Building on this result, we show several examples of how variance of predictions can be exploited in learning.

In this paper, we investigate the problem of cutting a tree originating from a pre-specified HC procedure through pairwise similarity queries generated by active learning algorithms.

However, the resulting methods often suffer from high computational complexity which has reduced their practical applicability. For example, in the case of multiclass logistic regression, the aggregating forecaster (Foster et al. (2018)) achievesaregret ofO(log(Bn))whereas Online Newton Step achieves O(eBlog(n))obtaining adouble exponential gaininB (aboundonthenormof comparativefunctions).

On the technical side, we show that the logarithmic loss and an informationtheoretic quantity called thetriangular discriminationplay a fundamental role in obtaining first-order guarantees, and we combine this observation with new refinements tothe regression oracle reduction framework ofFoster and Rakhlin [29].

SB-FBSDE isanewclass ofgenerativemodels that, inspiring bytherecent advance of understanding deep learning through the optimal control perspective [61-63], adopts Lemma 5 to generalize the score-based diffusion models.

In case of generic convex losses, we use the more complex parameterless algorithm AdaNormalHedge. The following theorem states a slightly more general bound that holds for anyη-exp-concave loss function (for completeness,theproofisgiveninAppendixD). Nownotethatalthough the algorithm is actually initialized withw1,i = 1, Lemma 1 shows that the regret remains the same if we assume the algorithm is initialized withwE1. Suppose that Algorithm 5 is run using predictions and updates provided by AdaNormalHedge. Asinourlocally-adaptive setting node experts are local learners,byi,t should be viewed as the prediction of the local online learning algorithm sitting at nodeiof the tree.

Inthis paper,we address several inadequacies ofcurrent video object segmentation pipelines. Firstly, a cyclic mechanism is incorporated to the standard semisupervised process to produce more robust representations.