Almost Optimal Variance-Constrained Best Arm Identification

We design and analyze Variance-Aware-Lower Upper Confidence Bound (VA-LUCB), a parameter-free algorithm, for identifying the best arm under fixed-confidence setup stringent constraint that variance of chosen is strictly smaller than given threshold. An upper bound on VA-LUCB’s sample complexity shown to be characterized by fundamental variance-aware hardness quantity $H_{\mathrm {VA}}$ . By proving an information-theoretic lower bound, we show VA-LUCB optimal up factor logarithmic in Extensive experiments corroborate dependence various terms comparing empirical performance close competitor RiskAverse-UCB-BAI David et al. (2018) our suggest has lowest this class risk-constrained identification problems, especially riskiest instances.