DeepAI AI Chat
Log In Sign Up

DRIP: Domain Refinement Iteration with Polytopes for Backward Reachability Analysis of Neural Feedback Loops

12/09/2022
by   Michael Everett, et al.
Google
Northeastern University
0

Safety certification of data-driven control techniques remains a major open problem. This work investigates backward reachability as a framework for providing collision avoidance guarantees for systems controlled by neural network (NN) policies. Because NNs are typically not invertible, existing methods conservatively assume a domain over which to relax the NN, which causes loose over-approximations of the set of states that could lead the system into the obstacle (i.e., backprojection (BP) sets). To address this issue, we introduce DRIP, an algorithm with a refinement loop on the relaxation domain, which substantially tightens the BP set bounds. Furthermore, we introduce a formulation that enables directly obtaining closed-form representations of polytopes to bound the BP sets tighter than prior work, which required solving linear programs and using hyper-rectangles. Furthermore, this work extends the NN relaxation algorithm to handle polytope domains, which further tightens the bounds on BP sets. DRIP is demonstrated in numerical experiments on control systems, including a ground robot controlled by a learned NN obstacle avoidance policy.

READ FULL TEXT
04/14/2022

Backward Reachability Analysis for Neural Feedback Loops

The increasing prevalence of neural networks (NNs) in safety-critical ap...
09/28/2022

Backward Reachability Analysis of Neural Feedback Loops: Techniques for Linear and Nonlinear Systems

The increasing prevalence of neural networks (NNs) in safety-critical ap...
10/14/2022

A Hybrid Partitioning Strategy for Backward Reachability of Neural Feedback Loops

As neural networks become more integrated into the systems that we depen...
01/05/2021

Efficient Reachability Analysis of Closed-Loop Systems with Neural Network Controllers

Neural Networks (NNs) can provide major empirical performance improvemen...
06/22/2021

Failing with Grace: Learning Neural Network Controllers that are Boundedly Unsafe

In this work, we consider the problem of learning a feed-forward neural ...
10/28/2021

Learning to Control using Image Feedback

Learning to control complex systems using non-traditional feedback, e.g....
07/06/2017

Convergence Analysis of Backpropagation Algorithm for Designing an Intelligent System for Sensing Manhole Gases

Human fatalities are reported due to the excessive proportional presence...