Lagrangian Reachtubes: The Next Generation

Gruenbacher, Sophie; Cyranka, Jacek; Lechner, Mathias; Islam, Md. Ariful; Smolka, Scott A.; Grosu, Radu

doi:10.1109/cdc42340.2020.9304042

Cited by 12 publications

(17 citation statements)

References 28 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Optimization-based safety frameworks. Recent advances in differentiable optimization methods show promising directions for safety guaranteed neural network controllers (Lechner et al, 2020b;Gruenbacher et al, 2020;Grunbacher et al, 2021;Gruenbacher et al, 2021;Massiani et al, 2021;. In (Amos and Kolter, 2017), a differentiable quadratic program (QP) layer, called OptNet, was introduced.…”

Section: Related Workmentioning

confidence: 99%

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Xiao¹,

Hasani²,

Li³

et al. 2021

Preprint

View full text Add to dashboard Cite

This paper introduces differentiable higher-order control barrier functions (CBF) that are end-toend trainable together with learning systems. CBFs are usually overly conservative, while guaranteeing safety. Here, we address their conservativeness by softening their definitions using environmental dependencies without loosing safety guarantees, and embed them into differentiable quadratic programs. These novel safety layers, termed a BarrierNet, can be used in conjunction with any neural network-based controller, and can be trained by gradient descent. BarrierNet allows the safety constraints of a neural controller be adaptable to changing environments. We evaluate them on a series of control problems such as traffic merging and robot navigations in 2D and 3D space, and demonstrate their effectiveness compared to state-of-the-art approaches.

show abstract

Section: Related Workmentioning

confidence: 99%

BarrierNet: A Safety-Guaranteed Layer for Neural Networks

Xiao¹,

Hasani²,

Li³

et al. 2021

Preprint

View full text Add to dashboard Cite

show abstract

“…We run our evaluations on a standard workstation machine setup (12 vCPUs, 64GB memory) equipped with single GPU, for a per-run timeout of 1 hour. (Gruenbacher et al, 2020). The first six benchmarks concern classical dynamical systems, whereas the two bottom rows correspond to time-continuous RNN models (LTC= liquid time-constant networks) in a closed feedback loop with an RL environment (Lechner et al, 2019;Hasani et al, , 2021bVorbach et al, 2021) Our first experimental evaluation concerns the over-approximation errors of the constructed bounding tubes.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…Consequently, as our comparison metric we will report the average volume of the bounding balls, with less volume is better. We use the benchmarks and settings of (Gruenbacher et al, 2020) (same radii, time horizons, and models) as basis of our evaluation. In particular, we compare GoTube to the deterministic, state-of-the-art reachablity tools LRT-NG, Flow*, CAPD and LRT.…”

Section: Experimental Evaluationmentioning

confidence: 99%

“…In our second experiment, we evaluate for how long GoTube and existing methods can construct a reachtube before exploding due to over-approxmiation errors. To do so, we extend the benchmark setup of (Gruenbacher et al, 2020) by increasing the time horizon for which the tube should be constructed and set GoTube to a 95% confidence level, that is, probability of being conservative.…”

Section: Gotube Provides Safety Bounds Up An Arbitrary Time Horizonmentioning

confidence: 99%

“…Deterministic verification approaches ensure conservative bounds (Chen et al, 2013a;Gowal et al, 2018;Mirman et al, 2018;Bunel et al, 2020a;Kapela et al, 2020;Gruenbacher et al, 2020), but often sacrifice speed and accuracy Figure 2: GoTube in a nutshell. The center x 0 of ball B 0 = B(x 0 , δ 0 ), with δ 0 the initial perturbation, and samples x drawn uniformly from B 0 's surface, are numerically integrated in time to χ(t j , x 0 ) and χ(t j , x), respectively.…”

mentioning

confidence: 99%

See 2 more Smart Citations

GoTube: Scalable Stochastic Verification of Continuous-Depth Models

Gruenbacher¹,

Lechner²,

Hasani³

et al. 2021

Preprint

Self Cite

View full text Add to dashboard Cite

We introduce a new stochastic verification algorithm that formally quantifies the behavioural robustness of any time-continuous process formulated as a continuousdepth model. The algorithm solves a set of global optimization (Go) problems over a given time horizon to construct a tight enclosure (Tube) of the set of all process executions starting from a ball of initial states. We call our algorithm GoTube. Through its construction, GoTube ensures that the bounding tube is conservative up to a desired probability. GoTube is implemented in JAX and optimized to scale to complex continuous-depth models. Compared to advanced reachability analysis tools for time-continuous neural networks, GoTube provably does not accumulate over-approximation errors between time steps, and avoids the infamous wrapping effect inherent in symbolic techniques. We show that GoTube substantially outperforms state-of-the-art verification tools in terms of the size of the initial ball, speed, time-horizon, task completion, and scalability, on a large set of experiments. GoTube is stable and sets the state-of-the-art for its ability to scale up to time-horizons well-beyond what has been possible before.

show abstract