Instance Dependent Regret

Instance-dependent regret analysis in online learning and reinforcement learning aims to refine performance bounds by considering the specific characteristics of individual problem instances, rather than relying solely on worst-case scenarios. Current research focuses on developing algorithms that achieve instance-dependent regret bounds, often logarithmic or even constant, across various settings including contextual bandits, linear and nonlinear Markov decision processes, and multi-agent systems. These advancements leverage techniques like optimistic exploration, pessimistic value iteration, and information-directed sampling, often within frameworks of linear or kernel function approximation. The resulting tighter regret bounds offer improved theoretical understanding and more accurate predictions of algorithm performance in practical applications.