Optimal Regret

Optimal regret in online learning focuses on minimizing the difference between an algorithm's cumulative performance and that of an optimal strategy, particularly in scenarios with limited or delayed feedback. Current research emphasizes developing algorithms with "best-of-both-worlds" properties, performing optimally in both stochastic and adversarial environments, often employing techniques like upper confidence bounds (UCB), Follow-The-Regularized-Leader (FTRL), and posterior sampling. These advancements are significant for improving efficiency in various applications, including online advertising, recommendation systems, and reinforcement learning, by providing theoretically sound and practically efficient methods for sequential decision-making under uncertainty. The field is also actively exploring the impact of constraints, delayed feedback, and high-dimensional data on achievable regret bounds.