# Optimizing Sharpe Ratio: Risk-Adjusted Decision-Making in Multi-Armed Bandits

arXiv: https://arxiv.org/abs/2406.06552 · HTML: https://mlsanity.com/paper/2406.06552/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 46 references that are in the map.
- First posted on arXiv 28 May 2024.

## Builds on (most cited first, 10 of 10)

- [Tight (Lower) Bounds for the Fixed Budget Best Arm Identification Bandit Problem](https://mlsanity.com/paper/1605.09004/) (2016)
- [Reliable training and estimation of variance networks](https://mlsanity.com/paper/1906.03260/) (2019)
- [Thompson Sampling Algorithms for Mean-Variance Bandits](https://mlsanity.com/paper/2002.00232/) (2020)
- [Efficient-UCBV: An Almost Optimal Algorithm using Variance Estimates](https://mlsanity.com/paper/1711.03591/) (2017)
- [Distribution oblivious, risk-aware algorithms for multi-armed bandits with unbounded rewards](https://mlsanity.com/paper/1906.00569/) (2019)
- [Almost Optimal Variance-Constrained Best Arm Identification](https://mlsanity.com/paper/2201.10142/) (2022)
- [Optimal Best Arm Identification in Two-Armed Bandits with a Fixed Budget under a Small Gap](https://mlsanity.com/paper/2201.04469/) (2022)
- [Stochastic Multi-armed Bandits with Non-stationary Rewards Generated by a Linear Dynamical System](https://mlsanity.com/paper/2204.05782/) (2022)
- [Profitable Bandits](https://mlsanity.com/paper/1805.02908/) (2018)
- [Near-Optimal MNL Bandits Under Risk Criteria](https://mlsanity.com/paper/2009.12511/) (2020)

## Built on by (most cited first, 2 of 2)

- [Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification](https://mlsanity.com/paper/2505.11985/) (2025)
- [Order Optimal Regret Bounds for Sharpe Ratio Optimization under Thompson Sampling](https://mlsanity.com/paper/2508.13749/) (2025)

## Abstract (arXiv)

Sharpe Ratio (SR) is a critical parameter in characterizing financial time series as it jointly considers the reward and the volatility of any stock/portfolio through its variance. Deriving online algorithms for optimizing the SR is particularly challenging since even offline policies experience constant regret with respect to the best expert Even-Dar et al (2006). Thus, instead of optimizing the usual definition of SR, we optimize regularized square SR (RSSR). We consider two settings for the RSSR, Regret Minimization (RM) and Best Arm Identification (BAI). In this regard, we propose a novel multi-armed bandit (MAB) algorithm for RM called UCB-RSSR for RSSR maximization. We derive a path-dependent concentration bound for the estimate of the RSSR. Based on that, we derive the regret guarantees of UCB-RSSR and show that it evolves as O(log n) for the two-armed bandit case played for a horizon n. We also consider a fixed budget setting for well-known BAI algorithms, i.e., sequential halving and successive rejects, and propose SHVV, SHSR, and SuRSR algorithms. We derive the upper bound for the error probability of all proposed BAI algorithms. We demonstrate that UCB-RSSR outperforms the only other known SR optimizing bandit algorithm, U-UCB Cassel et al (2023). We also establish its efficacy with respect to other benchmarks derived from the GRA-UCB and MVTS algorithms. We further demonstrate the performance of proposed BAI algorithms for multiple different setups. Our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems. Consequently, our research highlights that our proposed algorithms will find extensive applications in risk-aware portfolio management problems.