workaround for https://github.com/optuna/optuna/issues/1351

issue1351_handling_custom_metric.patch

diff --git a/optuna/integration/lightgbm_tuner/optimize.py b/optuna/integration/lightgbm_tuner/optimize.py
index f11c8326..4434e51c 100644
--- a/optuna/integration/lightgbm_tuner/optimize.py
+++ b/optuna/integration/lightgbm_tuner/optimize.py
@@ -112,7 +112,14 @@ class BaseTuner(object):
         else:
             raise NotImplementedError
 
+        if self.lgbm_params.get("metric") == "None":
+            if len(booster.best_score[valid_name].keys()) > 0:
+                metric = list(booster.best_score[valid_name].keys())[0]
+            else:
+                raise ValueError("No given metric in parameters.")
+
         val_score = booster.best_score[valid_name][metric]
+
         return val_score
 
     def _metric_with_eval_at(self, metric):

issue1351_reproducible_example.py

import numpy as np
import sklearn.datasets
from sklearn.metrics import accuracy_score
from sklearn.model_selection import train_test_split

import optuna.integration.lightgbm as lgb


def custom_metrics_func(preds, train_data):
    y = train_data.get_label()
    error_sum = (preds - y).sum()

    return ('custom_metrics', error_sum, False)


if __name__ == "__main__":
    data, target = sklearn.datasets.load_breast_cancer(return_X_y=True)
    train_x, val_x, train_y, val_y = train_test_split(data, target, test_size=0.25)
    dtrain = lgb.Dataset(train_x, label=train_y)
    dval = lgb.Dataset(val_x, label=val_y)

    params = {
        "objective": "binary",
        "metric": "None",
        "verbosity": -1,
        "boosting_type": "gbdt",
    }

    model = lgb.train(
        params, dtrain, valid_sets=[dtrain, dval], verbose_eval=100, early_stopping_rounds=100,
        feval=custom_metrics_func,
    )

    prediction = np.rint(model.predict(val_x, num_iteration=model.best_iteration))
    accuracy = accuracy_score(val_y, prediction)

    best_params = model.params
    print("Best params:", best_params)
    print("  Accuracy = {}".format(accuracy))
    print("  Params: ")
    for key, value in best_params.items():
        print("    {}: {}".format(key, value))