Efficient Algorithms for Learning to Control Bandits with Unobserved Contexts
This addresses a gap in contextual bandit research for scenarios with unobserved or noisy contexts, which is incremental as it builds on existing frameworks but introduces new technical approaches.
The paper tackles the problem of learning optimal control policies for contextual bandits with imperfectly observed contexts, presenting a posterior sampling algorithm that demonstrates efficiency in handling noisy observations and varying parameters like signal-to-noise ratios.
Contextual bandits are widely-used in the study of learning-based control policies for finite action spaces. While the problem is well-studied for bandits with perfectly observed context vectors, little is known about the case of imperfectly observed contexts. For this setting, existing approaches are inapplicable and new conceptual and technical frameworks are required. We present an implementable posterior sampling algorithm for bandits with imperfect context observations and study its performance for learning optimal decisions. The provided numerical results relate the performance of the algorithm to different quantities of interest including the number of arms, dimensions, observation matrices, posterior rescaling factors, and signal-to-noise ratios. In general, the proposed algorithm exposes efficiency in learning from the noisy imperfect observations and taking actions accordingly. Enlightening understandings the analyses provide as well as interesting future directions it points to, are discussed as well.