## Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising

Abstract: This work shows how to leverage causal inference to understand the behavior of complex learning systems interacting with their environment and predict the consequences of changes to the system. Such predictions allow both humans and algorithms to select changes that improve both the short-term and long-term performance of such systems. This work is illustrated by experiments carried out on the ad placement system associated with the Bing search engine.

Léon Bottou, Jonas Peters, Joaquin Quiñonero-Candela, Denis X. Charles, D. Max Chickering, Elon Portugaly, Dipankar Ray, Patrice Simard and Ed Snelson: Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising, Journal of Machine Learning Research, 14(Nov):3207–3260, 2013.

Link to the 2012 technical report page.

@article{bottou-jmlr-2013,
author = {Bottou, L\'eon and Peters, Jonas and Qui{\~n}onero-Candela, Joaquin
and Charles, Denis X. and Chickering, D. Max and Portugaly, Elon
and Ray, Dipankar and Simard, Patrice and Snelson, Ed},
title = {Counterfactual Reasoning and Learning Systems: The Example of Computational Advertising},
journal = {Journal of Machine Learning Research},
year = {2013},
volume = {14},
number = {Nov},
pages = {3207--3260},
url = {http://leon.bottou.org/papers/bottou-jmlr-2013},
}

### Erratum

The following typo has been corrected on 6/9/2014:

• The first equation page 3245 should read $V_a \approx \frac{\partial Z_a}{\partial b_a}\Big/\frac{\partial Y_a}{\partial b_a}~~$.