papers with an AI index.
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224 papers
A Stochastic Optimization Approach to Control-Affine Optimal Control Problems
Eloïse Berthier, Ziad Kobeissi, Francis Bach
We consider control-affine optimal control problems on the torus, where the dynamics and cost functions are only accessed through samples. Starting from a weak formulation of such…
Regularized Variational and Spectral Log-Density-Ratio Estimation in the Gaussian Location Model
Francis Bach
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 N(0,…
Variational Gaussian approximation of the Kushner optimal filter
Marc Lambert, Silvère Bonnabel, Francis Bach
In estimation theory, the Kushner equation provides the evolution of the probability density of the state of a dynamical system given continuous-time observations. Building upon ou…
Nonparametric Linear Feature Learning in Regression Through Regularisation
Bertille Follain, Francis Bach
Representation learning plays a crucial role in automated feature selection, particularly in the context of high-dimensional data, where non-parametric methods often struggle. In t…
Sum-of-squares relaxations for polynomial min-max problems over simple sets
Francis Bach
We consider min-max optimization problems for polynomial functions, where a multivariate polynomial is maximized with respect to a subset of variables, and the resulting maximal va…
Theory and applications of the Sum-Of-Squares technique
Francis Bach, Elisabetta Cornacchia, Luca Pesce +1
The Sum-of-Squares (SOS) approximation method is a technique used in optimization problems to derive lower bounds on the optimal value of an objective function. By representing the…