TOFU-POV Algorithm Achieves √T Regret with Partial Action Visibility
When only random coordinates of actions are visible, sublinear regret seemed impossible—until now.
Deep Dive
The paper proposes TOFU-POV, a stochastic linear bandit algorithm that handles partially observed actions (only a random subset of coordinates visible). It achieves sublinear regret scaling with intrinsic action subspace dimension, not ambient dimension. A rank-adaptive version works without knowing that dimension. A lower bound shows missingness-dependent cost is inevitable. Applications include recommendation systems and healthcare, where full action descriptions are unavailable.
Key Points
- TOFU-POV estimates latent action subspace using masked actions and imputes current actions with epoch-wise frozen representation
- Achieves √T regret scaling with intrinsic dimension, overcoming information-theoretic impossibility in general case
- Includes rank-adaptive variant that doesn't require prior knowledge of intrinsic dimension
Why It Matters
Enables effective sequential decision-making in recommendation and healthcare where action data is routinely incomplete.