HOW TO USE EXPERT ADVICE

We analyze algorithms that predict a binary value by combining the pre dictions of several prediction strategies, called experts. Our analysi s is for worst-case situations, i.e., we make no assumptions about the way the sequence of bits to be predicted is generated. We measure the performance of the algorithm by the difference between the expected n umber of mistakes it makes on the bit sequence and the expected number of mistakes made by the best expert on this sequence, where the expec tation is taken with respect to the randomization in the predictions. We show that the minimum achievable difference is on the order of the square root of the number of mistakes of the best expert, and we give efficient algorithms that achieve this. Our upper and lower bounds hav e matching leading constants in most cases. We then show how this lead s to certain kinds of pattern recognition/learning algorithms with per formance bounds that improve on the best results currently known in th is context. We also compare our analysis to the case in which log loss is used instead of the expected number of mistakes.