Many scientific experiments have an interest in the estimation of the average treatment effect (ATE), which is defined as the difference between the expected outcomes of two or more treatments. In this paper, we consider a situation called adaptive experimental design where research subjects sequentially visit a researcher, and the researcher assigns a treatment. For estimating the ATE efficiently, we consider changing the probability of assigning a treatment at a period by using past information obtained until the period . However, in this approach, it is difficult to apply the standard statistical method to construct an estimator because the observations are not independent and identically distributed. In this paper, to construct an efficient estimator, we overcome this conventional problem by using an algorithm of the multi-armed bandit problem and the theory of martingale. In the proposed method, we use the probability of assigning a treatment that minimizes the asymptotic variance of an estimator of the ATE. We also elucidate the theoretical properties of an estimatorobtained from the proposed algorithm for both infinite and finite samples . Finally, we experimentally show that the proposed algorithm outperforms the standard RCT in some cases .
The goal of many scientific experiments including A/B testing is to estimate the average treatment effect (ATE), which is defined as the difference between the expected outcomes of two or more treatments. In this paper, we consider a situation where an experimenter can assign a treatment to research subjects sequentially . In adaptive experimental design, the experimenter is allowed to change the probability of assigning a treatment using past observations for estimating the ATE efficiently . However, with this approach, it is difficult to apply a standard statistical method to construct an estimator because the observations are not independent and identically distributed. We thus propose an algorithm for efficient experiments with estimators constructed from dependent samples. We also introduce a sequential testing framework using the proposed estimator. To justify our proposed approach, we provide finite and infinite sample analyses . Finally, we experimentally show that the proposed algorithm exhibits preferable performance .
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Many scientific experiments have an interest in the estimation of the
The goal of many scientific experiments including A/B testing is to estimate the
R
called adaptive experimental design where
where an experimenter can assign a treatment to
R
visit a researcher, and the researcher assigns a treatment. For estimating the ATE efficiently, we consider changing the
. In adaptive experimental design, the experimenter is allowed to change the
R
at a period by using past information obtained until the period
using past observations for estimating the ATE efficiently
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in
with
R
the
a
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In this paper, to construct an efficient estimator, we overcome this conventional problem by using an algorithm of the multi-armed bandit problem and the theory of martingale. In the proposed method, we use the probability of assigning a treatment that minimizes the asymptotic variance of an estimator of the ATE. We also elucidate the theoretical properties of an estimatorobtained from the proposed algorithm for both infinite and finite samples
We thus propose an algorithm for efficient experiments with estimators constructed from dependent samples. We also introduce a sequential testing framework using the proposed estimator. To justify our proposed approach, we provide finite and infinite sample analyses
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outperforms the standard RCT in some cases
exhibits preferable performance