We give a geometry of interaction model for a typed lambda-calculus endowed with operators for sampling from a continuous uniform distribution and soft conditioning, namely a paradigmatic calculus for higher-order Bayesian programming. The model is based on the category of measurable spaces and partial measurable functions, and is proved adequate with respect to both a distribution-based and a sampling based operational semantics.

Joint work with Naohiko Hoshino

The manuscript is available at: http://research.crubille.lautre.net/main.pdf

Si, il y a 10.000 ans, il y avait un mot pour désigner un troupeau de moutons, ce mot voulait aussi dire «ensemble», même si cette notion d'ensemble était moins abstraite que celle que Bolzano, Dedekind et Cantor introduisirent à la fin du XIXe siècle. On pourrait croire qu'après la théorie des ensembles de Zermelo et Fraenkel, la question de savoir ce qu'est un ensemble était close. Ce n'est pas le cas comme le remarque par exemple Quine, auteur d'une théorie alternative, qui dit dans les années 60 que la question est toujours ouverte. Une nouvelle impulsion sera donnée par Lawvere avec sa théorie axiomatique de la catégorie des ensembles, et surtout par Lawvere et Tierney avec la notion de topos élémentaire. Cette dernière notion inspirera Volger, puis Lambek, qui définira la notion de «dogme». J'ai rebaptisé leur théorie en «théorie des ensembles de Volger-Lambek». J'en donnerai une description et j'expliquerai pourquoi elle est, à condition qu'elle soit un peu généralisée, la bonne théorie de formalisation non seulement des ensembles, mais de toute la mathématique telle que nous la pratiquons aujourd'hui.

Most real-world optimization problems do not have an explicit problem formulation, but only allow to compute the quality of selected solution candidates. Solving such black-box optimization problems requires iterative procedures which use the feedback gained from previous evaluations to determine the strategy by which the next solution candidates are generated. Many black-box optimization algorithms, such as Simulated Annealing, Evolutionary Algorithms, Swarm Intelligence Algorithms, are randomized – making it very difficult to analyze their performances mathematically.

In the last 15 years, the theory of randomized black-box optimization has advanced considerably, and has contributed to efficient optimization by providing insights into the working principles of black-box optimization which are hard or impossible to obtain by empirical means. On the other hand, empirically-guided benchmarking has opened up new research directions for theoretical investigations.

In this presentation we will discuss the state of the art in the theory of randomized black-box optimization algorithms. As part of this critical survey we will also mention a number of open questions and connections to other fields of Computer Science.

Most real-world optimization problems do not have an explicit problem formulation, but only allow to compute the quality of selected solution candidates. Solving such black-box optimization problems requires iterative procedures which use the feedback gained from previous evaluations to determine the strategy by which the next solution candidates are generated. Many black-box optimization algorithms, such as Simulated Annealing, Evolutionary Algorithms, Swarm Intelligence Algorithms, are randomized – making it very difficult to analyze their performances mathematically.

In the last 15 years, the theory of randomized black-box optimization has advanced considerably, and has contributed to efficient optimization by providing insights into the working principles of black-box optimization which are hard or impossible to obtain by empirical means. On the other hand, empirically-guided benchmarking has opened up new research directions for theoretical investigations.

In this presentation we will discuss the state of the art in the theory of randomized black-box optimization algorithms. As part of this critical survey we will also mention a number of open questions and connections to other fields of Computer Science.

Most real-world optimization problems do not have an explicit problem formulation, but only allow to compute the quality of selected solution candidates. Solving such black-box optimization problems requires iterative procedures which use the feedback gained from previous evaluations to determine the strategy by which the next solution candidates are generated. Many black-box optimization algorithms, such as Simulated Annealing, Evolutionary Algorithms, Swarm Intelligence Algorithms, are randomized – making it very difficult to analyze their performances mathematically.

In the last 15 years, the theory of randomized black-box optimization has advanced considerably, and has contributed to efficient optimization by providing insights into the working principles of black-box optimization which are hard or impossible to obtain by empirical means. On the other hand, empirically-guided benchmarking has opened up new research directions for theoretical investigations.

In this presentation we will discuss the state of the art in the theory of randomized black-box optimization algorithms. As part of this critical survey we will also mention a number of open questions and connections to other fields of Computer Science.

Most real-world optimization problems do not have an explicit problem formulation, but only allow to compute the quality of selected solution candidates. Solving such black-box optimization problems requires iterative procedures which use the feedback gained from previous evaluations to determine the strategy by which the next solution candidates are generated. Many black-box optimization algorithms, such as Simulated Annealing, Evolutionary Algorithms, Swarm Intelligence Algorithms, are randomized – making it very difficult to analyze their performances mathematically.

In the last 15 years, the theory of randomized black-box optimization has advanced considerably, and has contributed to efficient optimization by providing insights into the working principles of black-box optimization which are hard or impossible to obtain by empirical means. On the other hand, empirically-guided benchmarking has opened up new research directions for theoretical investigations.

In this presentation we will discuss the state of the art in the theory of randomized black-box optimization algorithms. As part of this critical survey we will also mention a number of open questions and connections to other fields of Computer Science.