Today I had a chance to read original paper of Hedge algorithm. The motivating problem was about betting on horse races. A gambler, decides to allow a group of his friends to make bets on his behalf and the question is how to combine the decisions of friends. This is exactly the setting of learning using expert advice. After reading, I thought about betting languages. Betting only on one horse as a winner is a special case of betting languages. Permutation betting and betting on a interval are another languages for betting. In permutation betting you bet on a permutation of all horses and in interval betting you bet on subset of size k of horses for first k ranks. Another betting language maybe be considered as pairwise betting. In this type of betting you bet on a mapping between horses and ranks. Now the question is that can we apply Hedge or other types of algorithms for learning betting of types of mentioned languages?
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