Policy Learning with Weak Signals

Benedikt Koch, Winston Chou, Aurélien Bibaut, Nathan Kallus

Policy learning in digital experimentation faces three challenges: weak signal-to-noise ratios, rich covariate spaces, and massive data volumes. We formalize this regime by modeling treatment-effect estimates from increasingly fine covariate partitions as Gaussian observations with bounded signal-to-noise ratios. We establish that, in general, the optimal treatment policy is not learnable in this setting. Even learning the optimal policy value suffers from impractically slow rates. However, when treatment effects vary smoothly, we derive minimax-adaptive policies based on linear smoothers that achieve vanishing welfare regret. We demonstrate the practical value of our framework by applying it to large-scale real-world experiments at Netflix, showing that personalized linear-smoothing policies can dominate unpersonalized policies even in this challenging empirical setting.