[Paper Review] Adaptive Experimental Design for Efficient Treatment Effect Estimation: Randomized Allocation via Contextual Bandit Algorithm.

Masahiro Kato, Takuya Ishihara+2 more|arXiv (Cornell University)|Feb 13, 2020

Advanced Bandit Algorithms Research4 citations

TL;DR

This paper proposes an adaptive experimental design using a contextual bandit algorithm to optimize treatment assignment probabilities in real-time, minimizing the asymptotic variance of average treatment effect (ATE) estimators. By leveraging martingale theory and past data, the method improves estimation efficiency over standard randomized controlled trials (RCTs), especially in finite samples, with empirical results showing superior performance in specific scenarios.

ABSTRACT

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 estimator obtained 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.

Motivation & Objective

• To address the inefficiency of standard randomized controlled trials (RCTs) in estimating average treatment effects (ATE) when treatment assignment is fixed.
• To develop a method that adaptively updates treatment assignment probabilities using historical data to reduce estimator variance.
• To overcome the challenge of dependent, non-i.i.d. observations in adaptive designs by applying martingale theory.
• To establish theoretical guarantees for the proposed estimator under both finite and asymptotic sample regimes.
• To empirically validate that the adaptive method outperforms standard RCTs in terms of estimation precision.

Proposed method

• The method uses a multi-armed bandit framework to dynamically adjust treatment assignment probabilities based on accumulated data up to each period.
• It formulates the optimal assignment probability as the one that minimizes the asymptotic variance of the ATE estimator.
• Martingale theory is applied to ensure valid statistical inference despite the dependence induced by adaptive design.
• The algorithm updates treatment assignment probabilities sequentially, using past outcomes to improve estimation efficiency.
• The proposed estimator is shown to be consistent and asymptotically normal under mild regularity conditions.
• The method accounts for contextual information in treatment assignment, enabling personalized and efficient allocation.

Experimental results

Research questions

• RQ1 Can adaptive treatment assignment based on past outcomes reduce the variance of ATE estimators compared to fixed randomization?
• RQ2 How can statistical inference be validly conducted when observations are dependent due to adaptive design?
• RQ3 What is the optimal probability of assigning a treatment at each stage to minimize the asymptotic variance of the ATE estimator?
• RQ4 How does the proposed method perform in finite samples compared to standard RCTs?
• RQ5 Under what conditions does the adaptive design significantly outperform traditional RCTs in estimation efficiency?

Key findings

• The proposed adaptive design achieves lower asymptotic variance in ATE estimation by optimally adjusting treatment assignment probabilities over time.
• The estimator derived from the algorithm is consistent and asymptotically normal, enabling valid inference despite adaptive sampling.
• Finite-sample simulations demonstrate that the method outperforms standard RCTs in terms of estimation precision under certain conditions.
• The use of martingale theory ensures that standard statistical properties, such as unbiasedness and normality, are preserved under the adaptive design.
• The algorithm effectively balances exploration and exploitation in treatment assignment, leading to more efficient estimation without compromising validity.
• Empirical results confirm that the adaptive approach reduces mean squared error of the ATE estimator compared to fixed randomization in specific experimental settings.