Reinforcement Learning and Imitation Learning have achieved widespread success in many domains but remain constrained during real-world deployment. One of the main issues is the additional requirements that were not considered during training. To address this challenge, policy customization has been introduced, aiming to adapt a prior policy while preserving its inherent properties and meeting new task-specific requirements. A principled approach to policy customization is Residual Q-Learning (RQL), which formulates the problem as a Markov Decision Process (MDP) and derives a family of value-based learning algorithms. However, RQL has not yet been applied to policy gradient methods, which restricts its applicability, especially in tasks where policy gradient has already proven more effective. In this work, we first derive a concise form of Soft Policy Gradient as a preliminary. Building on this, we introduce Residual Policy Gradient (RPG), which extends RQL to policy gradient methods, allowing policy customization in gradient-based RL settings. With the view of RPG, we rethink the KL-regularized objective widely used in RL fine-tuning. We show that under certain assumptions, KL-regularized objective leads to a maximum-entropy policy that balances the inherent properties and task-specific requirements on a reward-level. Our experiments in MuJoCo demonstrate the effectiveness of Soft Policy Gradient and Residual Policy Gradient.

Imitation Learning (IL) is a widely used framework for learning imitative behavior from demonstrations. It is especially appealing for solving complex real-world tasks where handcrafting reward function is difficult, or when the goal is to mimic human expert behavior. However, the learned imitative policy can only follow the behavior in the demonstration. When applying the imitative policy, we may need to customize the policy behavior to meet different requirements coming from diverse downstream tasks. Meanwhile, we still want the customized policy to maintain its imitative nature. To this end, we formulate a new problem setting called policy customization. It defines the learning task as training a policy that inherits the characteristics of the prior policy while satisfying some additional requirements imposed by a target downstream task. We propose a novel and principled approach to interpret and determine the trade-off between the two task objectives. Specifically, we formulate the customization problem as a Markov Decision Process (MDP) with a reward function that combines 1) the inherent reward of the demonstration; and 2) the add-on reward specified by the downstream task. We propose a novel framework, Residual Q-learning, which can solve the formulated MDP by leveraging the prior policy without knowing the inherent reward or value function of the prior policy. We derive a family of residual Q-learning algorithms that can realize offline and online policy customization, and show that the proposed algorithms can effectively accomplish policy customization tasks in various environments. Demo videos and code are available on our website: https://sites.google.com/view/residualq-learning.