Develops robust SGLD with non-asymptotic convergence bounds for non-convex DRO and applies it to neural network regression under adversarial corruption.
Bipolar Theorems for Sets of Non-negative Random Variables
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abstract
This paper assumes a robust, in general not dominated, probabilistic framework and provides necessary and sufficient conditions for a bipolar representation of subsets of the set of all quasi-sure equivalence classes of non-negative random variables, without any further conditions on the underlying measure space. This generalizes and unifies existing bipolar theorems proved under stronger assumptions on the robust framework. Applications are in areas of robust financial modeling.
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Robust SGLD algorithm for solving non-convex distributionally robust optimisation problems
Develops robust SGLD with non-asymptotic convergence bounds for non-convex DRO and applies it to neural network regression under adversarial corruption.