Thompson Sampling, one of the oldest heuristics for solving multi-armed bandits, has recently been shown to demonstrate state-of-the-art performance. The empirical success has led to great interests in theoretical understanding of this heuristic. In this paper, we approach this problem in a way very different from existing efforts. In particular, motivated by the connection between Thompson Sam...

In this paper, we give a decomposition of the moonshine module V ♮ with respect to an extremal Type II code over Z2k for an integer k ≥ 2. Then we obtain automorphisms of V ♮, some 4A and 2B elements of the Monster with respect to the decomposition. We give examples of such a decomposition for some k and give the McKay-Thompson series for a 4A element.

Thompson sampling is one of oldest heuristic to address the exploration / exploitation trade-off, but it is surprisingly unpopular in the literature. We present here some empirical results using Thompson sampling on simulated and real data, and show that it is highly competitive. And since this heuristic is very easy to implement, we argue that it should be part of the standard baselines to com...