In the previous championship CBP-4, the winner of the unlimited storage track [5], poTAGE-SC was combining several TAGE based predictors using different forms of histories (local, global, and frequency), a COLT inspired [3] prediction combiner and a statistical corrector (SC) predictor [8, 10] fed with various forms of branch histories. With MTAGE-SC, we improve this predictor in two ways. Firs...

For an n-variate order-d tensor A, define Amax := sup‖x‖2=1〈A, x ⊗d〉 to be the maximum value taken by the tensor on the unit sphere. It is known that for a random tensor with i.i.d. ±1 entries, Amax . √ n · d · log d w.h.p. We study the problem of efficiently certifying upper bounds on Amax via the natural relaxation from the Sum of Squares (SoS) hierarchy. Our results include: When A is a rand...

We consider the online sparse linear regression problem, which is the problem of sequentially making predictions observing only a limited number of features in each round, to minimize regret with respect to the best sparse linear regressor, where prediction accuracy is measured by square loss. We give an inefficient algorithm that obtains regret bounded by Õ( √ T ) after T prediction rounds. We...

We describe online algorithms for learning a rotation from pairs of unit vectors in R. We show that the expected regret of our online algorithm compared to the best fixed rotation chosen offline over T iterations is O( √ nT ). We also give a lower bound that proves that this expected regret bound is optimal within a constant factor. This resolves an open problem posed in COLT 2008. Our online a...