## An Alternating Direction Method for Dual MAP LP Relaxation

Citations: | 14 - 1 self |

### BibTeX

@MISC{Meshi_analternating,

author = {Ofer Meshi and Amir Globerson},

title = {An Alternating Direction Method for Dual MAP LP Relaxation},

year = {}

}

### OpenURL

### Abstract

Abstract. Maximum a-posteriori (MAP) estimation is an important task in many applications of probabilistic graphical models. Although finding an exact solution is generally intractable, approximations based on linear programming (LP) relaxation often provide good approximate solutions. In this paper we present an algorithm for solving the LP relaxation optimization problem. In order to overcome the lack of strict convexity, we apply an augmented Lagrangian method to the dual LP. The algorithm, based on the alternating direction method of multipliers (ADMM), is guaranteed to converge to the global optimum of the LP relaxation objective. Our experimental results show that this algorithm is competitive with other state-of-the-art algorithms for approximate MAP estimation.

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Citation Context ...lgorithm for projecting onto the local polytope. More recently, Martins et al. [17] proposed a globally convergent algorithm for MAP-LP based on the alternating direction method of multipliers (ADMM) =-=[8, 5, 4, 2]-=-. This method proceeds by iteratively updating primal and dual variables in order to find a saddle point of an augmented Lagrangian for the problem. They suggest to use an augmented Lagrangian of the ... |

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Citation Context ...P estimation. In this paper, we assumed that the model parameters were given. However, in many cases one wishes to learn these from data, for example by minimizing a prediction loss (e.g., hinge loss =-=[25]-=-). We have recently shown how to incorporate dual relaxation algorithms into such learning problems [18]. It will be interesting to apply our ADMM approach in this setting to yield an efficient learni... |

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Citation Context ...e, however, that for this scheme to work well, the Lagrange multipliers γ and µ should be also initialized accordingly. Another potential improvement is to use an adaptive penalty parameter ρt (e.g., =-=[11]-=-). This may improve convergence in practice, as well as reduce sensitivity to the initial choice of ρ. On the downside, the theoretical convergence guarantees of ADMM no longer hold in this case. Mart... |

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Citation Context ... wishes to learn these from data, for example by minimizing a prediction loss (e.g., hinge loss [25]). We have recently shown how to incorporate dual relaxation algorithms into such learning problems =-=[18]-=-. It will be interesting to apply our ADMM approach in this setting to yield an efficient learning algorithm for structured prediction problems. Acknowledgments. We thank Ami Wiesel and Elad Eban for ... |

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Citation Context ...tuck in suboptimal points under these conditions. One way to avoid this problem is to use a soft-max function which is smooth and strictly convex, hence this results in globally convergent algorithms =-=[6, 10, 12]-=-. Another class of algorithms [13, 16] uses the same dual objective, but employs variants of subgradient descent to it. While these methods are guaranteed to converge globally, they are typically slow... |

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Citation Context ...lso globally convergent, it has the disadvantage of using a double loop scheme where every update involves an iterative algorithm for projecting onto the local polytope. More recently, Martins et al. =-=[17]-=- proposed a globally convergent algorithm for MAP-LP based on the alternating direction method of multipliers (ADMM) [8, 5, 4, 2]. This method proceeds by iteratively updating primal and dual variable... |

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