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Entropy regularization is known to improve exploration in sequentialdecision-making problems. We show that this same mechanism can also lead tonearly unbiased and lower-variance estimates of the mean reward in theoptimize-and-estimate structured bandit setting. Mean reward estimation (i.e.,population estimation) tasks have recently been shown to be essential forpublic policy settings where legal constraints often require precise estimatesof population metrics. We show that leveraging entropy and KL divergence canyield a better trade-off between reward and estimator variance than existingbaselines, all while remaining nearly unbiased. These properties of entropyregularization illustrate an exciting potential for bridging the optimalexploration and estimation literatures.

Entropy Regularization for Population Estimation