Monotone Function

Monotone functions, characterized by their consistently non-decreasing or non-increasing behavior, are a fundamental concept across numerous scientific fields. Current research focuses on efficiently approximating and optimizing these functions, particularly within the contexts of machine learning (e.g., using monotone neural networks and boosted tree models like XGBoost adaptations) and algorithm design (e.g., developing query-optimal algorithms and analyzing convergence rates of quasi-Newton methods). These advancements have significant implications for diverse applications, including information retrieval, robust subset selection, and probabilistic modeling, by improving the efficiency, accuracy, and interpretability of algorithms and models.