# Profitable Bandits

arXiv: https://arxiv.org/abs/1805.02908 · HTML: https://mlsanity.com/paper/1805.02908/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 May 2018.

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

- [Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits](https://mlsanity.com/paper/2406.06552/) (2024)

## Abstract (arXiv)

Originally motivated by default risk management applications, this paper investigates a novel problem, referred to as the profitable bandit problem here. At each step, an agent chooses a subset of the K possible actions. For each action chosen, she then receives the sum of a random number of rewards. Her objective is to maximize her cumulated earnings. We adapt and study three well-known strategies in this purpose, that were proved to be most efficient in other settings: kl-UCB, Bayes-UCB and Thompson Sampling. For each of them, we prove a finite time regret bound which, together with a lower bound we obtain as well, establishes asymptotic optimality. Our goal is also to compare these three strategies from a theoretical and empirical perspective both at the same time. We give simple, self-contained proofs that emphasize their similarities, as well as their differences. While both Bayesian strategies are automatically adapted to the geometry of information, the numerical experiments carried out show a slight advantage for Thompson Sampling in practice.