Combinatorial Multi-Armed Bandits

Combinatorial multi-armed bandits study sequential decisions where each round selects a set, slate, path, or allocation of arms, often under budgets or other constraints. The goal is to earn high cumulative reward while learning from semi-bandit feedback about individual selected arms or full-bandit feedback about the choice as a whole. Common approaches include UCB and Thompson sampling, online optimization and primal-dual methods, and approximation algorithms for structured objectives such as submodular maximization. A central tension is balancing regret, computational cost, and feedback limits, especially when action spaces are huge or decisions must also satisfy fairness, resource, or multi-objective requirements.