SAFIP: a streaming algorithm for inverse problems

TL;DR

SAFIP is a streaming algorithm designed to efficiently approximate the solution set of inverse problems with minimal function evaluations, suitable for complex, high-dimensional scenarios.

Contribution

The paper introduces SAFIP, a novel streaming algorithm that effectively covers the solution set of inverse problems with limited evaluations, even in high-dimensional spaces.

Findings

Provides convergence proofs for SAFIP.

Demonstrates effectiveness on problems with dimensions from 2 to 10.

Achieves good coverage of solution sets with few function evaluations.

Abstract

This paper presents a new algorithm which aims at the resolution of inverse problems of the form f(x) = 0, for x a vector of dimension d and f an arbitrary function with mild regularity condition. The set of solutions S may be infinite. This algorithm produces a good coverage of S, with a limited number of evaluations of the function f. It is therefore appropriate for complex problems where those evaluations are costly. Various examples are presented, with d varying from 2 to 10. Proofs of convergence and of coverage of S are presented.