On conditional versus marginal bias in multi-armed bandits

Understand

The bias of the sample means of the arms in multi-armed bandits is an important issue in adaptive data analysis that has recently received considerable attention in the literature.

• Existing results relate in precise ways the sign and magnitude of the bias to various sources of data adaptivity, but do not apply to the conditional inference setting in which the sample means are computed only if some specific conditions are satisfied.
• In this paper, we characterize the sign of the conditional bias of monotone functions of the rewards, including the sample mean.
• Our results hold for arbitrary conditioning events and leverage natural monotonicity properties of the data collection policy.