# Thompson Sampling for Adversarial Bit Prediction

arXiv: https://arxiv.org/abs/1906.09059 · HTML: https://mlsanity.com/paper/1906.09059/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 1 of 1)

- [Best-Case Lower Bounds in Online Learning](https://mlsanity.com/paper/2106.12688/) (2021)

## Abstract (arXiv)

We study the Thompson sampling algorithm in an adversarial setting, specifically, for adversarial bit prediction. We characterize the bit sequences with the smallest and largest expected regret. Among sequences of length T with k < fracT2 zeros, the sequences of largest regret consist of alternating zeros and ones followed by the remaining ones, and the sequence of smallest regret consists of ones followed by zeros. We also bound the regret of those sequences, the worse case sequences have regret O(√T) and the best case sequence have regret O(1). We extend our results to a model where false positive and false negative errors have different weights. We characterize the sequences with largest expected regret in this generalized setting, and derive their regret bounds. We also show that there are sequences with O(1) regret.