Black-Box Reductions for Parameter-free Online Learning in Banach Spaces
This work addresses the challenge of parameter-free online learning in Banach spaces for researchers and practitioners in machine learning, offering incremental improvements through reductions.
The paper tackles the problem of designing adaptive and parameter-free online learning algorithms by introducing black-box reductions that simplify analysis, improve regret guarantees, and sometimes runtime, resulting in improved regret bounds for arbitrary norms.
We introduce several new black-box reductions that significantly improve the design of adaptive and parameter-free online learning algorithms by simplifying analysis, improving regret guarantees, and sometimes even improving runtime. We reduce parameter-free online learning to online exp-concave optimization, we reduce optimization in a Banach space to one-dimensional optimization, and we reduce optimization over a constrained domain to unconstrained optimization. All of our reductions run as fast as online gradient descent. We use our new techniques to improve upon the previously best regret bounds for parameter-free learning, and do so for arbitrary norms.