O$ Regret

Online learning, particularly in the context of resource allocation and decision-making under uncertainty, aims to minimize regret—the difference between an algorithm's performance and that of an optimal strategy with perfect foresight. Current research focuses on developing algorithms that achieve low regret under various conditions, including stochastic and adversarial environments, with a particular emphasis on efficient first-order methods and adaptive algorithms that adjust to changing conditions. These advancements are significant for improving the efficiency and robustness of online systems in diverse applications such as online advertising, revenue management, and reinforcement learning, where real-time decisions must be made with incomplete information. The development of "best-of-both-worlds" algorithms, achieving optimal performance across different input scenarios, is a key area of ongoing investigation.