Distributionally Safe Reinforcement Learning under Model Uncertainty: A Single-Level Approach by Differentiable Convex Programming

TL;DR

This paper introduces a novel, tractable reinforcement learning framework that ensures safety under distributional shifts by transforming a bi-level problem into a single-level, differentiable convex optimization problem, improving safety guarantees in uncertain environments.

Contribution

The paper presents the first single-level, differentiable convex programming approach for distributionally safe reinforcement learning under model uncertainty, enhancing safety guarantees.

Findings

Significant safety improvements over uncertainty-agnostic policies.

Effective handling of distributional shifts using Wasserstein metric.

Tractable end-to-end differentiable safety enforcement.

Abstract

Safety assurance is uncompromisable for safety-critical environments with the presence of drastic model uncertainties (e.g., distributional shift), especially with humans in the loop. However, incorporating uncertainty in safe learning will naturally lead to a bi-level problem, where at the lower level the (worst-case) safety constraint is evaluated within the uncertainty ambiguity set. In this paper, we present a tractable distributionally safe reinforcement learning framework to enforce safety under a distributional shift measured by a Wasserstein metric. To improve the tractability, we first use duality theory to transform the lower-level optimization from infinite-dimensional probability space where distributional shift is measured, to a finite-dimensional parametric space. Moreover, by differentiable convex programming, the bi-level safe learning problem is further reduced to a single-level one with two sequential computationally efficient modules: a convex quadratic program to guarantee safety followed by a projected gradient ascent to simultaneously find the worst-case uncertainty. This end-to-end differentiable framework with safety constraints, to the best of our knowledge, is the first tractable single-level solution to address distributional safety. We test our approach on first and second-order systems with varying complexities and compare our results with the uncertainty-agnostic policies, where our approach demonstrates a significant improvement on safety guarantees.