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We investigate the generalization behavior of sequential prediction (online) algorithms, when data are generated from a probability distribution. Using some newly developed probability inequalities, we are able to bound the total generalization performance of a learning algorithm in terms of its observed total loss. Consequences of this analysis will be illustrated with examples.
This paper resolves the problem of predicting as well as the best expert up to an additive term o(n), where n is the length of a sequence of letters from a finite alphabet. For the bounded games the paper introduces the Weak Aggregating Algorithm that allows us to obtain additive terms of the form . A modification of the Weak Aggregating Algorithm that covers unbounded games is also...
An algorithm is presented for online prediction that allows to track the best expert efficiently even if the number of experts is exponentially large, provided that the set of experts has a certain structure allowing efficient implementations of the exponentially weighted average predictor. As an example we work out the case where each expert is represented by a path in a directed graph and the loss...
This work studies external regret in sequential prediction games with arbitrary payoffs (nonnegative or non-positive). External regret measures the difference between the payoff obtained by the forecasting strategy and the payoff of the best action. We focus on two important parameters: M, the largest absolute value of any payoff, and Q*, the sum of squared payoffs of the best action. Given...
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