Approximate methods for sequential decision making using expert advice

We consider a game theoretic approach for sequentially choosing decisions by combining the suggestions of a fixed number of experts. Since the optimal decision making strategy is often computationally expensive, we present a methodology for obtaining approximate strategies with provably good performance. These methods are applicable to any decision problem with bounded payoff function, are computationally feasible, and arise naturally as approximations to the exact solution. We illustrate the ideas by applying our results to the problem of predicting a sequence of letters drawn from a finite alphabet with the goal being to minimize the number of mistakes made.