Stochastic Linear Bandits with Partially Observed Actions
2026-07-09 • Machine Learning
Machine Learning
AI summaryⓘ
The authors study a problem where a decision-maker tries to choose actions described by many features but only sees some of these features each time, making learning harder. They focus on cases where the actions actually lie in a smaller hidden space within the large feature space. Their algorithm, TOFU-POV, finds this smaller space and uses it to make better decisions, achieving good performance over time. They also create a version that works without knowing the size of this hidden space in advance. Their theoretical and experimental results show the benefits of their approach compared to simpler methods when faced with missing information.
stochastic linear banditpartial observabilityregretlatent subspacedimension reductionOFUL algorithmepoch-wise freezingrank adaptationmissing datasequential decision making
Authors
Gautam Dasarathy, Vineet Gattani, Lalit Jain
Abstract
The stochastic linear bandit, where actions are represented as vectors and rewards are linear, is a central paradigm for sequential decision making. We study a partially observed variant of this problem in which the learning agent only sees a random subset of coordinates for each action. Such partial observability arises naturally in settings like recommendation and healthcare, where full action descriptions can be expensive or even impossible to obtain. In general, this makes sublinear regret information-theoretically impossible. However, we show that this barrier can be overcome when the action vectors have low intrinsic dimension. We propose an algorithm, TOFU-POV, that estimates the latent action subspace using the masked actions, imputes current actions using an epoch-wise frozen representation, and runs OFUL in the resulting low-dimensional coordinates. Our theory shows that TOFU-POV enjoys a $\sqrt{T}$ regret that scales with the intrinsic action subspace dimension as opposed to the ambient dimension and quantifies the interaction between these quantities and the missingness, decision set size, and subspace conditioning. We also devise a rank-adaptive algorithm that does not require the knowledge of the intrinsic dimension. We complement these guarantees with a lower bound based on a novel product construction that separates usual reward-learning uncertainty from a missingness-dependent cost intrinsic to partial observation. Synthetic and real data experiments support our theory and show that TOFU-POV can substantially improve upon natural baselines in this challenging problem.