Modern large language models (LLMs) are capable of generating high-quality text fora variety of tasks. However, evaluating whether a text is truly "high-quality" is extremely difficult,and searching for such texts is an even more challenging problem. In this talk, we introducemethods such as Best-of-N sampling and Minimum Bayes Risk (MBR) decoding, which approachtext generation as an optimization problem to search for better texts. We will discuss how theuniversal challenges of search and evaluation are addressed in the context of LLMs.

Recently, mathematical optimization has been emerged with the widespread applicationsof machine learning, which enables decision-making and planning based on the analyses. Inparticular, many mathematical optimization solvers have become available and are rapidly gainingpopularity as effective tools for solving real-world problems. However, due to few experts and theircandidates in industry, the practical application of mathematical optimization in industry remainsquite limited. To address this challenge, we are working towards two goals: (1) cultivating expertsof mathematical optimization by supporting their solution for practical issues and building amathematical optimization framework for decision-making in industry, and (2) developing generalpurposeand high-performance mathematical optimization solvers for a wide variety of real-worldproblems in industry and academia. We introduce a part of our challenges in this presentaiton.