A new regret analysis for Adam-type algorithms

Ahmet Alacaoglu (1) , Yura Malitsky (1) , Panayotis Mertikopoulos (2, 3) , Volkan Cevher (1)

1 EPFL - Ecole Polytechnique Fédérale de Lausanne
2 POLARIS - Performance analysis and optimization of LARge Infrastructures and Systems
3 Criteo AI Lab

In this paper, we focus on a theory-practice gap for Adam and its variants (AMSgrad, AdamNC, etc.). In practice, these algorithms are used with a constant first-order moment parameter β 1 (typically between 0.9 and 0.99). In theory, regret guarantees for online convex optimization require a rapidly decaying β 1 → 0 schedule. We show that this is an artifact of the standard analysis, and we propose a novel framework that allows us to derive optimal, data-dependent regret bounds with a constant β 1 , without further assumptions. We also demonstrate the flexibility of our analysis on a wide range of different algorithms and settings.

Domaines: Optimisation et contrôle [math.OC]

Ahmet Alacaoglu, Yura Malitsky, Panayotis Mertikopoulos, Volkan Cevher. A new regret analysis for Adam-type algorithms. ICML 2020 - 37th International Conference on Machine Learning, Jul 2020, Vienna, Austria. pp.1-10. ⟨hal-03043697⟩