Reinforcement learning (RL) is widely investigated in diverse tasks, such as games and robotic controls, yet applications to real-world problems are limited. An outstanding issue preventing applications to real-world problems is the task dependency of hyperparameters of RL algorithms, which necessitates a hyperparameter tuning task by task. Because RL algorithms need enormous computational costs in training, it is often difficult to directly tune the hyperparameters in the target task. To mitigate this issue, this paper proposes a trust region radius adaptation mechanism for trust region policy optimization (TRPO), a prominent method that solves various continuous control tasks. Our adaptation mechanism updates the trust region radius so that the signal-to-noise ratio of a natural gradient is kept constant. We evaluate the proposed method in Brax benchmark tasks with hyperparameter optimization and find that our method can mitigate performance degradation when the same hyperparameters are applied to multiple tasks. We also demonstrate that the proposed method can be used for a real-world problem, i.e., automatic berthing control of a ship, with the hyperparameters obtained in the benchmark tasks.