Daume and Marcu 2005 Learning as Search Optimization: Approximate Large Margin Methods for Structured Prediction

Citation and Online Link

Learning as Search Optimization: Approximate Large Margin Methods for Structured Prediction An alternative formal analysis of Searn.

Summary

The authors present the Learning as Search Optimization (LaSO) framework. The algorithm is basically SEARN but analyzed differently (and also ~24 pages shorter).

Like SEARN, LaSO attempts to combine the learning of the model with the search that occurs during decoding. Instead of learning the model, and then doing a search during decoding to find the best output

${\hat {y}}={\text{arg}}\max _{y\in {\mathcal {Y}}}f(x,y;w)$

LaSO attempts to learn to search.

Method

The generic search (decoding) algorithm is shown below:

The enqueue function puts the nodes onto the queue in some order. Depending on the order that the enqueue function puts nodes on the queue, you can get depth-first, breadth-first, beam, heuristic, A*, etc search algorithms from standard AI textbooks. The thing that is different about LaSO is the function enqueue. It ranks the nodes according to g which is a linear function of features. The features can depend on the input x and the path to the current current node n:

$g=\mathbf {\omega } ^{\top }$

LaSO works by learning the enqueue function from the training examples. The learning algorithm is shown below:

Nodes for which there exists a path to the optimal goal are called "y-good" nodes. The siblings function denotes the set of nodes at the same depth as current node that can reach the goal (i.e. are y-good). The algorithm may have to backtrack to find them if they are not currently in the queue.

There many possible update functions for the weights. The two they propose in the paper are the perceptron update (shown below) and a variant of the approximate large margin update (ALMA).

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