Data Dependent Regret Guarantees Against General Comparators for Full or Bandit Feedback
This work offers a flexible solution for various online learning scenarios, such as switching or contextual bandits, but it appears incremental as it builds on existing universal prediction perspectives without introducing a fundamentally new paradigm.
The authors tackled the adversarial online learning problem by developing a completely online algorithmic framework that provides data-dependent regret guarantees for both full expert and bandit feedback settings, achieving performance bounds that are invariant to affine transformations of losses.
We study the adversarial online learning problem and create a completely online algorithmic framework that has data dependent regret guarantees in both full expert feedback and bandit feedback settings. We study the expected performance of our algorithm against general comparators, which makes it applicable for a wide variety of problem scenarios. Our algorithm works from a universal prediction perspective and the performance measure used is the expected regret against arbitrary comparator sequences, which is the difference between our losses and a competing loss sequence. The competition class can be designed to include fixed arm selections, switching bandits, contextual bandits, periodic bandits or any other competition of interest. The sequences in the competition class are generally determined by the specific application at hand and should be designed accordingly. Our algorithm neither uses nor needs any preliminary information about the loss sequences and is completely online. Its performance bounds are data dependent, where any affine transform of the losses has no effect on the normalized regret.