DPO: A Differential and Pointwise Control Approach to Reinforcement Learning

2024-04-24

AI Summary

To address low sample efficiency and physically inconsistent trajectories in reinforcement learning (RL) for continuous state-action spaces within scientific computing, this paper introduces differential RL—a novel paradigm grounded in continuous-time control theory. It establishes a differential dual framework and Hamiltonian-structured modeling to enable physics-constrained trajectory generation and optimization. We propose the first pointwise and phase-wise differential policy optimization (DPO) algorithms, delivering the first pointwise convergence guarantee and achieving an $O(K^{5/6})$ competitive regret bound. By adaptively updating policies via local trajectory motion operators, our method significantly improves data efficiency and physical fidelity. Empirically, it outperforms standard RL baselines across diverse scientific tasks—including surface modeling, mesh control, and molecular dynamics—under stringent physical constraints and limited training data.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Machine Learning: Reinforcement Learning
• Computer Vision: Diffusion Models for Vision

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

Abstract

Reinforcement learning (RL) in continuous state-action spaces remains challenging in scientific computing due to poor sample efficiency and lack of pathwise physical consistency. We introduce Differential Reinforcement Learning (Differential RL), a novel framework that reformulates RL from a continuous-time control perspective via a differential dual formulation. This induces a Hamiltonian structure that embeds physics priors and ensures consistent trajectories without requiring explicit constraints. To implement Differential RL, we develop Differential Policy Optimization (DPO), a pointwise, stage-wise algorithm that refines local movement operators along the trajectory for improved sample efficiency and dynamic alignment. We establish pointwise convergence guarantees, a property not available in standard RL, and derive a competitive theoretical regret bound of $O(K^{5/6})$. Empirically, DPO outperforms standard RL baselines on representative scientific computing tasks, including surface modeling, grid control, and molecular dynamics, under low-data and physics-constrained conditions.

Problem

• Improves sample efficiency in continuous RL
• Ensures pathwise physical consistency in control
• Optimizes local movement for dynamic alignment

Innovation

• Differential RL embeds physics via Hamiltonian structure
• DPO refines local movement operators stage-wise
• Pointwise convergence guarantees improve sample efficiency