A Scenario Approach to Risk-Aware Safety-Critical System Verification

Akella, Prithvi; Ahmadi, Mohamadreza; Ames, Aaron D.

doi:10.48550/arxiv.2203.02595

Cited by 2 publications

(4 citation statements)

References 20 publications

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“…to upper bound E π [f (X)]. This section will build on our prior work [38] from which we will utilize an optimization problem and theorem. The optimization problem is below, where { i } N i=1 is a set of scalar values ∈ R which will be defined whenever we require the solution to (UB-RP-N), e.g.…”

Section: A Scenario Approach To Bounding G-entropic Risk Measuresmentioning

confidence: 99%

“…Theorem 4 (Adapted from Theorem 2 in [38]). Let ζ * N be the solution to (UB-RP-N) for a set of N samples {x k } N i=k of a random variable X with unknown distribution function π.…”

Section: A Scenario Approach To Bounding G-entropic Risk Measuresmentioning

confidence: 99%

“…By further uniformly sampling initial conditions and parameters from their respective spaces i.e. sampling (x 0 , θ) from U[X 0 ×Θ], we generate the scalar randomized robustness variable R with distribution π R that was the subject of study in [38].…”

Section: Notation and Problem Settingmentioning

confidence: 99%

“…Risk-aware verification [38] is one example of a type of optimization problem that could potentially benefit from the sample-based probabilistic approaches developed in Section 3. Another optimization problem is risk-aware policy synthesis.…”

Section: Identification Of "Good" Solutions To Optimization Problemsmentioning

confidence: 99%

See 3 more Smart Citations

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

Akella¹,

Dixit²,

Ahmadi³

et al. 2022

Preprint

Self Cite

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The dramatic increase of autonomous systems subject to variable environments has given rise to the pressing need to consider risk in both the synthesis and verification of policies for these systems. This paper aims to address a few problems regarding risk-aware verification and policy synthesis, by first developing a sample-based method to bound the risk measure evaluation of a random variable whose distribution is unknown. These bounds permit us to generate high-confidence verification statements for a large class of robotic systems. Second, we develop a sample-based method to determine solutions to non-convex optimization problems that outperform a large fraction of the decision space of possible solutions. Both sample-based approaches then permit us to rapidly synthesize risk-aware policies that are guaranteed to achieve a minimum level of system performance. To showcase our approach in simulation, we verify a cooperative multi-agent system and develop a risk-aware controller that outperforms the system's baseline controller. We also mention how our approach can be extended to account for any g-entropic risk measure -the subset of coherent risk measures on which we focus.

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Section: A Scenario Approach To Bounding G-entropic Risk Measuresmentioning

confidence: 99%

“…Theorem 4 (Adapted from Theorem 2 in [38]). Let ζ * N be the solution to (UB-RP-N) for a set of N samples {x k } N i=k of a random variable X with unknown distribution function π.…”

Section: A Scenario Approach To Bounding G-entropic Risk Measuresmentioning

confidence: 99%

Section: Notation and Problem Settingmentioning

confidence: 99%

Section: Identification Of "Good" Solutions To Optimization Problemsmentioning

confidence: 99%

See 2 more Smart Citations

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

Akella¹,

Dixit²,

Ahmadi³

et al. 2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-Aware Verification

Qin,

Xia,

Zutshi

et al. 2024

ACM Trans. Cyber-Phys. Syst.

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Uncertainty in safety-critical cyber-physical systems can be modeled using a finite number of parameters or parameterized input signals. Given a system specification in Signal Temporal Logic (STL), we would like to verify that for all (infinite) values of the model parameters/input signals, the system satisfies its specification. Unfortunately, this problem is undecidable in general. Statistical model checking (SMC) offers a solution by providing guarantees on the correctness of CPS models by statistically reasoning on model simulations. We propose a new approach for statistical verification of CPS models for user-provided distribution on the model parameters. Our technique uses model simulations to learn surrogate models , and uses conformal inference to provide probabilistic guarantees on the satisfaction of a given STL property. Additionally, we can provide prediction intervals containing the quantitative satisfaction values of the given STL property for any user-specified confidence level. We compare this prediction interval with the interval we get using risk estimation procedures. We also propose a refinement procedure based on Gaussian Process (GP)-based surrogate models for obtaining fine-grained probabilistic guarantees over sub-regions in the parameter space. This in turn enables the CPS designer to choose assured validity domains in the parameter space for safety-critical applications. Finally, we demonstrate the efficacy of our technique on several CPS models.

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A Scenario Approach to Risk-Aware Safety-Critical System Verification

Cited by 2 publications

References 20 publications

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

Sample-Based Bounds for Coherent Risk Measures: Applications to Policy Synthesis and Verification

Statistical Verification using Surrogate Models and Conformal Inference and a Comparison with Risk-Aware Verification

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