Safe Convex Learning under Uncertain Constraints
Ilnura Usmanova, Andreas Krause, Maryam Kamgarpour · Repository for Publications and Research Data (ETH Zurich) · 2019
We address the problem of minimizing a convex smooth function f (x) over a compact polyhedral set D given a stochastic zerothorder constraint feedback model.This problem arises in safety-critical machine learning applications, such as personalized medicine and robotics.In such cases, one needs to ensure constraints are satisfied while exploring the decision space to find optimum of the loss function.We propose a new variant of the Frank-Wolfe algorithm, which applies to the case of uncertain linear constraints.Using robust optimization, we provide the convergence rate of the algorithm while guaranteeing feasibility of all iterates, with high probability.1