A Prediction Market Approach to Learning with Sequential Advice

We consider a new class of online classification problems motivated by Internet recommendation and forecasting applications in which the learner receives advice sequentially over time from experts who may be adversarial or genuine. We show that, for this set of problems, the use of a market trading metaphor is useful in constructing a learning algorithm. We illustrate this by considering the concrete problem of learning prediction sequences under partial monitoring. We use a nontraditional definition of regret under certain analytical assumptions. In a setting with m items, we prove that a measure of regret with respect to the collective information held by n experts is bounded by O(n √ m logm).