This synopsis summarizes the problems addressed in the dissertation and the main results obtained in the course of studying these problems. We examine stochastic multi-armed bandit (MAB) problems in rare event regimes with emphasis on Best Arm Identification (BAI) and also touch upon regret minimization. When arm rewards occur infrequently but are high in magnitude, we develop algorithms for BAI which are based on Poisson approximation and drastically reduce computational effort at the cost of negligible increase in sample complexity. For identifying the safest system among a given set of safety-critical systems with rare failures, we consider simulation models of the systems, and simulate from them following BAI methods. Reasonably accurate approximations of the lower bound on sample complexity reveal that sample complexity depends on the failure rate of the secondbest system, as opposed to the best. Further, standard regret minimization algorithms are shown to perform poorly in rare-event regimes where rewards are high-value but rarely seen, necessitating scaled modifications that ensure optimality
