Measurement Scheduling for ICU Patients with Offline Reinforcement Learning

Scheduling laboratory tests for ICU patients presents a significant challenge. Studies show that 20-40% of lab tests ordered in the ICU are redundant and could be eliminated without compromising patient safety. Prior work has leveraged offline reinforcement learning (Offline-RL) to find optimal policies for ordering lab tests based on patient information. However, new ICU patient datasets have since been released, and various advancements have been made in Offline-RL methods. In this study, we first introduce a preprocessing pipeline for the newly-released MIMIC-IV dataset geared toward time-series tasks. We then explore the efficacy of state-of-the-art Offline-RL methods in identifying better policies for ICU patient lab test scheduling. Besides assessing methodological performance, we also discuss the overall suitability and practicality of using Offline-RL frameworks for scheduling laboratory tests in ICU settings.

Matrix Multiplication: Verifying Strong Uniquely Solvable Puzzles

Cohn and Umans proposed a framework for developing fast matrix multiplication algorithms based on the embedding computation in certain groups algebras. In subsequent work with Kleinberg and Szegedy, they connected this to the search for combinatorial objects called strong uniquely solvable puzzles (strong USPs). We begin a systematic computer-aided search for these objects. We develop and implement constraint-based algorithms build on reductions to $\mathrm{SAT}$ and $\mathrm{IP}$ to verify that puzzles are strong USPs, and to search for large strong USPs. We produce tight bounds on the maximum size of a strong USP for width $k \le 5$, construct puzzles of small width that are larger than previous work, and improve the upper bounds on strong USP size for $k \le 12$. Although our work only deals with puzzles of small-constant width, the strong USPs we find imply matrix multiplication algorithms that run in $O(n^\omega)$ time with exponent $\omega \le 2.66$. While our algorithms do not beat the fastest algorithms, our work provides evidence and, perhaps, a path to finding families of strong USPs that imply matrix multiplication algorithms that are more efficient than those currently known.