Free Regret

Free regret, in the context of online learning and reinforcement learning, focuses on minimizing the difference between an algorithm's cumulative reward and that of an optimal strategy, even without knowing the reward structure beforehand. Current research emphasizes developing algorithms with regret bounds that are independent of the time horizon (horizon-free) and adaptive to the variance of rewards, often employing techniques like UCB (Upper Confidence Bound) and variations of least-squares estimators within models such as linear bandits and Markov Decision Processes (MDPs). These advancements are significant because they lead to more efficient and robust algorithms for various applications, including clinical trials, recommendation systems, and resource allocation problems, where the optimal strategy is unknown and the environment is dynamic.