A Robust Frank-Wolfe Method for MAP Inference

Finding maximum a posterior (MAP) estimation is common problem in computer vision, such as the inference in Markov random fields. However, it is in general intractable, and one has to resort to approximate solutions, e.g. quadratic programming. In this paper, we propose a robust Frank-Wolfe method [6] to do the MAP inference. Our algorithm optimizes the quadratic programming problem by alternating projections between the discrete domain and the continuous domain (relaxed space). If the solution in the discrete domain keeps the energy climbing in the current step in both the discrete and continuous domains, we push the algorithm ahead to that direction in the following steps. Otherwise, we backtrack our algorithm to the continuous domain, which can find a non-discrete solution and improve the quadratic function climbing towards the integer solution. We analyze our algorithm and show the backtrack step under the Frank-Wolfe Method framework can guarantee the energy increasing in the following gradient updating step. We show the advantages of our algorithm by significantly outperforming integer projected fixed point method (IPFP) and other baselines.