We introduce a novel approach (COpt) to Fixed-Budget Best-Arm Identification (FBBAI) specifically designed for contexts where both the expected rewards and their variances are unknown a priori.

Our methodology starts with the derivation of a general upper bound on the misidentification probability applicable to sub-Gaussian distributions. Based on this theoretical foundation, we develop an algorithm that iteratively solves a non-linear optimization problem over empirical estimators to determine the optimal allocation of the residual sampling budget among the arms.

We conducted empirical validation across a range of synthetic distribution classes and a real-world scenario based on the MovieLens dataset. Experimental results demonstrate that COpt consistently achieves superior accuracy compared to established algorithms, including Sequential Halving, VBR, and Gap-EV. Execution time remains within the range of tens of milliseconds, making it suitable for a wide range of applications.