  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.
