@inproceedings{9103,
  abstract     = {We introduce LRT-NG, a set of techniques and an associated toolset that computes a reachtube (an over-approximation of the set of reachable states over a given time horizon) of a nonlinear dynamical system. LRT-NG significantly advances the state-of-the-art Langrangian Reachability and its associated tool LRT. From a theoretical perspective, LRT-NG is superior to LRT in three ways. First, it uses for the first time an analytically computed metric for the propagated ball which is proven to minimize the ball’s volume. We emphasize that the metric computation is the centerpiece of all bloating-based techniques. Secondly, it computes the next reachset as the intersection of two balls: one based on the Cartesian metric and the other on the new metric. While the two metrics were previously considered opposing approaches, their joint use considerably tightens the reachtubes. Thirdly, it avoids the "wrapping effect" associated with the validated integration of the center of the reachset, by optimally absorbing the interval approximation in the radius of the next ball. From a tool-development perspective, LRT-NG is superior to LRT in two ways. First, it is a standalone tool that no longer relies on CAPD. This required the implementation of the Lohner method and a Runge-Kutta time-propagation method. Secondly, it has an improved interface, allowing the input model and initial conditions to be provided as external input files. Our experiments on a comprehensive set of benchmarks, including two Neural ODEs, demonstrates LRT-NG’s superior performance compared to LRT, CAPD, and Flow*.},
  author       = {Gruenbacher, Sophie and Cyranka, Jacek and Lechner, Mathias and Islam, Md Ariful and Smolka, Scott A. and Grosu, Radu},
  booktitle    = {Proceedings of the 59th IEEE Conference on Decision and Control},
  isbn         = {9781728174471},
  issn         = {0743-1546},
  location     = {Jeju Islang, Korea (South)},
  pages        = {1556--1563},
  publisher    = {IEEE},
  title        = {{Lagrangian reachtubes: The next generation}},
  doi          = {10.1109/CDC42340.2020.9304042},
  volume       = {2020},
  year         = {2020},
}

@inproceedings{7122,
  abstract     = {Data-rich applications in machine-learning and control have motivated an intense research on large-scale optimization. Novel algorithms have been proposed and shown to have optimal convergence rates in terms of iteration counts. However, their practical performance is severely degraded by the cost of exchanging high-dimensional gradient vectors between computing nodes. Several gradient compression heuristics have recently been proposed to reduce communications, but few theoretical results exist that quantify how they impact algorithm convergence. This paper establishes and strengthens the convergence guarantees for gradient descent under a family of gradient compression techniques. For convex optimization problems, we derive admissible step sizes and quantify both the number of iterations and the number of bits that need to be exchanged to reach a target accuracy. Finally, we validate the performance of different gradient compression techniques in simulations. The numerical results highlight the properties of different gradient compression algorithms and confirm that fast convergence with limited information exchange is possible.},
  author       = {Khirirat, Sarit and Johansson, Mikael and Alistarh, Dan-Adrian},
  booktitle    = {2018 IEEE Conference on Decision and Control},
  isbn         = {9781538613955},
  issn         = {0743-1546},
  location     = {Miami Beach, FL, United States},
  publisher    = {IEEE},
  title        = {{Gradient compression for communication-limited convex optimization}},
  doi          = {10.1109/cdc.2018.8619625},
  year         = {2019},
}