arXiv:2606. 28669v1 Announce Type: new Abstract: To address parameter misspecification and sudden structural environmental changes in conventional stochastic differential game (SDG) frameworks, this paper introduces a distributional control approach that characterizes optimal strategies as probability distributions over actions, conditioned on the continuous state, the discrete regime state, and parameters.
By Congde Hu, Zhuo Jin, Danping Li, Lin Xu
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
The paper introduces Diffusion-Augmented Markov Decision Processes (DA‑MDPs), a framework that extends Maximum Entropy Reinforcement Learning to diffusion-based policies. DA‑MDPs treat each reverse‑diffusion step as an RL decision, deriving a tractable reverse‑KL bound that decomposes across denoising transitions and yields diffusion‑augmented soft rewards, value functions, and policy objectives. The authors implement this framework with PPO, REPPO, and a maximum‑entropy WPO variant, showing improved continuous‑control performance, higher success rates on manipulation tasks, and memory‑efficient training with action chunking.
By Sebastian Sanokowski, Kaustubh Patil, Majid Khadiv
arXiv:2512. 04697v3 Announce Type: replace-cross Abstract: This paper studies the continuous-time reinforcement learning (RL) for optimal switching problems across multiple regimes.
By Yijie Huang, Mengge Li, Xiang Yu, Zhou Zhou
arXiv:2607. 14522v1 Announce Type: new Abstract: We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC).
By Zikun Zhang, Jiayuan Sheng, David D. Yao, Wenpin Tang
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:2605. 26078v3 Announce Type: replace Abstract: Wasserstein policy gradient (WPG) is a policy optimization method for reinforcement learning (RL) that exploits the optimal-transport geometry of action distributions.
By Zhaoyu Zhu, Rui Gao, Shuang Li
arXiv:2607. 03168v1 Announce Type: cross Abstract: Entropy regularization is widely used in continuous-time reinforcement learning (RL) to reduce sensitivity to environmental perturbations, yet its robustness benefits lack a rigorous theoretical foundation.
By Jialun Cao, Fernando Acero, David \v{S}i\v{s}ka, Yufei Zhang
In this paper, we introduce two neural-network-based numerical schemes for solving systems of coupled ergodic Backward Stochastic Differential Equations (eBSDEs), motivated by the approximation of optimal strategies within the framework of forward utilities in a regime-switching stochastic factor model. Our approach builds on the representation of such models through systems of eBSDEs introduced in [HLT20].
arXiv:2606. 24271v1 Announce Type: cross Abstract: In this paper, we introduce two neural-network-based numerical schemes for solving systems of coupled ergodic Backward Stochastic Differential Equations (eBSDEs), motivated by the approximation of optimal strategies within the framework of forward utilities in a regime-switching stochastic factor model.
By Guillaume Broux-Quemerais (LMM), Sarah Kaakai (LAGA), Anis Matoussi (LMM), Wissal Sabbagh (LMM)
The paper introduces a mesh‑free policy iteration framework that blends classical dynamic programming with physics‑informed neural networks (PINNs) to solve high‑dimensional, nonconvex Hamilton–Jacobi–Isaacs (HJI) equations. The method alternates between solving linear second‑order PDEs under fixed feedback policies and updating controls via pointwise minimax optimization using automatic differentiation. The authors prove local uniform convergence of the value function iterates to the unique viscosity solution under standard Lipschitz and uniform ellipticity assumptions, and demonstrate the approach’s accuracy and scalability in two‑, five‑, and ten‑dimensional stochastic games, outperforming direct PINN solvers.
By Hee Jun Yang, Minjung Gim, Yeoneung Kim
arXiv:2607. 06935v1 Announce Type: cross Abstract: Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory.
By Denis Belomestny, Alexander Gasnikov, Egor Gladin, Alexey Naumov, Artemy Rubtsov, Yuri Sapronov, Daniil Tiapkin, Nikita Yudin