Product Betting Martingale
A method for constructing anytime-valid bounds using betting strategies, in which a product martingale is constructed and Ville's inequality is applied to obtain time-uniform boundaries.
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The paper provides several ready-made boundary construction methods: continuous mixture, discrete mixture, stitching, and product betting martingale.
The core idea of the product betting martingale is to choose a predictable betting function such that the expectation of the product martingale does not exceed 1, and then apply Ville's inequality to obtain that the probability of exceeding 1/α is at most α.
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The paper provides several ready-made boundary construction methods: continuous mixture, discrete mixture, stitching, and product betting martingale.
50%UnverifiedThe core idea of the product betting martingale is to choose a predictable betting function such that the expectation of the product martingale does not exceed 1, and then apply Ville's inequality to obtain that the probability of exceeding 1/α is at most α.
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