[Paper Review] Learning-based Model Predictive Control for Safe Exploration and Reinforcement Learning

Torsten Koller, Felix Berkenkamp+3 more|arXiv (Cornell University)|Jun 27, 2019

Advanced Control Systems Optimization44 references52 citations

TL;DR

A learning-based MPC approach that provides high-probability safety guarantees for nonlinear systems with input-dependent uncertainty, enabling safe exploration and integration with reinforcement learning.

ABSTRACT

Reinforcement learning has been successfully used to solve difficult tasks in complex unknown environments. However, these methods typically do not provide any safety guarantees during the learning process. This is particularly problematic, since reinforcement learning agent actively explore their environment. This prevents their use in safety-critical, real-world applications. In this paper, we present a learning-based model predictive control scheme that provides high-probability safety guarantees throughout the learning process. Based on a reliable statistical model, we construct provably accurate confidence intervals on predicted trajectories. Unlike previous approaches, we allow for input-dependent uncertainties. Based on these reliable predictions, we guarantee that trajectories satisfy safety constraints. Moreover, we use a terminal set constraint to recursively guarantee the existence of safe control actions at every iteration. We evaluate the resulting algorithm to safely explore the dynamics of an inverted pendulum and to solve a reinforcement learning task on a cart-pole system with safety constraints.

Motivation & Objective

• Motivate safe learning in unknown environments where exploration must respect safety constraints.
• Learn a statistical model of system dynamics to capture unknown errors with confidence intervals.
• Develop multi-step ahead predictions that handle input-dependent uncertainty.
• Guarantee feasibility and safety at every iteration through a safe set and terminal constraints.
• Enable safe exploration and task-driven data collection for RL by combining planning with learning.

Proposed method

• Model unknown dynamics as x_{t+1} = h(x_t,u_t) + g(x_t,u_t) with a known prior h and unknown, Lipschitz g.
• Use Gaussian processes to model g, deriving point estimates μ_n and uncertainty σ_n with high-probability confidence bounds.
• Construct reliable confidence intervals that accommodate input-dependent uncertainty (β·σ) using RKHS properties and GP theory.
• Develop ellipsoidal over-approximations for multi-step state predictions to propagate uncertainty over time.
• Formulate a robust MPC that ensures safety constraints and a safe terminal set, guaranteeing feasible safe actions.
• Integrate safe exploration by combining safety-driven trajectories with performance-driven planning to drive RL.

Experimental results

Research questions

• RQ1 How can we guarantee safety with high probability during learning-based control in the presence of input-dependent uncertainty?
• RQ2 Can we propagate multi-step uncertainty through predictions to plan safe trajectories and maintain feasibility?
• RQ3 How can safe exploration be integrated with reinforcement learning to improve task performance without violating constraints?
• RQ4 What is the role of a guaranteed safe terminal set in ensuring recursive feasibility under learning dynamics?

Key findings

• The proposed MPC scheme provides high-probability safety guarantees throughout learning.
• Two uncertainty propagation techniques are developed to handle input-dependent uncertainties in multi-step predictions.
• Confidence intervals for model error g are derived from GP/RKHS assumptions, enabling reliable safety bounds.
• The approach supports safe exploration and safe model-based RL by planning safety trajectories and task-relevant performance trajectories.
• Experiments demonstrate safe exploration on an inverted pendulum and safe RL on a cart-pole with safety constraints.
• The method combines a safety backup controller with learning-based planning to ensure constraint satisfaction and progress toward goals.