Say that you want to persuade a group of people to go out and vote. You can reach people by phone, mail, f2f, or email. And the cost of reaching out f2f > phone > mail > email. Your objective is to convert as many people as possible. How would you do it?
Thompson sampling provides one answer. Thompson sampling “randomly allocates subjects to treatment arms according to their probability of returning the highest reward under a Bayesian posterior.”
To exploit it, start by predicting persuasion (or persuasion/$) based on whatever you know about the person, and assignment to treatment or control. Conventionally, this means using a random forest model to estimate heterogeneous treatment effects but really use whatever gets you the best fit after including interactions in the inputs. (Make sure you get calibrated probabilities back.) Use the forecasted probabilities to find the treatment arm with the highest reward and probabilistically assign people to that.
Here’s the fun part: the strategy also accounts for compliance. The kinds of people who don’t ‘comply’ with one method, e.g., don’t pick up the phone, will be likelier to be assigned to another method.