Parameter-free Mirror Descent
This work addresses the need for efficient, parameter-free optimization algorithms in machine learning, offering incremental improvements over existing methods.
The paper tackled the problem of designing adaptive, parameter-free algorithms for online linear optimization in unbounded domains, resulting in the first algorithm achieving an optimal dynamic regret bound and improved scale-free methods.
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.