I'm developing a multi-armed bandit which learns the best information to display to persuade someone to donate to charity.
Suppose I have treatments A, B, C, D (which are each one paragraph of text). The bandit selects one treatment to show to a person. The person is given $1 and has to decide how much (if any) to donate, in increments of one cent. The donation decision is recorded and fed to the multi-armed bandit, who will then re-optimize before another person is shown a treatment selected by the bandit.
How should I program the bandit if my objective is to maximize total donations? For example, can I use Thompson sampling, and if a participant donates $0.80, I count that as 80 successes and 20 failures?