Abstract

Acceleration in first-order methods is often viewed through the lens of momentum or extrapolation, but these interpretations can become opaque in non-Euclidean geometries. In this talk, we introduce the Adaptive Integrated Mean (AIM), a novel framework that interprets acceleration as an adaptive averaging process integrated directly into the optimization step. Using AIM, we first provide a transparent recovery of the optimal $O(1/k^2)$ rate for FISTA. We then tackle the more challenging ``smooth adaptability" framework, where classical acceleration is typically elusive. We derive the Bregman Accelerated Proximal Gradient (BAPG) method and demonstrate that for the Boltzmann-Shannon entropy kernel, BAPG achieves a nearly-optimal $O(\log k/k^2)$ rate. This result provides the first accelerated guarantee for this fundamental geometry, bridging the gap between Euclidean acceleration and smooth adaptability. This talk is based on joint work with Roey Merchav and Marc Teboulle.

Bioography

Shoham Sabach joined the School of Operations Research and Information Engineering at Cornell in 2025 as an Associate Professor. His research focuses on mathematical optimization, spanning both theoretical foundations and applications in areas such as machine learning, data science, and artificial intelligence. Prior to Cornell, he was an associate professor on the faculty of Data and Decision Sciences at the Technion – Israel Institute of Technology and served as an Amazon Scholar at Amazon Research, where he worked on optimization for large-scale AI systems, including large language models. He received his Ph.D. in Mathematics from the Technion in 2012. His honors include the 2019 Rothblum Award – ORSIS Prize for Excellence in Research in OR, the 2018 Cooper Prize for Research Excellence at the Technion, the 2017 SIAM Activity Group on Optimization (SIAG/OPT) Prize for the Most Outstanding Paper in Optimization, and a Humboldt Postdoctoral Fellowship.