Part of Advances in Neural Information Processing Systems 36 (NeurIPS 2023) Main Conference Track
Ahmed Khaled, Konstantin Mishchenko, Chi Jin
This paper proposes a new easy-to-implement parameter-free gradient-based optimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG is efficient---matching the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor without tuning any parameters, and universal---automatically adapting to both smooth and nonsmooth problems. While popular algorithms following the AdaGrad framework compute a running average of the squared gradients, DoWG maintains a new distance-based weighted version of the running average, which is crucial to achieve the desired properties. To complement our theory, we also show empirically that DoWG trains at the edge of stability, and validate its effectiveness on practical machine learning tasks.