New Bandit Algorithm Handles Partially Observed Actions for Better Recommendations.

Traditional stochastic linear bandit problems assume full observation of action features. However, in real-world applications like recommendation systems or healthcare, obtaining complete action descriptions can be costly or impossible, leading to partial observability. This paper addresses this challenge by proposing a novel algorithm called TOFU-POV. TOFU-POV works by first estimating the underlying low-dimensional subspace of actions using the available masked data. It then imputes the missing parts of current actions based on a frozen representation from a previous epoch. Finally, it applies the OFUL (Optimism in the Face of Uncertainty) principle within these reduced-dimensional coordinates. The theoretical analysis demonstrates that TOFU-POV achieves a square-root regret that scales with the intrinsic dimension of the action subspace, rather than the higher ambient dimension. This performance is robust across varying levels of missingness and decision set sizes, and the paper also introduces a rank-adaptive version that doesn't require prior knowledge of the intrinsic dimension.