Related papers: Adjoints and Automatic (Algorithmic) Differentiati…
Automatic differentiation is a technique which allows a programmer to define a numerical computation via compositions of a broad range of numeric and computational primitives and have the underlying system support the computation of partial…
In this paper we consider distributed optimization problems in which the cost function is separable, i.e., a sum of possibly non-smooth functions all sharing a common variable, and can be split into a strongly convex term and a convex one.…
Cylindrical Algebraic Decomposition (CAD) is a key tool in computational algebraic geometry, best known as a procedure to enable Quantifier Elimination over real-closed fields. However, it has a worst case complexity doubly exponential in…
Tools for algorithmic differentiation (AD) provide accurate derivatives of computer-implemented functions for use in, e. g., optimization and machine learning (ML). However, they often require the source code of the function to be available…
Differentiation along algorithms, i.e., piggyback propagation of derivatives, is now routinely used to differentiate iterative solvers in differentiable programming. Asymptotics is well understood for many smooth problems but the…
Automated planning is a prominent area of Artificial Intelligence, and an important component for intelligent autonomous agents. A cornerstone of domain-independent planning is the separation between planning logic, i.e. the automated…
We describe an approximate dynamic programming (ADP) approach to compute approximations of the optimal strategies and of the minimal losses that can be guaranteed in discounted repeated games with vector-valued losses. Such games…
Algorithmic discrimination is an important aspect when data is used for predictive purposes. This paper analyzes the relationships between discrimination and classification, data set partitioning, and decision models, as well as…
We consider a scalar function depending on a numerical solution of an initial value problem, and its second-derivative (Hessian) matrix for the initial value. The need to extract the information of the Hessian or to solve a linear system…
We discuss the role of automatic differentiation tools in optimization software. We emphasize issues that are important to large-scale optimization and that have proved useful in the installation of nonlinear solvers in the NEOS Server. Our…
Over the past a few years, research and development has made significant progresses on big data analytics. A fundamental issue for big data analytics is the efficiency. If the optimal solution is unable to attain or not required or has a…
Discrete optimization is a central problem in artificial intelligence. The optimization of the aggregated cost of a network of cost functions arises in a variety of problems including (W)CSP, DCOP, as well as optimization in stochastic…
Forward Automatic Differentiation (AD) is a technique for augmenting programs to compute derivatives. The essence of Forward AD is to attach perturbations to each number, and propagate these through the computation. When derivatives are…
Automatic differentiation (autodiff) has revolutionized machine learning. It allows to express complex computations by composing elementary ones in creative ways and removes the burden of computing their derivatives by hand. More recently,…
We introduce a quantum algorithm to compute the market risk of financial derivatives. Previous work has shown that quantum amplitude estimation can accelerate derivative pricing quadratically in the target error and we extend this to a…
By using a jump transformation associated to the Romik map, we define a new continued fraction algorithm called odd-odd continued fraction, whose principal convergents are rational numbers of odd denominators and odd numerators. Among…
There exist many applications where it is necessary to approximate numerically derivatives of a function which is given by a computer procedure. In particular, all the fields of optimization have a special interest in such a kind of…
The purpose of this paper is to introduce two new classes of accelerated distributed proximal conjugate gradient algorithms for multi-agent constrained optimization problems; given as minimization of a function decomposed as a sum of M…
Adjoint method is widely used in aerodynamic design because only once solution of flow field is required for adjoint method to obtain the gradients of all design variables. However, the calculation cost of adjoint vector is approximately…
Many algorithms feature an iterative loop that converges to the result of interest. The numerical operations in such algorithms are generally implemented using finite-precision arithmetic, either fixed- or floating-point, most of which…