def get_hyperparameter_configurations(self, num, r, config_generator):
        """generate num hyperparameter configurations from search space using Bayesian optimization

        Parameters
        ----------
        num: int
            the number of hyperparameter configurations

        Returns
        -------
        list
            a list of hyperparameter configurations. Format: [[key1, value1], [key2, value2], ...]
        """
        global _KEY
        assert self.i == 0
        hyperparameter_configs = dict()
        for _ in range(num):
            params_id = create_bracket_parameter_id(self.s, self.i)
            params = config_generator.get_config(r)
            params[_KEY] = r
            hyperparameter_configs[params_id] = params
        self._record_hyper_configs(hyperparameter_configs)
        return [[key, value] for key, value in hyperparameter_configs.items()]