Aggregating strategies

The following situation is considered. At each moment of discrete time a decision maker, who does not know the current state of Nature but knows all its past states, must make a decision. The decision together with the current state of Nature determines the loss of the decision maker. The performance of the decision maker is measured by his total loss. We suppose that there is a pool of decision maker's potential strategies one of which is believed to perform well, and construct an "aggregating" strategy for which the total loss is not much bigger than the total loss under strategies in the pool, whatever states of Nature. Our construction generalizes both the Weighted Majority Algorithm of N. Littlestone and M. K. Warmuth and the Bayesian rule.