Second Order Regret Bounds Against Generalized Expert Sequences under Partial Bandit Feedback
This work addresses the challenge of making robust predictions in online learning with limited feedback, which is incremental as it extends existing frameworks to more adversarial loss revelation scenarios.
The paper tackles the problem of expert advice under partial bandit feedback by developing a sequential minimax optimal algorithm that works in a generalized partial monitoring setting, achieving second-order regret bounds in terms of the sum of squared losses.
We study the problem of expert advice under partial bandit feedback setting and create a sequential minimax optimal algorithm. Our algorithm works with a more general partial monitoring setting, where, in contrast to the classical bandit feedback, the losses can be revealed in an adversarial manner. Our algorithm adopts a universal prediction perspective, whose performance is analyzed with regret against a general expert selection sequence. The regret we study is against a general competition class that covers many settings (such as the switching or contextual experts settings) and the expert selection sequences in the competition class are determined by the application at hand. Our regret bounds are second order bounds in terms of the sum of squared losses and the normalized regret of our algorithm is invariant under arbitrary affine transforms of the loss sequence. Our algorithm is truly online and does not use any preliminary information about the loss sequences.