Zobrazeno 1 - 10
of 78
pro vyhledávání: '"Chizat, Lénaïc"'
Autor:
Chizat, Lénaïc
Publikováno v:
Open Journal of Mathematical Optimization, Vol 3, Iss , Pp 1-19 (2023)
We study the convergence rate of Bregman gradient methods for convex optimization in the space of measures on a $d$-dimensional manifold. Under basic regularity assumptions, we show that the suboptimality gap at iteration $k$ is in $O(\log (k)k^{-1})
Externí odkaz:
https://doaj.org/article/c635d1c8f7c44f52a9cf3120fb43dc05
Autor:
Chizat, Lénaïc
Sinkhorn's algorithm is a method of choice to solve large-scale optimal transport (OT) problems. In this context, it involves an inverse temperature parameter $\beta$ that determines the speed-accuracy trade-off. To improve this trade-off, practition
Externí odkaz:
http://arxiv.org/abs/2408.11620
We study the convergence rate of Sinkhorn's algorithm for solving entropy-regularized optimal transport problems when at least one of the probability measures, $\mu$, admits a density over $\mathbb{R}^d$. For a semi-concave cost function bounded by $
Externí odkaz:
http://arxiv.org/abs/2407.01202
Mean-field Langevin dynamics (MLFD) is a class of interacting particle methods that tackle convex optimization over probability measures on a manifold, which are scalable, versatile, and enjoy computational guarantees. However, some important problem
Externí odkaz:
http://arxiv.org/abs/2406.17054
Autor:
Marion, Pierre, Chizat, Lénaïc
The largest eigenvalue of the Hessian, or sharpness, of neural networks is a key quantity to understand their optimization dynamics. In this paper, we study the sharpness of deep linear networks for univariate regression. Minimizers can have arbitrar
Externí odkaz:
http://arxiv.org/abs/2405.13456
Autor:
Chizat, Lénaïc, Netrapalli, Praneeth
Deep learning succeeds by doing hierarchical feature learning, yet tuning hyper-parameters (HP) such as initialization scales, learning rates etc., only give indirect control over this behavior. In this paper, we introduce a key notion to predict and
Externí odkaz:
http://arxiv.org/abs/2311.18718
Autor:
Chizat, Lénaïc, Vaškevičius, Tomas
We study the computation of doubly regularized Wasserstein barycenters, a recently introduced family of entropic barycenters governed by inner and outer regularization strengths. Previous research has demonstrated that various regularization paramete
Externí odkaz:
http://arxiv.org/abs/2307.13370
Autor:
Wang, Guillaume, Chizat, Lénaïc
We study the convergence to local Nash equilibria of gradient methods for two-player zero-sum differentiable games. It is well-known that such dynamics converge locally when $S \succ 0$ and may diverge when $S=0$, where $S\succeq 0$ is the symmetric
Externí odkaz:
http://arxiv.org/abs/2305.17275
In supervised learning, the regularization path is sometimes used as a convenient theoretical proxy for the optimization path of gradient descent initialized from zero. In this paper, we study a modification of the regularization path for infinite-wi
Externí odkaz:
http://arxiv.org/abs/2303.17805
Autor:
Chizat, Lénaïc
We study a general formulation of regularized Wasserstein barycenters that enjoys favorable regularity, approximation, stability and (grid-free) optimization properties. This barycenter is defined as the unique probability measure that minimizes the
Externí odkaz:
http://arxiv.org/abs/2303.11844