Reinforcement learning (RL) has shown its strength in challenging sequential decision-making problems. The reward function in RL is crucial to the learning performance, as it serves as a measure of the task completion degree. In real-world problems, the rewards are predominantly human-designed, which requires laborious tuning, and is easily affected by human cognitive biases. To achieve automatic auxiliary reward generation, we propose a novel representation learning approach that can measure the ``transition distance'' between states. Building upon these representations, we introduce an auxiliary reward generation technique for both single-task and skill-chaining scenarios without the need for human knowledge. The proposed approach is evaluated in a wide range of manipulation tasks. The experiment results demonstrate the effectiveness of measuring the transition distance between states and the induced improvement by auxiliary rewards, which not only promotes better learning efficiency but also increases convergent stability.

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