Markovian Interference in Experiments

Farias, Vivek F.; Li, Andrew A.; Peng, Tianyi; Zheng, Andrew

doi:10.48550/arxiv.2206.02371

Cited by 2 publications

(2 citation statements)

References 37 publications

(72 reference statements)

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“…( 14) attain the nominal coverage rate. (Liu et al, 2021b;Johari et al, 2022;Farias et al, 2022) and the switch-back designs (Sneider et al, 2018;Bojinov et al, 2022;Glynn et al, 2020). The surveys by Kohavi & Thomke (2017); Bojinov & Gupta (2022) contain detailed accounts of A/B testing in internet markets.…”

Section: Methodsmentioning

confidence: 99%

Statistical Inference and A/B Testing for First-Price Pacing Equilibria

Liao¹,

Kroer²

2023

Preprint

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We initiate the study of statistical inference and A/B testing for first-price pacing equilibria (FPPE). The FPPE model captures the dynamics resulting from large-scale first-price auction markets where buyers use pacing-based budget management. Such markets arise in the context of internet advertising, where budgets are prevalent.We propose a statistical framework for the FPPE model, in which a limit FPPE with a continuum of items models the long-run steady-state behavior of the auction platform, and an observable FPPE consisting of a finite number of items provides the data to estimate primitives of the limit FPPE, such as revenue, Nash social welfare (a fair metric of efficiency), and other parameters of interest. We develop central limit theorems and asymptotically valid confidence intervals. Furthermore, we establish the asymptotic local minimax optimality of our estimators. We then show that the theory can be used for conducting statistically valid A/B testing on auction platforms. Numerical simulations verify our central limit theorems, and empirical coverage rates for our confidence intervals agree with our theory.

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Section: Methodsmentioning

confidence: 99%

Statistical Inference and A/B Testing for First-Price Pacing Equilibria

Liao¹,

Kroer²

2023

Preprint

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“…A number of papers bound the data requirements of TD. See for example Mannor et al (2004), Lu (2005)), Lazaric et al (2010), Pires & Szepesvári (2012), Tagorti & Scherrer (2015)), Bhandari et al (2018), , Khamaru et al (2020), Chen et al (2020), or Farias et al (2022). These show certain problem instances have low data requirements, but do not clarify when enforcing temporal consistency in value estimates produces large efficiency gains.…”

Section: Related Workmentioning

confidence: 99%

On the Statistical Benefits of Temporal Difference Learning

Cheikhi¹,

Russo²

2023

Preprint

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Given a dataset on actions and resulting long-term rewards, a direct estimation approach fits value functions that minimize prediction error on the training data. Temporal difference learning (TD) methods instead fit value functions by minimizing the degree of temporal inconsistency between estimates made at successive time-steps. Focusing on finite state Markov chains, we provide a crisp asymptotic theory of the statistical advantages of this approach. First, we show that an intuitive inverse trajectory pooling coefficient completely characterizes the percent reduction in mean-squared error of value estimates. Depending on problem structure, the reduction could be enormous or nonexistent. Next, we prove that there can be dramatic improvements in estimates of the difference in value-to-go for two states: TD's errors are bounded in terms of a novel measure -the problem's trajectory crossing time -which can be much smaller than the problem's time horizon.1. The relative benefits of TD are determined by a natural 'inverse trajectory pooling coefficient.' TD uses value-to-go at intermediate states as a surrogate Athey et al. (2019); Prentice (1989).

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Markovian Interference in Experiments

Cited by 2 publications

References 37 publications

Statistical Inference and A/B Testing for First-Price Pacing Equilibria

Statistical Inference and A/B Testing for First-Price Pacing Equilibria

On the Statistical Benefits of Temporal Difference Learning

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