On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints

Abstract

We consider a misspecified optimization problem that requires minimizing of a convex function $f(x;{\theta }^{\ast })$ in x over a constraint set represented by $h(x;{\theta }^{\ast })\le 0$, where ${\theta }^{\ast }$ is an unknown (or misspecified) vector of parameters. Suppose ${\theta }^{\ast }$ can be learnt by a distinct process that generates a sequence of estimators ${\theta }_k$, each of which is an increasingly accurate approximation of ${\theta }^{\ast }$. We develop a first-order augmented Lagrangian scheme for computing an optimal solution $x^{\ast }$ while simultaneously learning ${\theta }^{\ast }$.

For the extended journal version of this preliminary work, see arXiv:1608.01879 [math.OC]

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• On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints

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• On the rate analysis of inexact augmented Lagrangian schemes for convex optimization problems with misspecified constraints