2 PhD positions in Combinatorial Optimization, Leuven (Belgium)

KU Leuven is looking for two excellent PhD Researchers to strengthen Bart Bogaerts' research group on Knowledge Representation and Combinatorial Optimization, which is part of the Declarative Languages and Artificial Intelligence (DTAI) section of the department of Computer Science of KU Leuven.

There are two (related) positions. One succesful candidate will focus on *proof logging*, the other candidate on *explanations*.

The field of combinatorial optimization is concerned with developing generic tools that take a declarative problem description and automatically compute an optimal solution to it. Often, users specify their problem in a high-level, human-understandable formal language. This specification is first translated into a low-level specification a solver understands and subsequently solved. Thanks to tremendous progress in solving technology, we can now solve a wide variety of NP-hard (or worse) problems in practice. Moreover, these tools are increasingly used in real-life applications, including high-value and life-affecting decisions. Therefore, it is of utmost importance that they be completely reliable.
One of the central objectives of our research group is to develop methodologies and tools with which we can guarantee with 100% certainty that the right problem has been solved correctly. To achieve this ambitious objective, we will build on recent breakthroughs in proof logging, where solvers do not just output an answer, but also a machine-verifiable proof (or certificate) of correctness. However, a major limitation of current techniques is that correctness is not proven relative to the human-understandable specification written by the user, but relative to the low-level translation that the solver receives, meaning that there is no guarantee that the solver is solving the original problem. In this project, we will investigate end-to end guarantees of correctness. When successful, this will have a major impact on the way combinatorial optimization software is developed, evaluated, and used: the proofs produced will enable (1) debugging, since proofs contain detailed information about where bugs occurred,
(2) auditability, since proofs can be stored and checked by an independent third party, and even (3) rigorous evaluation of algorithmic improvements.
For some inspiration on this topic, see the CertiFOX project page: https://www.bartbogaerts.eu/projects/CertiFOX/
Another long-standing objective is to develop methods by which we can explain the reasoning that leads to a certain decision made by combinatorial optimizer in a human-understandable way. This can range from explaining why a problem has no solutions, to explaining why a solution is optimal, or why a problem has a unique solution and how a user could have seen this. Explanations are crucial for building trust in declarative solutions and for future-proofing our tools for new laws and regulations such as the GDPR, which requires that all AI with an impact on human lives needs to be accountable.
Examples of such explanations in a puzzle domain can be found on the ZebraTutor webpage https://bartbog.github.io/zebra/
The selected candidate will contribute to this ongoing project by investigating explanations at different levels of abstraction or by investigating the link between explanations and proofs.