Parameter-free Mirror Descent
Abstract
We develop a modified online mirror descent framework that is suitable for building adaptive and parameter-free algorithms in unbounded domains. We leverage this technique to develop the first unconstrained online linear optimization algorithm achieving an optimal dynamic regret bound, and we further demonstrate that natural strategies based on Follow-the-Regularized-Leader are unable to achieve similar results. We also apply our mirror descent framework to build new parameter-free implicit updates, as well as a simplified and improved unconstrained scale-free algorithm.
Cite
@article{arxiv.2203.00444,
title = {Parameter-free Mirror Descent},
author = {Andrew Jacobsen and Ashok Cutkosky},
journal= {arXiv preprint arXiv:2203.00444},
year = {2024}
}
Comments
59 pages. v4: Added a new section (7. Trade-offs in the Horizon Dependence) discussing how to achieve an alternative type of parameter-free bound using our framework; v3: published at COLT 2022 + fixed typos; v2: improved the algorithms in sections 3, 5, and 6 (tighter regret, simpler updates and analysis), corrected minor technical details and fixed typos