Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems

• URL: http://arxiv.org/abs/2304.03671v2
• Date: Sun, 10 Dec 2023 00:21:38 GMT
• Title: Contraction-Guided Adaptive Partitioning for Reachability Analysis of Neural Network Controlled Systems
• Authors: Akash Harapanahalli, Saber Jafarpour, Samuel Coogan
• Abstract summary: We present a contraction-guided adaptive partitioning algorithm for improving interval-valued reachable set estimates in a nonlinear feedback loop. By leveraging a decoupling of the neural network verification step and reachability partitioning layers, the algorithm can provide accuracy improvements for little computational cost. We report a sizable improvement in the accuracy of reachable set estimation in a fraction of the runtime as compared to state-of-the-art methods.
• Score: 5.359060261460183
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this paper, we present a contraction-guided adaptive partitioning algorithm for improving interval-valued robust reachable set estimates in a nonlinear feedback loop with a neural network controller and disturbances. Based on an estimate of the contraction rate of over-approximated intervals, the algorithm chooses when and where to partition. Then, by leveraging a decoupling of the neural network verification step and reachability partitioning layers, the algorithm can provide accuracy improvements for little computational cost. This approach is applicable with any sufficiently accurate open-loop interval-valued reachability estimation technique and any method for bounding the input-output behavior of a neural network. Using contraction-based robustness analysis, we provide guarantees of the algorithm's performance with mixed monotone reachability. Finally, we demonstrate the algorithm's performance through several numerical simulations and compare it with existing methods in the literature. In particular, we report a sizable improvement in the accuracy of reachable set estimation in a fraction of the runtime as compared to state-of-the-art methods.

Related papers

• Eliminating Ratio Bias for Gradient-based Simulated Parameter Estimation [0.7673339435080445]
  This article addresses the challenge of parameter calibration in models where the likelihood function is not analytically available. We propose a gradient-based simulated parameter estimation framework, leveraging a multi-time scale that tackles the issue of ratio bias in both maximum likelihood estimation and posterior density estimation problems.
  arXiv  Detail & Related papers  (2024-11-20T02:46:15Z)
• Verification of Geometric Robustness of Neural Networks via Piecewise Linear Approximation and Lipschitz Optimisation [57.10353686244835]
  We address the problem of verifying neural networks against geometric transformations of the input image, including rotation, scaling, shearing, and translation. The proposed method computes provably sound piecewise linear constraints for the pixel values by using sampling and linear approximations in combination with branch-and-bound Lipschitz. We show that our proposed implementation resolves up to 32% more verification cases than present approaches.
  arXiv  Detail & Related papers  (2024-08-23T15:02:09Z)
• Stochastic Unrolled Federated Learning [85.6993263983062]
  We introduce UnRolled Federated learning (SURF), a method that expands algorithm unrolling to federated learning. Our proposed method tackles two challenges of this expansion, namely the need to feed whole datasets to the unrolleds and the decentralized nature of federated learning.
  arXiv  Detail & Related papers  (2023-05-24T17:26:22Z)
• Interval Reachability of Nonlinear Dynamical Systems with Neural Network Controllers [5.543220407902113]
  This paper proposes a computationally efficient framework, based on interval analysis, for rigorous verification of nonlinear continuous-time dynamical systems with neural network controllers. Inspired by mixed monotone theory, we embed the closed-loop dynamics into a larger system using an inclusion function of the neural network and a decomposition function of the open-loop system. We show that one can efficiently compute hyper-rectangular over-approximations of the reachable sets using a single trajectory of the embedding system.
  arXiv  Detail & Related papers  (2023-01-19T06:46:36Z)
• Scalable computation of prediction intervals for neural networks via matrix sketching [79.44177623781043]
  Existing algorithms for uncertainty estimation require modifying the model architecture and training procedure. This work proposes a new algorithm that can be applied to a given trained neural network and produces approximate prediction intervals.
  arXiv  Detail & Related papers  (2022-05-06T13:18:31Z)
• Asynchronous Distributed Reinforcement Learning for LQR Control via Zeroth-Order Block Coordinate Descent [7.6860514640178]
  We propose a novel zeroth-order optimization algorithm for distributed reinforcement learning. It allows each agent to estimate its local gradient by cost evaluation independently, without use of any consensus protocol.
  arXiv  Detail & Related papers  (2021-07-26T18:11:07Z)
• Differentiable Annealed Importance Sampling and the Perils of Gradient Noise [68.44523807580438]
  Annealed importance sampling (AIS) and related algorithms are highly effective tools for marginal likelihood estimation. Differentiability is a desirable property as it would admit the possibility of optimizing marginal likelihood as an objective. We propose a differentiable algorithm by abandoning Metropolis-Hastings steps, which further unlocks mini-batch computation.
  arXiv  Detail & Related papers  (2021-07-21T17:10:14Z)
• Communication-Efficient Distributed Stochastic AUC Maximization with Deep Neural Networks [50.42141893913188]
  We study a distributed variable for large-scale AUC for a neural network as with a deep neural network. Our model requires a much less number of communication rounds and still a number of communication rounds in theory. Our experiments on several datasets show the effectiveness of our theory and also confirm our theory.
  arXiv  Detail & Related papers  (2020-05-05T18:08:23Z)
• Study of Diffusion Normalized Least Mean M-estimate Algorithms [0.8749675983608171]
  This work proposes diffusion normalized least mean M-estimate algorithm based on the modified Huber function. We analyze the transient, steady-state and stability behaviors of the algorithms in a unified framework. Simulations in various impulsive noise scenarios show that the proposed algorithms are superior to some existing diffusion algorithms.
  arXiv  Detail & Related papers  (2020-04-20T00:28:41Z)
• Parallelization Techniques for Verifying Neural Networks [52.917845265248744]
  We introduce an algorithm based on the verification problem in an iterative manner and explore two partitioning strategies. We also introduce a highly parallelizable pre-processing algorithm that uses the neuron activation phases to simplify the neural network verification problems.
  arXiv  Detail & Related papers  (2020-04-17T20:21:47Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.