arXiv Machine Learning
Sep 24

Limiting-Kernel Q($\lambda$): Bridging Short and Long Horizons

Limiting‑Kernel Q(λ) (LKQL) is an off‑policy value estimator that blends n‑step truncation with a long‑horizon approximation based on the limiting kernel. It maintains the computational efficiency of n‑step methods while improving policy evaluation accuracy, especially for long‑horizon tasks. The authors prove faster convergence of LKQL’s operator under aperiodicity and near‑on‑policy conditions, and demonstrate empirical gains on MuJoCo continuous‑control benchmarks.

By Tolga Ok, Arman Sharifi Kolarijani, Peyman Mohajerin Esfahani, Mohamad Amin Sharifi Kolarijani
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