Getting Feasible Variable Estimates From Infeasible Ones: MRF Local Polytope Study

TL;DR

This paper introduces an efficient method to derive feasible primal solutions from dual solutions in large-scale optimization problems with separability, specifically applied to Markov Random Fields, improving over existing approaches.

Contribution

The paper presents a novel approach for constructing feasible primal solutions from dual estimates in large-scale problems, with a focus on Markov Random Fields, avoiding complex projections.

Findings

Method effectively produces feasible solutions from dual estimates.

Demonstrates superiority over existing methods in MRF inference.

Properties similar to Euclidean projection influence convergence.

Abstract

This paper proposes a method for construction of approximate feasible primal solutions from dual ones for large-scale optimization problems possessing certain separability properties. Whereas infeasible primal estimates can typically be produced from (sub-)gradients of the dual function, it is often not easy to project them to the primal feasible set, since the projection itself has a complexity comparable to the complexity of the initial problem. We propose an alternative efficient method to obtain feasibility and show that its properties influencing the convergence to the optimum are similar to the properties of the Euclidean projection. We apply our method to the local polytope relaxation of inference problems for Markov Random Fields and demonstrate its superiority over existing methods.