Thisworkdiscusses howtoachieveworst-case Out-Of-Distribution(OOD) generalization for avariety of distributions based on arelatively small labeling cost.

A matching process on a two-sided market can determine who gets which job [40, 31], school place[44],orspouse.

Namely,thattheempirical lossofall the functions in the class is -close to the true loss. Finally, we develop a set of tools for calculating the approximate description length of classes of functions that can be presented as a composition of linear function classes and non-linear functions.

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It is not clear, however, whether these theoretical results apply to actual distributions such as images.

We show that the VC-Dimension of the model class which canrobustlyinterpolate any n samples is lower bounded byΩ(nd) where d is the dimension. In contrast, there are neural net architectures that can interpolaten samples with onlyO(n) parameters and VC-Dimension atmostO(nlogn).

However, the labeling process can be tedious, costly, and error-prone in practice. In this paper, we propose to unify active learning (AL) and message passing towards minimizing labeling costs, e.g.,making useoffewandunreliable labels thatcan beobtainedcheaply.

Finally, we want our algorithm to have low computational overhead, so that itcan be applied asawrapper on top ofarbitrary prediction methods, for both regression and classification.

Therefore, we help address the open problem on agnosticQ-learning proposed in [Wen and Van Roy,2013].

Generalization to out-of-distribution (OOD) data is one of the central problems in modern machine learning. Recently, there is a surge of attempts to propose algorithms that mainly build upon the idea of extracting invariant features.