Efficient MRF Energy Minimization via Adaptive Diminishing Smoothing

We consider the linear programming relaxation of an energy minimization problem for Markov Random Fields. The dual objective of this problem can be treated as a concave and unconstrained, but non-smooth function. The idea of smoothing the objective prior to optimization was recently proposed in a series of papers. Some of them suggested the idea to decrease the amount of smoothing (so called temperature) while getting closer to the optimum. However, no theoretical substantiation was provided. We propose an adaptive smoothing diminishing algorithm based on the duality gap between relaxed primal and dual objectives and demonstrate the efficiency of our approach with a smoothed version of Sequential Tree-Reweighted Message Passing (TRW-S) algorithm. The strategy is applicable to other algorithms as well, avoids adhoc tuning of the smoothing during iterations, and provably guarantees convergence to the optimum.