10 accepted papers
We present several advances on neural operators by viewing the action of operator layers as the minimizers of Bregman regularized optimization problems over Banach function spaces. The proposed framework allows interpreting the activation operators as Bregman proximity operators from dual to primal…
We study the problem of efficiently computing the derivative of the fixed-point of a parametric nondifferentiable contraction map. This problem has wide applications in machine learning, including hyperparameter optimization, meta-learning and data poisoning attacks. We analyze two popular approache…
In this work we propose a batch multimarginal version of the Greenkhorn algorithm for the entropic-regularized optimal transport problem. This framework is general enough to cover, as particular cases, existing Sinkhorn and Greenkhorn algorithms for the bi-marginal setting, and greedy MultiSinkhorn…
We present a framework based on bilevel optimization for learning multilayer, deep data representations. On the one hand, the lower-level problem finds a representation by successively minimizing layer-wise objectives made of the sum of a prescribed regularizer as well as a fidelity term and some li…
Bilevel optimization problems are receiving increasing attention in machine learning as they provide a natural framework for hyperparameter optimization and meta-learning. A key step to tackle these problems is the efficient computation of the gradient of the upper-level objective (hypergradient). I…
We study a general class of bilevel problems, consisting in the minimization of an upper-level objective which depends on the solution to a parametric fixed-point equation. Important instances arising in machine learning include hyperparameter optimization, meta-learning, and certain graph and recur…
We present a novel algorithm to estimate the barycenter of arbitrary probability distributions with respect to the Sinkhorn divergence. Based on a Frank-Wolfe optimization strategy, our approach proceeds by populating the support of the barycenter incrementally, without requiring any pre-allocation.…
We introduce a framework based on bilevel programming that unifies gradient-based hyperparameter optimization and meta-learning. We show that an approximate version of the bilevel problem can be solved by taking into explicit account the optimization dynamics for the inner objective. Depending on th…
Regression with group-sparsity penalty plays a central role in high-dimensional prediction problems. Most of existing methods require the group structure to be known a priori. In practice, this may be a too strong assumption, potentially hampering the effectiveness of the regularization method. To c…
In this paper, we discuss how a suitable family of tensor kernels can be used to efficiently solve nonparametric extensions of lp regularized learning methods. Our main contribution is proposing a fast dual algorithm, and showing that it allows to solve the problem efficiently. Our results contrast…