For illustration  purposes, we also train a LightGBM gradient-boosting tree ensemble with default settings and the multiclass objective:

param = {'objective':'multiclass', 'num_class': 5}
booster = lgb.train(params=param,
                    train_set=lgb_train,
                    num_boost_round=500,
                    early_stopping_rounds=20,
                    valid_sets=[lgb_train, lgb_test])

The basic settings do not improve on multinomial logistic regression, but further parameter tuning remains an unused option:

y_pred_class = booster.predict(test_dtm_numeric.astype(float))
accuracy_score(test.stars, y_pred_class.argmax(1) + 1)
0.738665855696524