I understand the basics of Thomson Sampling, but how is it implemented in practice? If there are three variants each with a 1/3 of traffic allocated to them on day 1, how is traffic dynamically allocated on day 2, 3, and so forth? All of the examples I've read show a simulation of posterior sampling, but how can this be done in a real world application of bandit testing?
I guess that by "in practice" you meant that you want to group your reward feedback and action decision by batch (e.g. every day).
If you do a single Thomson sampling round and allocate 100% of your traffic to the best arm (e.g. variant), your exploration might not be very smooth and you may underperform.
I would do few (~1000 per arm) Thomson sampling iterations at each batch and allocate the traffic given the proportion of win in this few iterations. I don't have a theory to support this idea, but it seems like it keeps intact the core idea of Thomson sampling (i.e. pull the arm with a frequency equals to its probability to be the best given the data available).