Strategies for prediction under imperfect monitoring.
We propose simple randomized strategies for sequential decision (or prediction) under imperfect monitoring, that is, when the decision maker (forecaster) does not have access to the past outcomes but rather to a feedback signal. The proposed strategies are consistent in the sense that they achieve, asymptotically, the best possible average reward among all ﬁxed actions. It was Rustichini  who ﬁrst proved the existence of such consistent predictors. The forecasters presented here oﬀer the ﬁrst constructive proof of consistency. Moreover, the proposed algorithms are computationally eﬃcient. We also establish upper bounds for the rates of convergence. In the case of deterministic feedback signals, these rates are optimal up to logarithmic terms.