TY - JOUR

T1 - Functional Sequential Treatment Allocation

AU - Kock, Anders Bredahl

AU - Preinerstorfer, David

AU - Veliyev, Bezirgen

PY - 2022

Y1 - 2022

N2 - Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present article, we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies. for this article are available online.

AB - Consider a setting in which a policy maker assigns subjects to treatments, observing each outcome before the next subject arrives. Initially, it is unknown which treatment is best, but the sequential nature of the problem permits learning about the effectiveness of the treatments. While the multi-armed-bandit literature has shed much light on the situation when the policy maker compares the effectiveness of the treatments through their mean, much less is known about other targets. This is restrictive, because a cautious decision maker may prefer to target a robust location measure such as a quantile or a trimmed mean. Furthermore, socio-economic decision making often requires targeting purpose specific characteristics of the outcome distribution, such as its inherent degree of inequality, welfare or poverty. In the present article, we introduce and study sequential learning algorithms when the distributional characteristic of interest is a general functional of the outcome distribution. Minimax expected regret optimality results are obtained within the subclass of explore-then-commit policies, and for the unrestricted class of all policies. for this article are available online.

KW - Distributional characteristics

KW - Minimax optimal expected regret

KW - Multi-armed bandits

KW - Randomized controlled trials

KW - Robustness

KW - Sequential treatment allocation

KW - REGRET TREATMENT CHOICE

KW - INEQUALITY

KW - SIZE

KW - MAXIMIZATION

KW - ECONOMETRICS

KW - STATISTICAL-INFERENCE

KW - POVERTY

KW - MODELS

U2 - 10.1080/01621459.2020.1851236

DO - 10.1080/01621459.2020.1851236

M3 - Journal article

VL - 117

SP - 1311

EP - 1323

JO - Journal of the American Statistical Association

JF - Journal of the American Statistical Association

SN - 0162-1459

IS - 539

ER -