Zobrazeno 1 - 10
of 36
pro vyhledávání: '"Eisenmann, Monika"'
Choosing the optimization algorithm that performs best on a given machine learning problem is often delicate, and there is no guarantee that current state-of-the-art algorithms will perform well across all tasks. Consequently, the more reliable metho
Externí odkaz:
http://arxiv.org/abs/2406.16640
Autor:
Eisenmann, Monika, Stillfjord, Tony
In this paper, we combine the operator splitting methodology for abstract evolution equations with that of stochastic methods for large-scale optimization problems. The combination results in a randomized splitting scheme, which in a given time step
Externí odkaz:
http://arxiv.org/abs/2210.05375
Autor:
Eisenmann, Monika, Stillfjord, Tony
In this paper, we introduce the tamed stochastic gradient descent method (TSGD) for optimization problems. Inspired by the tamed Euler scheme, which is a commonly used method within the context of stochastic differential equations, TSGD is an explici
Externí odkaz:
http://arxiv.org/abs/2106.09286
We consider a stochastic version of the proximal point algorithm for optimization problems posed on a Hilbert space. A typical application of this is supervised learning. While the method is not new, it has not been extensively analyzed in this form.
Externí odkaz:
http://arxiv.org/abs/2010.12348
Publikováno v:
BIT Numer. Math. (2021)
In this paper, we derive error estimates of the backward Euler-Maruyama method applied to multi-valued stochastic differential equations. An important example of such an equation is a stochastic gradient flow whose associated potential is not continu
Externí odkaz:
http://arxiv.org/abs/1906.11538
Autor:
Eisenmann, Monika, Hansen, Eskil
Nonlinear parabolic equations are frequently encountered in applications and efficient approximating techniques for their solution are of great importance. In order to provide an effective scheme for the temporal approximation of such equations, we p
Externí odkaz:
http://arxiv.org/abs/1902.10023
For initial value problems associated with operator-valued Riccati differential equations posed in the space of Hilbert--Schmidt operators existence of solutions is studied. An existence result known for algebraic Riccati equations is generalized and
Externí odkaz:
http://arxiv.org/abs/1803.11152
Autor:
Eisenmann, Monika, Kruse, Raphael
In this paper we study the numerical quadrature of a stochastic integral, where the temporal regularity of the integrand is measured in the fractional Sobolev-Slobodeckij norm in $W^{\sigma,p}(0,T)$, $\sigma \in (0,2)$, $p \in [2,\infty)$. We introdu
Externí odkaz:
http://arxiv.org/abs/1712.08152
Publikováno v:
Found. Comput. Math. 19 (2019), 1387-1430
In this paper we introduce a randomized version of the backward Euler method, that is applicable to stiff ordinary differential equations and nonlinear evolution equations with time-irregular coefficients. In the finite-dimensional case, we consider
Externí odkaz:
http://arxiv.org/abs/1709.01018
Autor:
Eisenmann, Monika, Hansen, Eskil
Domain decomposition based time integrators allow the usage of parallel and distributed hardware, making them well-suited for the temporal discretization of parabolic systems, in general, and degenerate parabolic problems, in particular. The latter i
Externí odkaz:
http://arxiv.org/abs/1708.01479