Our framework may be thought of as a generalization of the synthetic control and synthetic interventions frameworks, where data is collected via an adaptive intervention assignment policy.

The fundamental problem of non-parametric two-sample testing consists in detecting the difference between any two distributions having access only to samples from these.

However, these results can be too general to be applicable to natural data distributions. Indeed, humans are quite robust for tasks involving vision.

We show that the answer to this question depends on the properties of underlying preference distributions.

Our analysis of the generalization error is based on an extension of Gordon's Gaussian process inequality [ R is a continuous function, which is convex in the first argument and concave in the second argument. The main result of CGMT is to connect the above two random optimization problems. The CGMT framework has been used to infer statistical properties of estimators in certain high-dimensional asymptotic regime. Second, derive the point-wise limit of the AO objective in terms of a convex-concave optimization problem, over only few scalar variables.

Huber's contaminated heavy-tailed rewards and meanwhile needs to ensure differential privacy.