\Gamma$ Regret

Gamma-regret (γ-regret) quantifies the performance of online algorithms against a benchmark that is a fraction (γ) of the optimal solution, addressing scenarios where finding the exact optimum is computationally intractable. Current research focuses on extending this framework to handle complex constraints, such as resource allocation fairness and adversarial environments, often employing adaptive regret minimization techniques and novel algorithms designed to handle non-additive reward functions. Understanding and minimizing γ-regret is crucial for developing efficient and robust algorithms in various applications, including online resource management, fair allocation, and mechanism design, where achieving optimal solutions is computationally prohibitive.