High Probability Bound

High-probability bounds in machine learning and optimization aim to provide strong guarantees on the performance of algorithms, going beyond the weaker expectation bounds. Current research focuses on developing and analyzing algorithms that achieve near-optimal high-probability bounds for various problems, including contextual bandits, newsvendor problems, and stochastic optimization with heavy-tailed noise, often employing techniques like martingale inequalities and refined concentration bounds. These advancements are crucial for ensuring reliable performance in real-world applications where the risk of a single poor outcome can be significant, improving the robustness and trustworthiness of machine learning models and optimization solutions.