  We propose a method that achieves near-optimal rates for smooth stochastic
convex optimization and requires essentially no prior knowledge of problem
parameters. This improves on prior work which requires knowing at least the
initial distance to optimality d0. Our method, U-DoG, combines UniXGrad (Kavis
et al., 2019) and DoG (Ivgi et al., 2023) with novel iterate stabilization
techniques. It requires only loose bounds on d0 and the noise magnitude,
provides high probability guarantees under sub-Gaussian noise, and is also
near-optimal in the non-smooth case. Our experiments show consistent, strong
performance on convex problems and mixed results on neural network training.
