The paper investigates reinforcement learning in Markov decision processes whose dynamics are perturbed by non‑Markovian external events. It identifies conditions that make the problem tractable by limiting consideration to a finite history of events, and proposes a policy iteration algorithm that learns state‑dependent policies conditioned on this history. The authors provide theoretical guarantees for policy improvement, analyze sample complexity for least‑squares evaluation and improvement, and extend their results to discrete‑time Hawkes processes with Gaussian marks, validating their approach with experiments in control environments.
By Ranga Shaarad Ayyagari, Revanth Raj Eega, Ambedkar Dukkipati
arXiv:2506. 08121v2 Announce Type: replace-cross Abstract: We introduce a continuous policy-value iteration algorithm where the approximations of the value function of a stochastic control problem and the optimal control are simultaneously updated through Langevin-type dynamics.
By Qi Feng, Gu Wang
Discounted exponential utility provides a principled criterion for risk-sensitive sequential decision-making, but its nonlinear structure complicates reinforcement learning. A recent work \citep{thoppe2026reinforcement} addressed this difficulty by introducing a Bellman-compatible surrogate and two model-free fixed-point algorithms for optimizing it over stationary policies.
arXiv:2606. 18183v1 Announce Type: cross Abstract: Temporal difference (TD) learning with linear function approximation is a core method for policy evaluation.
By M. Forzo, E. Monzio Compagnoni, A. Russo, A. Pacchiano
arXiv:2608. 01917v1 Announce Type: new Abstract: Discounted exponential utility provides a principled criterion for risk-sensitive sequential decision-making, but its nonlinear structure complicates reinforcement learning.
By Ankur Naskar, Vivek T A, Aditya Kumar, Gugan Thoppe, Prashanth L. A
arXiv:2405.08253v4 Announce Type: replace-cross
Abstract: This paper develops a framework for learning in discounted infinite-horizon Markov decision processes (MDPs) with Borel state and action spac...
By Daniel Adelman, Cagla Keceli, Alba V. Olivares-Nadal
The paper introduces reinforcement learning for Continuous-Time Jump Markov Decision Processes (CTJMDPs) with general discrete state spaces and continuous/discrete actions. It develops entropy‑regularized continuous‑time control and establishes theoretical foundations for q‑learning in this setting, providing model‑free algorithms that outperform naive discretization. Numerical tests on network dynamic pricing demonstrate the method’s ability to learn near‑optimal policies and scale to large networks.
By Huiling Meng, Ningyuan Chen, Xuefeng Gao
arXiv:2411. 01982v2 Announce Type: replace-cross Abstract: We study the problem of learning controlled stochastic differential equations (SDEs) \[ dX_t = b(t,X_t,u_t)\,dt + \sigma(t,X_t,u_t)\,dW_t, \] whose drift and diffusion depend nonlinearly on time, state, and control values.
By Luc Brogat-Motte, Riccardo Bonalli, Alessandro Rudi
The paper investigates continuous‑time stochastic control problems with unknown drift and running reward functions, using an exploratory reinforcement learning framework that incorporates relaxed controls and entropy regularization. It develops policy‑iteration algorithms based on probabilistic representations of the optimal value function and its gradient, proving convergence and demonstrating performance through numerical examples. The study also extends to a special case with control‑dependent diffusion, requiring a Hessian representation.
By Jin Ma, Gaozhan Wang, Jianfeng Zhang, Xunyu Zhou
arXiv:2607. 11005v1 Announce Type: cross Abstract: This paper develops a model-free reinforcement learning framework for continuous--time extended mean field control problems, where both the dynamics and reward may depend on the joint distribution of states and controls.
By Ziheng Cheng, Xin Guo, Huy\^en Pham, Yufei Zhang
arXiv:2607. 22399v1 Announce Type: cross Abstract: We consider the problem of learning from a single finite trajectory of an ergodic stochastic dynamical system.
By Oleksii Kachaiev, Silvia Villa, Lorenzo Rosasco
arXiv:2608. 01151v1 Announce Type: cross Abstract: In this paper, we consider stochastic optimal control problems with infinite-horizon joint chance constraints.
By Francesco Cordiano, Kanghui He, Bart De Schutter