In Naples last month, at the European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML PKDD), Amazon senior applied scientist Hamed Karimi and colleagues won the 2026 ECML PKDD Test-of-Time Award for their 2016 paper “Linear convergence of gradient and proximal-gradient methods under the Polyak–Łojasiewicz condition”. The award recognizes research published a decade earlier that has had a lasting impact.
The paper, written with Julie Nutini and Mark Schmidt while Karimi was a postdoctoral researcher at the University of British Columbia, has helped to organize a previously scattered field of machine learning optimization and offers useful approaches to analyzing new training methods.
“When we wrote the paper in 2016, we genuinely didn’t expect it to make a splash,” Karimi says. “We did not know that the result would become part of the way researchers analyze optimization in machine learning.”
Karimi and his coauthors showed that the Polyak-Łojasiewicz condition, a 1963 mathematical inequality that had been largely overlooked in machine learning, can prove that the standard method for training machine learning models closes in on…