Deterministic and stochastic fixed-point iterations in normed spaces.

Abstract:

In this talk, we present a survey of techniques and results on error bounds and convergence rates for both deterministic and stochastic fixed-point iterations, with a focus on methods such as the Krasnoselskii-Mann and Halpern iterations. Our primary emphasis is on general normed spaces, where we employ tools from optimal transport to derive tight error bounds. For spaces with additional structure, such as Hilbert spaces, we also discuss existing techniques and the sharp results established in the literature. Finally, we highlight applications of these findings in reinforcement learning and optimization, and outline open questions and potential directions for future research.

Posted on Jun 12, 2025 in Seminars, SIPo (Seminario de Investigadores Postdoctorales)