Logarithmic Regret

Logarithmic regret, in the context of online learning, aims to minimize the cumulative difference between an algorithm's performance and that of an optimal strategy with perfect foresight. Current research focuses on achieving logarithmic regret in various challenging settings, including multi-armed bandits with heavy-tailed distributions, decentralized matching markets, and constrained Markov decision processes, often employing algorithms like UCB variants, Thompson Sampling, and Explore-then-Commit strategies. These advancements are significant because they improve the efficiency and robustness of online decision-making systems across diverse applications, from resource allocation and recommendation systems to reinforcement learning and online advertising. The pursuit of logarithmic regret drives the development of more efficient and adaptable algorithms for complex sequential decision problems.