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We consider a finite-armed structured bandit problem in which mean rewards ofdifferent arms are known functions of a common hidden parameter $\theta^*$.Since we do not place any restrictions of these functions, the problem settingsubsumes several previously studied frameworks that assume linear or invertiblereward functions. We propose a novel approach to gradually estimate the hidden$\theta^*$ and use the estimate together with the mean reward functions tosubstantially reduce exploration of sub-optimal arms. This approach enables usto fundamentally generalize any classic bandit algorithm including UCB andThompson Sampling to the structured bandit setting. We prove via regretanalysis that our proposed UCB-C algorithm (structured bandit versions of UCB)pulls only a subset of the sub-optimal arms $O(\log T)$ times while the othersub-optimal arms (referred to as non-competitive arms) are pulled $O(1)$ times.As a result, in cases where all sub-optimal arms are non-competitive, which canhappen in many practical scenarios, the proposed algorithms achieve boundedregret. We also conduct simulations on the Movielens recommendations dataset todemonstrate the improvement of the proposed algorithms over existing structuredbandit algorithms.

A Unified Approach to Translate Classical Bandit Algorithms to the Structured Bandit Setting