Related papers: Verification and Validation of Convex Optimization…
In this paper, we consider the problem of formally verifying the safety of an autonomous robot equipped with a Neural Network (NN) controller that processes LiDAR images to produce control actions. Given a workspace that is characterized by…
Convex programming plays a fundamental role in machine learning, data science, and engineering. Testing convexity structure in nonlinear programs relies on verifying the convexity of objectives and constraints. Grant et al. (2006)…
Planning safe motions for legged robots requires sophisticated safety verification tools. However, designing such tools for such complex systems is challenging due to the nonlinear and high-dimensional nature of these systems' dynamics. In…
We present recent advances in formal verification and control for autonomous systems with practical safety guarantees enabled by conformal prediction (CP), a statistical tool for uncertainty quantification. This survey is particularly…
As control systems become increasingly more complex, there exists a pressing need to find systematic ways of verifying them. To address this concern, there has been significant work in developing test generation schemes for black-box…
Quantum computing technology may soon deliver revolutionary improvements in algorithmic performance, but these are only useful if computed answers are correct. While hardware-level decoherence errors have garnered significant attention, a…
In model-based reinforcement learning for safety-critical control systems, it is important to formally certify system properties (e.g., safety, stability) under the learned controller. However, as existing methods typically apply formal…
Convexity, though extremely important in mathematical programming, has not drawn enough attention in the field of dynamic programming. This paper gives conditions for verifying convexity of the cost-to-go functions, and introduces an…
Efficient algorithms for convex optimization, such as the ellipsoid method, require an a priori bound on the radius of a ball around the origin guaranteed to contain an optimal solution if one exists. For linear and convex quadratic…
The complexity of modern-day System-on-Chips (SoCs) is continually increasing, and it becomes increasingly challenging to deliver dependable and credible chips in a short time-to-market. Especially, in the case of test chips, where the aim…
Code verification plays an important role in establishing the credibility of computational simulations by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, the numerical…
In mechanism design, the gold standard solution concepts are dominant strategy incentive compatibility and Bayesian incentive compatibility. These solution concepts relieve the (possibly unsophisticated) bidders from the need to engage in…
Algorithmic verification of realistic systems to satisfy safety and other temporal requirements has suffered from poor scalability of the employed formal approaches. To design systems with rigorous guarantees, many approaches still rely on…
This paper presents rigorous forward error bounds for linear conic optimization problems. The error bounds are formulated in a quite general framework; the underlying vector spaces are not required to be finite-dimensional, and the convex…
Autonomous air taxis are poised to revolutionize urban mass transportation, however, ensuring their safety and reliability remains an open challenge. Validating autonomy solutions on air taxis in the real world presents complexities, risks,…
This paper addresses the problem of formally verifying desirable properties of neural networks, i.e., obtaining provable guarantees that neural networks satisfy specifications relating their inputs and outputs (robustness to bounded norm…
We propose an automated verification technique for hypersafety properties, which express sets of valid interrelations between multiple finite runs of a program. The key observation is that constructing a proof for a small representative set…
We present a method for verifying the correctness of imperative programs which is based on the automated transformation of their specifications. Given a program prog, we consider a partial correctness specification of the form $\{\varphi\}$…
Deep learning operators are fundamental components of modern deep learning frameworks. With the growing demand for customized operators, it has become increasingly common for developers to create their own. However, designing and…
Recent advances in convex optimization have leveraged computer-assisted proofs to develop optimized first-order methods that improve over classical algorithms. However, each optimized method is specially tailored for a particular problem…