Experimenting with targeted features

Suppose you run a website and you have some experience or feature that you think might be good for some subset of your users (but ineffective, at best, for others).  You might try to (1) identify who would benefit based on observed characteristics  then (2) alter the experience only for a targeted subset users expected to benefit.

To make things concrete, in some cities, Uber offers “UberFamily” which means the Uber comes with a car seat. For us (I have two kids), UberFamily is awesome, but the option takes up valuable screen real estate and for a user that Uber thinks does not have kids, adding it to the app screen is a waste. So Uber would like to both (a) figure out if it is likely that I have kids and then (b) adjust the experience based on that model. But they’d also like to know if it’s worth it in general to offer this service even among those they think could use it. This isn’t the example that motivated this blog post, but it makes the scenario clear.

If you are testing features of this sort, then you want to both (a) assess your targeting and (b) assess the feature itself. How should you proceed? I’m sure there’s probably some enormous literature on this question (there’s a literature on everything), but I figure by offering my thoughts and potentially being wrong on the Internet, I can be usefully corrected.

I think what you want to do is not test your targeting experimentally but rather role out the feature for everyone you reasonably can than evaluate your targeting algorithms on your experimental data. So, you would run the experiment with a design that maximizes power to detect treatment effects (e.g., 50 to treatment, 50 control). In other words, completely ignore your targeting algorithm recommendations.

Then, after the experimental data comes in, look for heterogeneous treatment effects conditioned on the predictive model score, where the score can be thought of as a measure of how much we think a person should have benefitted from the treatment. The simplest thing you could do to would be to normalize all scores (so the scores have the same mean and variance across algorithms, making model coefficients directly interpretable across algorithms). Then just run the regression:

$y = \beta_0 + \beta_1 (score \times trt) + \beta_2 score + \beta_3 trt$

Hopefully, if the treatment was better for people the model thought would be helped, then $\hat{\beta_1}$ should be positive (assuming the y is such that bigger is better).

You’d also want to finding the minimum score such that you should be targeting people i.e., the score such that the expected benefit from targeting is first positive. You can then simply select the algorithm with the greatest expected improvement, given the minimum score for targeting.

This seems like a reasonable approach (and maybe bordering on obvious but it wasn’t obvious to me at first). Any other suggestions?