Optimisation in a Synchronised Prediction Setting

The standard approach to solve prediction tasks is to apply inductive methods such as, e.g., the straight rule. Such methods are proven to be access-optimal in specific prediction settings, but not in all. Within the optimality-approach of meta-induction, success-based weighted prediction methods are proven to be access-optimal in all possible continuous prediction settings. However, meta-induction fails to be access-optimal in so-called demonic discrete prediction environments where the predicted value is inversely correlated with the true outcome. In this paper the problem of discrete prediction environments is addressed by embedding them into a synchronised prediction setting. In such a setting the task consists in providing a discrete and a continuous prediction. It is shown that synchronisation constraints exclude the possibility of demonic environments.