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[Bug]: automl.best_run_id is None after fitting when using max_iter #1403

@tsoernes

Description

@tsoernes

Describe the bug

I have this setup:

settings = {
    "max_iter": 1,
    #"time_budget": time_budget, # Total running time in seconds
    "estimator_list": ['prophet'],  # estimator_list for spark35 forecasting 
    "starting_points": {'prophet': starting_params},  # Starting hyperparameters
        "fit_kwargs_by_estimator": {
        "prophet": {
            "holidays": holidays_df,  # Pass as fixed parameter
            "weekly_seasonality":True,
            "daily_seasonality":True,
            "yearly_seasonality":True
        }
    },
    "task": "ts_forecast",  # Task type 
    "log_file_name": "flaml_experiment.log",  # FLAML log file
    "seed": 41 , # Random seed 
    "mlflow_exp_name": "Notebook1-AutoMLExperiment",  # MLflow experiment name
    "use_spark": True,  # whether to use Spark for distributed training
    "n_concurrent_trials": 3,  # the maximum number of concurrent trials 
    "verbose": 1, 
    "featurization": "off", 
    "metric": "rmse",  # Root Mean Squared Error
    "mlflow_logging": False,
}

# Create an AutoML instance
automl_24h = AutoML(**settings)
with mlflow.start_run(nested=True, run_name="AutoMLModel-Prophet") as run:
    automl_24h.fit(
        X_train=X,
        y_train=y_train_24h,  # target column of the training data
        period=24, # (a period is 1 hour)
        X_val=X,
        y_val=y_train_24h,
        split_ratio=0,
        force_cancel=False,
    )

However, after 1 successful run, automl_24h.best_run_id is None. This does not happen when using a time budged

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