El Instituto de Ingeniería Matemática y Computacional (IMC) los saluda atentamente y los invita al seminario que se dictará la próxima semana.
Juan Pablo Contreras, Instituto de Ingeniería Matemática y Computacional (IMC), Pontificia Universidad Católica de Chile.
Miércoles 23 de octubre de 2024, 13:40 hrs. (Presencial en auditorio Edificio San Agustín; link Zoom disponible escribiendo a Esta dirección de correo electrónico está siendo protegida contra los robots de spam. Necesita tener JavaScript habilitado para poder verlo.)
ABSTRACT
Fixed-point iterations provide a systematic method to approximate solutions for a wide range of problems, including operator equations, nonlinear equations, and optimization tasks. Recently, stochastic variants of these iterations have garnered attention due to their applicability in scenarios where the underlying operators are uncertain, noisy, or random. However, despite this growing interest, stochastic fixed-point iterations in non-Euclidean settings remain underexplored compared to related frameworks, such as stochastic monotone inclusions, variational inequalities, or stochastic optimization, which are predominantly studied in Euclidean spaces.
In this talk, we analyze the oracle complexity of stochastic Mann-type iterations designed to approximate fixed points of nonexpansive and contractive maps in a finite-dimensional space equipped with a general norm. We establish both upper and lower bounds on the convergence rate of the fixed-point residual and provide conditions for almost sure convergence of the iterates. Our findings have potential applications in reinforcement learning and bilevel optimization.
