Seems closely related. The update of the distributions in a Thompson sampler can be thought of as a multiplicative update, considering the old dist as a prior.

Seems closely related. The update of the distributions in a Thompson sampler can be thought of as a multiplicative update, considering the old dist as a prior. Those updates become relatively smaller with time though, as the distributions become better known. So TS has a more complicated update rule. Then there's the decision rule. I think of TS as approximating the probability that a given observable is the best, by drawing from the distributions. This effectively just uses a softmax on the weights. Which seems close in spirit, and probably more open to analysis than TS, which often gets complicated under analysis.