Fighting Uncertainty with Gradients: Offline Reinforcement Learning via Diffusion Score Matching

TL;DR

This paper introduces Score-Guided Planning (SGP), a novel offline RL method that leverages learned gradient scores via diffusion score matching to efficiently navigate high-dimensional spaces and reduce model bias.

Contribution

It proposes a new approach to estimate data uncertainty through gradients learned with score matching, enabling scalable first-order planning in offline RL.

Findings

SGP outperforms zeroth-order methods in high-dimensional tasks.

Score-matching gradients facilitate efficient uncertainty minimization.

The approach effectively reduces model bias and local minima issues.

Abstract

Gradient-based methods enable efficient search capabilities in high dimensions. However, in order to apply them effectively in offline optimization paradigms such as offline Reinforcement Learning (RL) or Imitation Learning (IL), we require a more careful consideration of how uncertainty estimation interplays with first-order methods that attempt to minimize them. We study smoothed distance to data as an uncertainty metric, and claim that it has two beneficial properties: (i) it allows gradient-based methods that attempt to minimize uncertainty to drive iterates to data as smoothing is annealed, and (ii) it facilitates analysis of model bias with Lipschitz constants. As distance to data can be expensive to compute online, we consider settings where we need amortize this computation. Instead of learning the distance however, we propose to learn its gradients directly as an oracle for first-order optimizers. We show these gradients can be efficiently learned with score-matching techniques by leveraging the equivalence between distance to data and data likelihood. Using this insight, we propose Score-Guided Planning (SGP), a planning algorithm for offline RL that utilizes score-matching to enable first-order planning in high-dimensional problems, where zeroth-order methods were unable to scale, and ensembles were unable to overcome local minima. Website: https://sites.google.com/view/score-guided-planning/home