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Complexity and uncertainty associated with commodity resource valuation and extraction requires stochastic control methods suitable for high dimensional states. Recent progress in duality and trajectory-wise techniques has introduced a…
A new challenge to quantitative finance after the recent financial crisis is the study of credit valuation adjustment (CVA), which requires modeling of the future values of a portfolio. In this paper, following recent work in [Weinan…
The paper proposes a control-theoretic framework for verification of numerical software systems, and puts forward software verification as an important application of control and systems theory. The idea is to transfer Lyapunov functions…
Penetration testing (or pentesting) is one of the widely used and important methodologies to assess the security of computer systems and networks. Traditional pentesting relies on the domain expert knowledge and requires considerable human…
In this article we focus on the parameterized complexity of the Multidimensional Binary Vector Assignment problem (called \BVA). An input of this problem is defined by $m$ disjoint sets $V^1, V^2, \dots, V^m$, each composed of $n$ binary…
We apply program verification technology to the problem of specifying and verifying automatic differentiation (AD) algorithms. We focus on define-by-run, a style of AD where the program that must be differentiated is executed and monitored…
Computing reachability probabilities is at the heart of probabilistic model checking. All model checkers compute these probabilities in an iterative fashion using value iteration. This technique approximates a fixed point from below by…
Automatic differentiation is involved for long in applied mathematics as an alternative to finite difference to improve the accuracy of numerical computation of derivatives. Each time a numerical minimization is involved, automatic…
Static program analysis by abstract interpretation is an efficient method to determine properties of embedded software. One example is value analysis, which determines the values stored in the processor registers. Its results are used as…
Many machine learning models are susceptible to adversarial attacks, with decision-based black-box attacks representing the most critical threat in real-world applications. These attacks are extremely stealthy, generating adversarial…
Nowadays, as machine-learned software quickly permeates our society, we are becoming increasingly vulnerable to programming errors in the data pre-processing or training software, as well as errors in the data itself. In this paper, we…
Most leading implementations of black-box variational inference (BBVI) are based on optimizing a stochastic evidence lower bound (ELBO). But such approaches to BBVI often converge slowly due to the high variance of their gradient estimates…
Machine learning (ML) models are becoming integral in healthcare technologies, presenting a critical need for formal assurance to validate their safety, fairness, robustness, and trustworthiness. These models are inherently prone to errors,…
Providing safety guarantees for stochastic dynamical systems is a central problem in various fields, including control theory, machine learning, and robotics. Existing methods either employ Stochastic Barrier Functions (SBFs) or rely on…
The X-valuation adjustment (XVA) problem, which is a recent topic in mathematical finance, is considered and analyzed. First, the basic properties of backward stochastic differential equations (BSDEs) with a random horizon in a…
The paper proposes a theoretical approach of the debugging of constraint programs based on a notion of explanation tree. The proposed approach is an attempt to adapt algorithmic debugging to constraint programming. In this theoretical…
A new approach to the solution of boundary value problems within the so-called fictitious domain methods philosophy is proposed which avoids well known shortcomings of other fictitious domain methods, including the need to generate…
We consider dynamic programming problems with finite, discrete-time horizons and prohibitively high-dimensional, discrete state-spaces for direct computation of the value function from the Bellman equation. For the case that the value…
Bayesian Optimization (BO) is a method for globally optimizing black-box functions. While BO has been successfully applied to many scenarios, developing effective BO algorithms that scale to functions with high-dimensional domains is still…
The size-change abstraction (SCA) is an important program abstraction for termination analysis, which has been successfully implemented in many tools for functional and logic programs. In this paper, we demonstrate that SCA is also a highly…