label_gain used in 'rank_xendcg' objective despite docs saying only 'lambdarank'

[AlexKC99]

Description

https://lightgbm.readthedocs.io/en/latest/Parameters.html
From the docs, label_gain is purported to only apply to 'lambdarank' applications. However, when using the 'rank_xendcg' objective, changing the label_gain parameter impacts the training result. I highlight this in a dummy example below:

Reproducible example

import lightgbm as lgb
import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split

np.random.seed(42)
num_samples = 100
num_features = 5

X = pd.DataFrame(np.random.rand(num_samples, num_features), columns=[f"feature_{i}" for i in range(num_features)])
y = np.random.choice([0, 1, 2, 3, 4], size=num_samples)
groups = [20] * 5

X_train, X_val, y_train, y_val = train_test_split(X, y, test_size=0.2, random_state=42)

train_size = int(len(X_train) / num_samples * sum(groups))
groups_train = groups[:train_size // 20]
groups_val = groups[train_size // 20:]

train_data = lgb.Dataset(X_train, label=y_train, group=groups_train)
val_data = lgb.Dataset(X_val, label=y_val, group=groups_val, reference=train_data)

params = {
'objective': 'rank_xendcg',
'metric': 'ndcg',
'num_leaves': 31,
'learning_rate': 0.05,
'eval_at':[20],
'verbose': -1
}

print("Training with default label_gain...")
ranker_model_default = lgb.train(
params,
train_data,
num_boost_round=10,
valid_sets=[train_data, val_data],
valid_names=['train', 'val'],
)

params['label_gain'] = [0, 1, 2, 3, 4]
print("\nTraining with custom label_gain...")
ranker_model_custom_gain = lgb.train(
params,
train_data,
num_boost_round=10,
valid_sets=[train_data, val_data],
valid_names=['train', 'val'],
)

print("\nDefault label_gain NDCG:", ranker_model_default.best_score)
print("Custom label_gain NDCG:", ranker_model_custom_gain.best_score)

Default label_gain NDCG: defaultdict(<class 'collections.OrderedDict'>, {'train': OrderedDict([('ndcg@20', 0.8419975079526356)]), 'val': OrderedDict([('ndcg@20', 0.6362625303185142)])})
Custom label_gain NDCG: defaultdict(<class 'collections.OrderedDict'>, {'train': OrderedDict([('ndcg@20', 0.8813059338868674)]), 'val': OrderedDict([('ndcg@20', 0.7695575603309358)])})

Environment info

Name: lightgbm
Version: 4.0.0
Summary: LightGBM Python Package

Additional Comments

This leads to undesirable behaviour where changing target values does not map to changes in desired gain. Am I missing something?