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This paper proposes a new easy-to-implement parameter-free gradient-basedoptimizer: DoWG (Distance over Weighted Gradients). We prove that DoWG isefficient -- matching the convergence rate of optimally tuned gradient descentin convex optimization up to a logarithmic factor without tuning anyparameters, and universal -- automatically adapting to both smooth andnonsmooth problems. While popular algorithms following the AdaGrad frameworkcompute a running average of the squared gradients to use for normalization,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, andvalidate its effectiveness on practical machine learning tasks.

DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method