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In the rank objective, lambdas and hessians need to factor sigmoid_ into the computation. #2322

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Aug 17, 2019
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In the rank objective, lambdas and hessians need to factor sigmoid_ into the computation. #2322

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4f943ce
Lambdas and hessians need to factor sigmoid_ into the computation. Ad…
sbruch Aug 12, 2019
69ea3da
Update unit test
sbruch Aug 12, 2019
52aca7b
Also remove a heuristic that normalizes the gradient by the differenc…
sbruch Aug 12, 2019
d3f1e33
Also fix unit test after removing the heuristic
sbruch Aug 12, 2019
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19 changes: 4 additions & 15 deletions src/objective/rank_objective.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -104,13 +104,6 @@ class LambdarankNDCG: public ObjectiveFunction {
}
std::stable_sort(sorted_idx.begin(), sorted_idx.end(),
[score](data_size_t a, data_size_t b) { return score[a] > score[b]; });
// get best and worst score
const double best_score = score[sorted_idx[0]];
data_size_t worst_idx = cnt - 1;
if (worst_idx > 0 && score[sorted_idx[worst_idx]] == kMinScore) {
worst_idx -= 1;
}
const double wrost_score = score[sorted_idx[worst_idx]];
// start accmulate lambdas by pairs
for (data_size_t i = 0; i < cnt; ++i) {
const data_size_t high = sorted_idx[i];
Expand Down Expand Up @@ -141,16 +134,12 @@ class LambdarankNDCG: public ObjectiveFunction {
const double paired_discount = fabs(high_discount - low_discount);
// get delta NDCG
double delta_pair_NDCG = dcg_gap * paired_discount * inverse_max_dcg;
// regular the delta_pair_NDCG by score distance
if (high_label != low_label && best_score != wrost_score) {
delta_pair_NDCG /= (0.01f + fabs(delta_score));
}
// calculate lambda for this pair
double p_lambda = GetSigmoid(delta_score);
double p_hessian = p_lambda * (2.0f - p_lambda);
double p_hessian = p_lambda * (1.0f - p_lambda);
// update
p_lambda *= -delta_pair_NDCG;
p_hessian *= 2 * delta_pair_NDCG;
p_lambda *= -sigmoid_ * delta_pair_NDCG;
p_hessian *= sigmoid_ * sigmoid_ * delta_pair_NDCG;
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I am thinking about eliminating sigmoid_ here. That is, no sigmoid_ in p_lambda, and only sigmoid_ in p_hessian. What is your opinion?

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So the LambdaMART (implicit) cost function has the following form:

log(1 + exp(-sigmoid_ * (s_i - s_j)))

The first derivative of the above has the sigmoid_ term -- so mathematically p_lambda in the code must have the sigmoid_ term in its computation. The second derivative will have sigmoid_^2 as proposed in the code change.

For more details, please see Section 7 of this paper: http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.180.634&rep=rep1&type=pdf

high_sum_lambda += p_lambda;
high_sum_hessian += p_hessian;
lambdas[low] -= static_cast<score_t>(p_lambda);
Expand Down Expand Up @@ -193,7 +182,7 @@ class LambdarankNDCG: public ObjectiveFunction {
// cache
for (size_t i = 0; i < _sigmoid_bins; ++i) {
const double score = i / sigmoid_table_idx_factor_ + min_sigmoid_input_;
sigmoid_table_[i] = 2.0f / (1.0f + std::exp(2.0f * score * sigmoid_));
sigmoid_table_[i] = 1.0f / (1.0f + std::exp(score * sigmoid_));
}
}

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4 changes: 2 additions & 2 deletions tests/python_package_test/test_sklearn.py
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Expand Up @@ -82,8 +82,8 @@ def test_lambdarank(self):
eval_group=[q_test], eval_at=[1, 3], early_stopping_rounds=5, verbose=False,
callbacks=[lgb.reset_parameter(learning_rate=lambda x: 0.95 ** x * 0.1)])
self.assertLessEqual(gbm.best_iteration_, 12)
self.assertGreater(gbm.best_score_['valid_0']['ndcg@1'], 0.65)
self.assertGreater(gbm.best_score_['valid_0']['ndcg@3'], 0.65)
self.assertGreater(gbm.best_score_['valid_0']['ndcg@1'], 0.6173)
self.assertGreater(gbm.best_score_['valid_0']['ndcg@3'], 0.6479)

def test_regression_with_custom_objective(self):
def objective_ls(y_true, y_pred):
Expand Down