arXiv:2605. 07116v2 Announce Type: replace Abstract: We analyze a neural semi-discrete method for high-dimensional first-order Hamilton-Jacobi-Bellman (HJB) equations with known or learned dynamics.
arXiv:2508. 01718v2 Announce Type: replace Abstract: We develop a physics-informed policy-iteration method for stationary second-order Hamilton--Jacobi--Bellman equations arising in continuous-time stochastic control.
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.
arXiv:2606. 01122v1 Announce Type: new Abstract: We propose a five-step diagnostic protocol for residual-trained neural HJB-PIDE solvers with control-dependent L\'evy jumps, targeting a general failure mode of neural PDE methods: a learned solution can match headline scalar diagnostics while miscomputing an operator inside its training loss.
arXiv:2606. 26498v1 Announce Type: cross Abstract: This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available.
The paper introduces Fast Regularized Policy Mirror Descent (PMD) that pairs policy updates with a single temporal-difference (TD) critic step. It proves global linear convergence for finite discounted MDPs using exact coordinate-wise Bellman updates and any positive actor stepsize, regardless of critic initialization. For stochastic TD-PMD with strongly convex mirror maps, the authors achieve an expected value gap of ε after “~O(1/((1-γ)^5 σ_b ε))” transitions, without requiring trajectory resets, generative models, or nested policy evaluation loops.
This paper addresses model-free continuous-time mean-field control in a setting where the population dynamics evolve continuously according to an unknown McKean-Vlasov stochastic differential equation, while only discrete-time transition data are available. In the model-based formulation, policy evaluation is naturally described by a stationary Hamilton-Jacobi-Bellman equation on $\mathcal P_2(\mathbb R^d)$, but this equation involves the drift and diffusion coefficients of the controlled McKean-Vlasov dynamics, which are not identifiable when only discrete-time data are available.
The paper introduces a model‑free continuous‑time reinforcement learning algorithm that learns from a fixed batch of discrete‑time off‑policy data. It builds on the PhiBE‑Q framework to create a PhiBE‑PI policy iteration that uses a single state‑action critic, avoiding explicit drift or diffusion estimation. The authors provide a local end‑to‑end suboptimality guarantee under linear function approximation, analyze error propagation from discretization, function approximation, and finite samples, and reveal a bias‑variance trade‑off where finer time discretization can worsen statistical error.
arXiv:2607. 19628v1 Announce Type: new Abstract: In this work we investigate reinforcement learning (RL) as a framework for the robust control of parametrized dynamical systems in presence of measurements and model uncertainties.
arXiv:2610.27193v1 Announce Type: cross Abstract: Physics-informed neural networks (PINNs) and other residual-trained solvers judge a candidate solution by the size of its sampled PDE residual. For f...
arXiv:2512.23927v3 Announce Type: replace-cross Abstract: Fitted \(Q\)-iteration (FQI) is a standard regression-based method for optimal control in offline reinforcement learning, but its stability u...
arXiv:2610.10054v1 Announce Type: cross Abstract: Sampling transitions between metastable states is a central problem in dynamical systems theory and molecular dynamics in particular. A key challenge...
arXiv:2606. 24999v1 Announce Type: new Abstract: High-dimensional partial differential equations (PDEs) with unknown coefficients arise widely in scientific machine learning, including continuous-time reinforcement learning, yet solving them efficiently in a data-driven way remains challenging.