arXiv subjects

Sabrina Khurshid

Publications and source records attributed to Sabrina Khurshid.

3 recordsLinked to original sources

arXiv2026

Order Optimal Regret Bounds for Sharpe Ratio Optimization under Thompson Sampling

In this paper, we study sequential decision-making for maximizing the Sharpe ratio (SR) in a stochastic multi-armed bandit (MAB) setting. Unlike standard bandit formulations that maximize cumulative reward, SR optimization requires balancing expected return and reward variability. As a result, the learning objective depends jointly on the mean and variance of the reward distribution and takes a fractional form. To address this problem, we propose the Sharpe Ratio Thompson Sampling \texttt{SRTS}, a Bayesian algorithm for risk-adjusted exploration. For Gaussian reward models, the algorithm employs a Normal-Gamma conjugate posterior to capture uncertainty in both the mean and the precision of each arm. In contrast to additive mean-variance (MV) formulations, which often require different algorithms across risk regimes, the fractional SR objective yields a single sampling rule that applies uniformly across risk tolerances. On the theoretical side, we develop a regret decomposition tailored to the SR objective and introduce a decoupling approach that separates the contributions of mean and variance uncertainty. This framework allows us to control the interaction between the Gaussian mean samples and the Gamma precision samples arising in the posterior. Using these results, we establish a finite-time distribution-dependent $\mathcal{O}(\log n)$ upper bound on the expected regret. We further derive a matching information-theoretic lower bound using a change-of-measure argument, showing that the proposed algorithm is order-optimal. Finally, experiments on synthetic bandit environments illustrate the performance of \texttt{SRTS} and demonstrate improvements over existing risk-aware bandit algorithms across a range of risk-return settings.

cs.LG↗

arXiv2026

Variance-Optimal Arm Selection: Misallocation Minimization and Best Arm Identification

This paper focuses on selecting the arm with the highest variance from a set of $K$ independent arms. Specifically, we focus on two settings: (i) misallocation minimization setting, that penalizes the number of pulls of suboptimal arms in terms of variance, and (ii) fixed-budget best arm identification setting, that evaluates the ability of an algorithm to determine the arm with the highest variance after a fixed number of pulls. We develop a novel online algorithm called UCB-VV for the misallocation minimization (MM) and show that its upper bound on misallocation for bounded rewards evolves as $\mathcal{O}\left(\log{n}\right)$ where $n$ is the horizon. By deriving the lower bound on the misallocation, we show that UCB-VV is order optimal. For the fixed budget best arm identification (BAI) setting we propose the SHVV algorithm. We show that the upper bound of the error probability of SHVV evolves as $\exp\left(-\frac{n}{\log(K) H}\right)$, where $H$ represents the complexity of the problem, and this rate matches the corresponding lower bound. We extend the framework from bounded distributions to sub-Gaussian distributions using a novel concentration inequality on the sample variance and standard deviation. Leveraging the same, we derive a concentration inequality for the empirical Sharpe ratio (SR) for sub-Gaussian distributions, which was previously unknown in the literature. Empirical simulations show that UCB-VV consistently outperforms $ε$-greedy across different sub-optimality gaps though it is surpassed by VTS, which exhibits the lowest misallocation, albeit lacking in theoretical guarantees. We also illustrate the superior performance of SHVV, for a fixed budget setting under 6 different setups against uniform sampling. Finally, we conduct a case study to empirically evaluate the performance of the UCB-VV and SHVV in call option trading on $100$ stocks generated using GBM.

cs.LG↗

arXiv2024

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

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.

q-fin.PM↗