DPO: Differential reinforcement learning with application to optimal configuration search

Reinforcement learning (RL) with continuous state and action spaces remains one of the most challenging problems within the field. Most current learning methods focus on integral identities such as value functions to derive an optimal strategy for the learning agent. In this paper, we instead study the dual form of the original RL formulation to propose the first differential RL framework that can handle settings with limited training samples and short-length episodes. Our approach introduces Differential Policy Optimization (DPO), a pointwise and stage-wise iteration method that optimizes policies encoded by local-movement operators. We prove a pointwise convergence estimate for DPO and provide a regret bound comparable with the best current theoretical derivation. Such pointwise estimate ensures that the learned policy matches the optimal path uniformly across different steps. We then apply DPO to a class of practical RL problems with continuous state and action spaces, and which search for optimal configurations with Lagrangian rewards. DPO is easy to implement, scalable, and shows competitive results on benchmarking experiments against several popular RL methods.