We study the fundamental mistake bound and sample complexity in the strategic1 classification, where agents can strategically manipulate their feature vector up2 to an extent in order to be predicted as positive. For example, given a classifier3 determining college admission, student candidates may try to take easier classes to4 improve their GPA, retake SAT and change schools in an effort to fool the classifier.5 Ball manipulations are a widely studied class of manipulations in the literature,6 where agents can modify their feature vector within a bounded radius ball. Unlike7 most prior work, our work consider manipulations to be personalized, meaning8 that agents can have different levels of manipulation abilities (e.g., varying radii9 for ball manipulations), and unknown to the learner.10 We formalize the learning problem in an interaction model where the learner11 first deploys a classifier and the agent manipulates the feature vector within their12 manipulation set to game the deployed classifier. We investigate various scenarios13 in terms of the information available to the learner during the interaction, such14 as observing the original feature vector before or after deployment, observing the15 manipulated feature vector, or not seeing either the original or the manipulated16 feature vector. We begin by providing online mistake bounds and PAC sample17 complexity in these scenarios for ball manipulations. We also explore non-ball18 manipulations and show that, even in the simplest scenario where both the original19 and the manipulated feature vectors are revealed, the mistake bounds and sample20 complexity are lower bounded by Ω(|H|) when the target function belongs to a21 known class H.22

Mixability has been shown to be a powerful tool to obtain algorithms with optimal regret. 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)) achieves a regret of O(log(Bn)) whereas Online Newton Step achieves O(eBlog(n)) obtaining a double exponential gain in B (a bound on the norm of comparative functions). However, this high statistical performance is at the price of a prohibitive computational complexity O(n37). In this paper, we use quadratic surrogates to make aggregating forecasters more efficient. We show that the resulting algorithm has still high statistical performance for a large class of losses. In particular, we derive an algorithm for multi-class logistic regression with a regret bounded by O(Blog(n)) and a computational complexity of only O(n4).

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.