Minimisation of Quasar-Convex Functions Using Random Zeroth-Order Oracles

This paper presents a random Gaussian smoothing zeroth-order (ZO) algorithm for minimizing quasar-convex (QC) and strongly quasar-convex (SQC) functions, establishing convergence and complexity bounds for both unconstrained and constrained scenarios. It introduces the concept of proximal-quasar-convexity for constrained optimization and shows that the algorithm can converge to a controlled neighborhood of the global minimum. These findings have practical implications for machine learning applications, particularly in areas like linear dynamical system identification and generalized linear models, where quasar-convexity is relevant.