Combinatorial Multi-armed Bandits: Arm Selection via Group Testing
Abstract: This paper considers the problem of combinatorial multi-armed bandits with semi-bandit feedback and a cardinality constraint on the super-arm size. Existing algorithms for solving this problem typically involve two key sub-routines: (1) a *parameter estimation* routine that sequentially estimates a set of base-arm parameters, and (2) a *super-arm selection* policy for selecting a subset of base arms deemed optimal based on these parameters. State-of-the-art algorithms assume access to an *exact* oracle for super-arm selection with unbounded computational power. At each instance, this oracle evaluates a list of score functions, the number of which grows as low as linearly and as high as exponentially with the number of arms. This can be prohibitive in the regime of a large number of arms. This paper introduces a novel realistic alternative to the perfect oracle. This algorithm uses a combination of *group-testing* for selecting the super arms and *quantized* Thompson sampling for parameter estimation. Under a general separability assumption on the reward function, the proposed algorithm reduces the complexity of the super-arm-selection oracle to be *logarithmic* in the number of base arms while achieving the same regret order as the state-of-the-art algorithms that use exact oracles. This translates to *at least an exponential* reduction in complexity compared to the oracle-based approaches.
Submission Length: Regular submission (no more than 12 pages of main content)
Previous TMLR Submission Url: https://openreview.net/forum?id=6vbwTJ6ggJ
Changes Since Last Submission: The paper was desk-rejected due to fonts being modified from the TMLR template. This has now been changed to the template font.
Assigned Action Editor: ~Vidya_Muthukumar3
Submission Number: 3981
Loading