Regret Analysis

Regret analysis in online learning focuses on quantifying the cumulative difference between an algorithm's performance and that of an optimal strategy with perfect foresight. Current research emphasizes developing algorithms with provably low regret for various settings, including multi-armed bandits, Markov decision processes (MDPs), and contextual bandits, often employing techniques like Upper Confidence Bounds (UCB), Thompson Sampling, and Follow-The-Regularized-Leader (FTRL). These advancements are crucial for improving the efficiency and robustness of decision-making systems in dynamic environments, with applications ranging from online advertising and recommendation systems to robotics and control theory. The field is also exploring extensions to handle delayed feedback, non-stationarity, and constraints, as well as investigating the potential for quantum speedups.