DoWG Unleashed: An Efficient Universal Parameter-Free Gradient Descent Method
This addresses the need for efficient, universal optimization methods in machine learning, though it appears incremental as it builds on the AdaGrad framework.
The paper tackles the problem of parameter tuning in gradient-based optimization by proposing DoWG, a parameter-free optimizer that matches the convergence rate of optimally tuned gradient descent in convex optimization up to a logarithmic factor and adapts to both smooth and nonsmooth problems.
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 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, and validate its effectiveness on practical machine learning tasks.