Tail Bound

Tail bounds are probabilistic tools used to quantify the likelihood of a random variable deviating significantly from its expected value. Current research focuses on extending their application beyond simple scalar variables to high-dimensional data and complex algorithms, including those involving evolutionary computation, stochastic optimization, and machine learning (e.g., bandit algorithms, kernel regression). These advancements are crucial for providing stronger theoretical guarantees and improved performance in various fields, such as AI, robotics, and statistical inference, by enabling more robust analysis of algorithm runtime and prediction uncertainty.