  This paper investigates the best arm identification (BAI) problem in
stochastic multi-armed bandits in the fixed confidence setting. The general
class of the exponential family of bandits is considered. The existing
algorithms for the exponential family of bandits face computational challenges.
To mitigate these challenges, the BAI problem is viewed and analyzed as a
sequential composite hypothesis testing task, and a framework is proposed that
adopts the likelihood ratio-based tests known to be effective for sequential
testing. Based on this test statistic, a BAI algorithm is designed that
leverages the canonical sequential probability ratio tests for arm selection
and is amenable to tractable analysis for the exponential family of bandits.
This algorithm has two key features: (1) its sample complexity is
asymptotically optimal, and (2) it is guaranteed to be $\delta-$PAC. Existing
efficient approaches focus on the Gaussian setting and require Thompson
sampling for the arm deemed the best and the challenger arm. Additionally, this
paper analytically quantifies the computational expense of identifying the
challenger in an existing approach. Finally, numerical experiments are provided
to support the analysis.
