Lower Bound

Lower bounds in computer science and statistics aim to establish fundamental limits on the performance of algorithms and estimators, providing benchmarks against which to measure progress. Current research focuses on tightening existing lower bounds for various problems, including optimization (e.g., Adam, boosting), machine learning (e.g., bandit problems, differentially private learning), and statistical estimation (e.g., covariance matrices, mixture models), often employing techniques like Fano's inequality, Le Cam's method, and information-theoretic approaches. These advancements refine our understanding of computational and statistical complexity, informing the design of more efficient algorithms and guiding the development of more realistic expectations for performance in diverse applications.