# Minimum Error Rate Training using Powell Search for Machine Translation

From the tutorial slides: http://mt-class.org/jhu/slides/lecture-tuning.pdf, (slide 37) the powell search algorithm goes as such:

Input: sentences with n-best list of translations, initial parameter values
1: repeat
2:   for all parameter do
3:     set of threshold points T = {}
4:     for all sentence do
5:       for all translation do
6:         compute line l: parameter value → score
7:       end for
8:       find line l with steepest descent
9:       while find line l2 that intersects with l first do
10:        add parameter value at intersection to set of threshold points T
11:        l = l2
12:      end while
13:    end for
14:    sort set of threshold points T by parameter value
15:    compute score for value before first threshold point
16:    for all threshold point t ∈ T do
17:      compute score for value after threshold point t
18:      if highest do record max score and threshold point t
19:    end for
20:    if max score is higher than current do update parameter value
21:    end for
22: until no changes to parameter values applied


And on slide 31, there's a formula to compute the line l which is used for line 6 of the pseudo code above:

p(ei|f) = λai + bi


However, it's unclear what should the values be for ai and bi.

Given a sentence from the nbest list as such:

0 ||| including options , чтобы buy 20 больше planes , соотношении volume - в том 26 миллиардов долларов .  ||| LexicalReordering0= -3.10978 0 0 -6.72232 0 0 Distortion0= 0 LM0= -111.207 WordPenalty0= -18 PhrasePenalty0= 16 TranslationModel0= -13.1426 -8.45991 -12.0762 -11.3076 ||| -746.351


When computing the score for this line for the first parameter of LexicalReordering0, is the p(ei|f) this?:

p(ei|f) = λ*-3.10978 + bi


But what is the value of bi in this case?

Is p(ei|f) = -746.351 for this sentence ?

Does the → score on line 6 of the pseudo code mean -746.351 from the nbest list or does it mean the MT evaluation metric score for this translation with respect to the reference translation (e.g. BLEU)?

What should line 6 of the pseudo code do?