Abstract. For the prediction with expert advice setting, we consider methods to construct algorithms that have low adaptive regret. The adaptive regret of an algorithm on a time interval [t1, t2] is the loss of the algorithm there minus the loss of the best expert. Adaptive regret measures how well the algorithm approximates the best expert locally, and it is therefore somewhere between the classical regret (measured on all outcomes) and the tracking regret, where the algorithm is compared to a good sequence of experts. We investigate two existing intuitive methods to derive algorithms with low adaptive regret, one based on specialist experts and the other based on restarts. Quite surprisingly, we show that both methods lead to the same algorithm, namely Fixed Share, which is known for its tracking regret. Our main result is a thorough analysis of the adaptive regret of Fixed Share. We obtain the exact worst-case adaptive regret for Fixed Share, from which the classical tracking bounds can be derived. We also prove that Fixed Share is optimal, in the sense that no algorithm can have a better adaptive regret bound.

Abstract. The main aim of this paper is to compare the results of several methods of prediction with confidence. In particular we compare the results of Venn Machine with Platt's Method of estimating confidence. The results are presented and discussed.

This paper formulates the protocol for prediction of packs, which a special case of prediction under delayed feedback. Under this protocol, the learner must make a few predictions without seeing the outcomes and then the outcomes are revealed. We develop the theory of prediction with expert advice for packs. By applying Vovk's Aggregating Algorithm to this problem we obtain a number of algorithms with tight upper bounds. We carry out empirical experiments on housing data.

Abstract-The paper proposes the vicinities merging algorithm for prediction with side information. The algorithm is based on specialist experts techniques. We use vicinities in the side information domain to identify relevant past examples, apply standard learning techniques to them, and then use prediction with expert advice tools to merge those predictions. Guarantees from the theory of prediction with expert advice ensure that helpful vicinities are selected dynamically. The algorithm automatically converges on the right vicinities from an initial broad selection. We apply the resulting algorithms to two problems, prediction of implied volatility of options and prediction of students' performance at tests. On the problem of predicting implied volatility, the algorithm consistently outperforms naive competitors and a highly-tuned proprietary method used in the industry. When applied to the students' performance, the algorithm never falls behind the baseline and outperforms it when the side information is beneficial.