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تسجيل مستخدم جديدGambling and Renyi Divergence
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For gambling on horses, a one-parameter family of utility functions is proposed, which contains Kellys logarithmic criterion and the expected-return criterion as special cases. The strategies that maximize the utility function are derived, and the connection to the Renyi divergence is shown. Optimal strategies are also derived when the gambler has some side information; this setting leads to a novel conditional Renyi divergence.
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Renyi divergence is related to Renyi entropy much like Kullback-Leibler divergence is related to Shannons entropy, and comes up in many settings. It was introduced by Renyi as a measure of information that satisfies almost the same axioms as Kullback
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