Generalized Translation and Scale Invariant Online Algorithm for Adversarial Multi-Armed Bandits

TL;DR

This paper introduces a fully online, translation and scale-invariant algorithm for adversarial multi-armed bandits, capable of competing against diverse classes of loss sequences without prior knowledge.

Contribution

It presents a novel, universal prediction framework that maintains invariance under transformations and adapts to various competition classes in adversarial bandit problems.

Findings

Achieves second-order regret bounds based on squared losses.

Invariance under affine transformations of loss sequences.

Applicable to fixed, switching, and contextual bandit scenarios.

Abstract

We study the adversarial multi-armed bandit problem and create a completely online algorithmic framework that is invariant under arbitrary translations and scales of the arm losses. We study the expected performance of our algorithm against a generic competition class, 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 arm selection 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, 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 the second order bounds in terms of sum of the squared losses, where any affine transform of the losses has no effect on the normalized regret.