Optimal universal learning and prediction of probabilistic concepts

We consider the following setting of the (supervised) learning problem. A sequence of input data x₁,…,x_t,…, is given, one by one, and the goal is to predict the corresponding outputs y₁,…,y_t,…. Our proposed solution for the supervised learning problem is Bayesian, and the contribution of this work lies in determining the optimal way to choose the Bayesian “prior” for the supervised learning problem, and observing the strong sequential, non-anticipating, structure of the resulting universal predictor