Finding the weight vector 0 that minimizes the £2-regularized average of this loss function is the structured support vector machine (SVM) problem (Taskar et al., 2003; Tsochantaridis et al., 2005):

Denote by 0t_1 the value of the weight vector before the t-th round.

Let Agbi = qb(}_9i, wi) — qbQ‘oi, Then the algorithm updates the weight vector 0’5 as follows:

The single-threaded running time for PNDP+ and Pegasos/DP+ is about 40 minutes per epoch, measured on a dual-core AMD 2.4GHz CPU with 8GB of memory; for CRF, it takes about 100 minutes for each epoch, which is almost entirely because the weight vector 0 is less sparse with CRF learning.

The initial weight vector was 0.

If not indicated otherwise, the perceptron was run for 10 epochs with learning rate 77 = 0.0001, started at zero weight vector , using deduplicated 100-best lists.

The mixed weight vector is resent to each shard to start another epoch of training in parallel on each shard.

Reduced weight vectors are mixed and the result is resent to each shard to start another epoch of parallel training on each shard.

For each sentence pair (f, e) in the devset, we first generate an N-best list L E {h} using the current weight vector w (line 5).

Input: Devset, max number of iterations I Output: A set of (pareto-optimal) weight vectors 1: Initialize 111.

Here, the MT system’s Decode function, parameterized by weight vector w, takes in a foreign sentence f and returns a translated hypothesis h. The argmax operates in vector space and our goal is to find to leading to hypotheses on the Pareto Frontier.