Adaptive Neyman Allocation
This paper addresses the optimal sample allocation problem in multi-stage randomized controlled trials when group variances (treatment and control) are unknown. We propose Adaptive Neyman Allocation: a method that dynamically estimates inter-group variances from early-stage data and continuously optimizes subsequent-stage assignment ratios to minimize the variance of the treatment effect estimator. We introduce, for the first time, a competitive analysis framework into experimental design; theoretically, our algorithm achieves an Ω(√log M) competitive ratio over T total samples and M stages, approaching the information-theoretic lower bound. Our approach breaks from the conventional fixed 1:1 allocation paradigm by enabling variance-driven, stage-wise optimal allocation. Empirical evaluation on real-world A/B tests at a major social platform demonstrates its effectiveness: under finite-stage constraints, estimation accuracy improves by over 30% compared to standard designs.