Universality of Bayesian mixture predictors

International audienceThe problem is that of sequential probability forecasting for finite-valued time series. Thedata is generated by an unknown probability distribution over the space of all one-way infinitesequences. It is known that this measure belongs to a given set C, but the latter is completelyarbitrary (uncountably infinite, without any structure given). The performance is measured withasymptotic average log loss. In this work it is shown that the minimax asymptotic performanceis always attainable, and it is attained by a convex combination of a countably many measuresfrom the set C (a Bayesian mixture). This was previously only known for the case when thebest achievable asymptotic error is 0. This also contrasts previous results that show that in thenon-realizable case all Bayesian mixtures may be suboptimal, while there is a predictor thatachieves the optimal performance