We need to optimize something (product, drug, prototype etc) by testing it on users.

Let's say we have a 6 factor 3 level full factorial experimental design. So we have 3x3x3x3x3x3 = 729 variations.

We want to limit a sample size of subjects. So we assume to use Multi-Armed Bandit algorithm (MAB), particularly Thompson sampling.

In addition, I think machine learning algorithms such as random forests can help.

Any thoughts on how to implement that from methodological point of view?