arXiv Machine Learning

Soft Fitted Q-Iteration without Bellman Completeness: Occupancy Reweighting and Temperature Annealing

arXiv Machine Learning
Sep 1

Fitted Q-Evaluation without Bellman Completeness via Occupancy Weighting

The paper introduces occupancy-weighted Fitted Q-Evaluation (FQE), a regression-based off‑policy evaluation method that replaces the standard offline distribution weights with a target‑policy discounted occupancy ratio. This weighting aligns the projection norm with the target policy’s dynamics, restoring contraction of the Bellman operator and eliminating the need for Bellman completeness. The authors provide finite‑sample guarantees that separate iteration, statistical, approximation, and ratio‑estimation errors, and show that exact occupancy weighting combined with fitted occupancy‑ratio evaluation yields consistent estimation under coverage without requiring critic‑side completeness.

By Lars van der Laan, Nathan Kallus
arXiv Machine Learning
Sep 17

A Convergence Framework for Deep $V$-Learning: Error Propagation and Sharp Action-Gap Bounds

The paper presents a convergence framework for deep $V$‑learning over a finite horizon $H$, deriving explicit bounds on policy loss by decomposing the Bellman update error into six residuals. It shows how $L^s$ concentrability controls expected $L^1$ loss, quantifies the impact of shared sampling across horizon levels, and provides optimal and near‑optimal sample allocations for statistical error rates. The work also establishes sharp action‑gap bounds under a margin condition, transfers optimal‑gap results to frozen‑iterate gaps, and offers consistency guarantees for generative‑reset approximate‑ERM procedures with exact action scores.

By Yury Kolomeytsev