
Minimizing Nonconvex Population Risk from Rough Empirical Risk
Population riskthe expectation of the loss over the sampling mechanis...
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Nonuniqueness of Solutions of a Class of ℓ_0minimization Problems
Recently, finding the sparsest solution of an underdetermined linear sys...
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Excess risk bounds in robust empirical risk minimization
This paper investigates robust versions of the general empirical risk mi...
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GenDICE: Generalized Offline Estimation of Stationary Values
An important problem that arises in reinforcement learning and Monte Car...
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Diametrical Risk Minimization: Theory and Computations
The theoretical and empirical performance of Empirical Risk Minimization...
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Optimization of InfConvolution Regularized Nonconvex Composite Problems
In this work, we consider nonconvex composite problems that involve inf...
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A new analytical approach to consistency and overfitting in regularized empirical risk minimization
This work considers the problem of binary classification: given training...
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Statistical Analysis of Stationary Solutions of Coupled Nonconvex Nonsmooth Empirical Risk Minimization
This paper has two main goals: (a) establish several statistical properties—consistency, asymptotic distributions, and convergence rates—of stationary solutions and values of a class of coupled nonconvex and nonsmoothempirical risk minimization problems, and (b) validate these properties by a noisy amplitudebased phase retrieval problem, the latter being of much topical interest.Derived from available data via sampling, these empirical risk minimization problems are the computational workhorse of a population risk model which involves the minimization of an expected value of a random functional. When these minimization problems are nonconvex, the computation of their globally optimal solutions is elusive. Together with the fact that the expectation operator cannot be evaluated for general probability distributions, it becomes necessary to justify whether the stationary solutions of the empirical problems are practical approximations of the stationary solution of the population problem. When these two features, general distribution and nonconvexity, are coupled with nondifferentiability that often renders the problems "nonClarke regular", the task of the justification becomes challenging. Our work aims to address such a challenge within an algorithmfree setting. The resulting analysis is therefore different from the much of the analysis in the recent literature that is based on local search algorithms. Furthermore, supplementing the classical minimizercentric analysis, our results offer a first step to close the gap between computational optimization and asymptotic analysis of coupled nonconvex nonsmooth statistical estimation problems, expanding the former with statistical properties of the practically obtained solution and providing the latter with a more practical focus pertaining to computational tractability.
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