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On conditional versus marginal bias in multi-armed bandits
Jaehyeok Shin · Aaditya Ramdas · Alessandro Rinaldo

Wed Jul 15 08:00 AM -- 08:45 AM & Wed Jul 15 07:00 PM -- 07:45 PM (PDT) @ Virtual #None

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. We further demonstrate, through several examples from sequential testing and best arm identification, that the sign of the conditional and marginal bias of the sample mean of an arm can be different, depending on the conditioning event. Our analysis offers new and interesting perspectives on the subtleties of assessing the bias in data adaptive settings.

Author Information

Jaehyeok Shin (Carnegie Mellon University)
Aaditya Ramdas (Carnegie Mellon University)

Aaditya Ramdas is an assistant professor in the Departments of Statistics and Machine Learning at Carnegie Mellon University. These days, he has 3 major directions of research: 1. selective and simultaneous inference (interactive, structured, post-hoc control of false discovery/coverage rate,…), 2. sequential uncertainty quantification (confidence sequences, always-valid p-values, bias in bandits,…), and 3. assumption-free black-box predictive inference (conformal prediction, calibration,…).

Alessandro Rinaldo (Carnegie Mellon University)

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