High-Confidence Predictions under Adversarial Uncertainty

Andrew Drucker

We study the setting in which the bits of an unknown infinite binary sequence x are revealed sequentially to an observer. We show that very limited assumptions about x allow one to make successful predictions about unseen bits of x . Our main focus is the problem of successfully predicting a single 0 from among the bits of x . In our model we get just one chance to make a prediction, at a time of our choosing. This models a variety of situations in which we need to perform an action of fixed duration, and must predict a "safe" time-interval to perform it. Letting N_t denote the number of 1s among the first t bits of x , we say that x is "eps-weakly sparse" if lim inf (N_t/t)

https://www.ias.edu/video/csdm/drucker