Finding the maximum a-posteriori (MAP) assignment is a central task for structured prediction. Since modern applications give rise to very large structured problem instances, there is increasing need for efficient solvers. In this work we propose to improve the efficiency of coordinate-minimization-based dual-decomposition solvers by running their updates asynchronously in parallel. In this case messagepassing inference is performed by multiple processing units simultaneously without coordination, all reading and writing to shared memory. We analyze the convergence properties of the resulting algorithms and identify settings where speedup gains can be expected. Our numerical evaluations show that this approach indeed achieves significant speedups in common computer vision tasks.

Recently, several works have shown that natural modifications of the classical conditional gradient method (aka Frank-Wolfe algorithm) for constrained convex optimization, provably converge with a linear rate when: i) the feasible set is a polytope, and ii) the objective is smooth and strongly-convex. However, all of these results suffer from two significant shortcomings: 1. large memory requirement due to the need to store an explicit convex decomposition of the current iterate, and as a consequence, large running-time overhead per iteration 2. the worst case convergence rate depends unfavorably on the dimension In this work we present a new conditional gradient variant and a corresponding analysis that improves on both of the above shortcomings. In particular: 1. both memory and computation overheads are only linear in the dimension 2. in case the optimal solution is sparse, the new convergence rate replaces a factor which is at least linear in the dimension in previous work, with a linear dependence on the number of non-zeros in the optimal solution At the heart of our method and corresponding analysis, is a novel way to compute decomposition-invariant away-steps. While our theoretical guarantees do not apply to any polytope, they apply to several important structured polytopes that capture central concepts such as paths in graphs, perfect matchings in bipartite graphs, marginal distributions that arise in structured prediction tasks, and more. Our theoretical findings are complemented by empirical evidence which shows that our method delivers state-of-the-art performance.

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