Replenishable Knapsack

Replenishable knapsack problems address the challenge of optimizing resource allocation under constraints, where resources can be replenished over time. Current research focuses on developing algorithms that efficiently balance exploration and exploitation, often employing primal-dual methods, online learning techniques (like contextual bandits), and regression oracles to handle various input models (stochastic, adversarial, non-stationary). These advancements are significant because they improve the efficiency and robustness of resource management in diverse applications, including online advertising, revenue management, and fair allocation of resources. The field is actively exploring the interplay between different constraint types (packing, covering) and the impact of high-dimensionality and non-linear relationships between rewards and costs.