arXiv AI

Long-Term Sequential Decision Making under Risk

arXiv:2607. 19914v1 Announce Type: new Abstract: We study finite-horizon MDP planning under \emph{root-based} (resolute) risk objectives that apply a rank-dependent functional to the distribution of total returns.

arXiv Machine Learning
5d ago

Learning Chance-Constrained MDPs with Bellman Distributional Certificates

The paper introduces a new approach to learning chance-constrained Markov decision processes (CCMDPs) using a Bellman distributional certificate. It provides both model-based and model-free algorithms with theoretical guarantees, including matching upper and lower bounds for tabular discounted CCMDPs with bounded successor support. Numerical experiments on synthetic CCMDPs and an IEEE 14-bus energy storage benchmark demonstrate the safety and effectiveness of the proposed methods.

By Chenbei Lu, Hongyu Yi
arXiv Machine Learning
Aug 28

Sequential Additivity in Distributionally Robust Ranking and Selection

The paper studies distributionally robust ranking and selection (DRR&S), where the goal is to identify the best alternative under input uncertainty by considering multiple plausible input distributions. It introduces the concept of sequential additivity, showing that efficient sampling should focus on a small, additive set of critical scenarios rather than a multiplicative number. The authors prove an algorithm‑independent lower bound on sampling, design an additive allocation (AA) procedure that meets this bound and achieves exponentially decreasing error probability, and extend the approach to a general additive allocation (GAA) framework that incorporates traditional R&S sampling rules.

By Zaile Li, Yuchen Wan, L. Jeff Hong
arXiv Machine Learning
Sep 23

Tight Sample Complexity Bounds for Entropic Best Policy Identification

The paper investigates best‑policy identification in finite‑horizon, risk‑sensitive reinforcement learning using the entropic risk measure. It identifies a gap between known lower bounds ≥ η(e^{|eta|H}) and upper bounds ≤ O(e^{2|eta|H}) for sample complexity, attributing the excess factor to loose concentration bounds for exponential utilities. By employing a forward‑model algorithm with KL‑based exploration bonuses and a novel stopping rule, the authors achieve a sample complexity that matches the lower bound, closing the previously open exponential gap.

By Amer Essakine, Claire Vernade