Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version

• URL: http://arxiv.org/abs/2604.13147v1
• Date: Tue, 14 Apr 2026 16:32:46 GMT
• Title: Adaptive Learning via Off-Model Training and Importance Sampling for Fully Non-Markovian Optimal Stochastic Control. Complete version
• Abstract summary: This paper studies continuous-time control problems whose controlled states are fully non-Markovian and depend on unknown model parameters.<n>Building on the discrete skeleton approach developed in earlier work, we propose a Monte Carlo learning methodology for the embedded backward dynamic programming equation.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper studies continuous-time stochastic control problems whose controlled states are fully non-Markovian and depend on unknown model parameters. Such problems arise naturally in path-dependent stochastic differential equations, rough-volatility hedging, and systems driven by fractional Brownian motion. Building on the discrete skeleton approach developed in earlier work, we propose a Monte Carlo learning methodology for the associated embedded backward dynamic programming equation. Our main contribution is twofold. First, we construct explicit dominating training laws and Radon--Nikodym weights for several representative classes of non-Markovian controlled systems. This yields an off-model training architecture in which a fixed synthetic dataset is generated under a reference law, while the dynamic programming operators associated with a target model are recovered by importance sampling. Second, we use this structure to design an adaptive update mechanism under parametric model uncertainty, so that repeated recalibration can be performed by reweighting the same training sample rather than regenerating new trajectories. For fixed parameters, we establish non-asymptotic error bounds for the approximation of the embedded dynamic programming equation via deep neural networks. For adaptive learning, we derive quantitative estimates that separate Monte Carlo approximation error from model-risk error. Numerical experiments illustrate both the off-model training mechanism and the adaptive importance-sampling update in structured linear-quadratic examples.

Related papers

• Symbolic Neural ODEs: Learning interpretable models from time-series data [0.0]
  We present a machine learning framework for identifying sparse, interpretable models of dynamical systems from time-series data.<n>Our approach parameterizes the underlying vector field using a neural architecture and trains it by minimizing a multi-step prediction loss over a finite horizon.<n>We show that multi-step training yields models with accurate short-term dynamics and strong agreement in long-time statistical properties.
  arXiv  Detail & Related papers  (2026-08-22T21:31:07Z)
• Physics-Aware Sparse Learning and Selective Online Adaptation for Euler-Lagrange Robot Dynamics [3.247008128557575]
  Most learning-based correction methods improve prediction accuracy by introducing a single additive residual.<n>We propose a structure-preserving residual learning framework that decomposes model mismatch into an inertia correction, the corresponding induced Coriolis term, and a generalized-force residual.<n> Experiments across multiple robotic platforms, including mobile, aerial, and manipulator systems, show that the proposed method improves dynamics prediction and trajectory tracking under coupled and time-varying dynamics.
  arXiv  Detail & Related papers  (2026-06-08T15:36:00Z)
• ODELoRA: Training Low-Rank Adaptation by Solving Ordinary Differential Equations [54.886931928255564]
  Low-rank adaptation (LoRA) has emerged as a widely adopted parameter-efficient fine-tuning method in deep transfer learning.<n>We propose a novel continuous-time optimization dynamic for LoRA factor matrices in the form of an ordinary differential equation (ODE)<n>We show that ODELoRA achieves stable feature learning, a property that is crucial for training deep neural networks at different scales of problem dimensionality.
  arXiv  Detail & Related papers  (2026-02-07T10:19:36Z)
• Stochastic Control for Fine-tuning Diffusion Models: Optimality, Regularity, and Convergence [19.484676783876306]
  Diffusion models have emerged as powerful tools for generative modeling.<n>We propose a control framework for fine-tuning diffusion models.<n>We show that PI-FT achieves global convergence at a linear rate.
  arXiv  Detail & Related papers  (2024-12-24T04:55:46Z)
• Data-driven Nonlinear Model Reduction using Koopman Theory: Integrated Control Form and NMPC Case Study [56.283944756315066]
  We propose generic model structures combining delay-coordinate encoding of measurements and full-state decoding to integrate reduced Koopman modeling and state estimation. A case study demonstrates that our approach provides accurate control models and enables real-time capable nonlinear model predictive control of a high-purity cryogenic distillation column.
  arXiv  Detail & Related papers  (2024-01-09T11:54:54Z)
• End-to-End Reinforcement Learning of Koopman Models for Economic Nonlinear Model Predictive Control [45.84205238554709]
  We present a method for reinforcement learning of Koopman surrogate models for optimal performance as part of (e)NMPC. We show that the end-to-end trained models outperform those trained using system identification in (e)NMPC.
  arXiv  Detail & Related papers  (2023-08-03T10:21:53Z)
• Kalman Filter for Online Classification of Non-Stationary Data [101.26838049872651]
  In Online Continual Learning (OCL) a learning system receives a stream of data and sequentially performs prediction and training steps. We introduce a probabilistic Bayesian online learning model by using a neural representation and a state space model over the linear predictor weights. In experiments in multi-class classification we demonstrate the predictive ability of the model and its flexibility to capture non-stationarity.
  arXiv  Detail & Related papers  (2023-06-14T11:41:42Z)
• Learning Residual Model of Model Predictive Control via Random Forests for Autonomous Driving [13.865293598486492]
  One major issue in predictive control (MPC) for autonomous driving is the contradiction between the system model's prediction and computation. This paper reformulates the MPC tracking accuracy as a program (QP) problem optimization as a program (QP) can effectively solve it.
  arXiv  Detail & Related papers  (2023-04-10T03:32:09Z)
• Data-driven Control of Agent-based Models: an Equation/Variable-free Machine Learning Approach [0.0]
  We present an Equation/Variable free machine learning (EVFML) framework for the control of the collective dynamics of complex/multiscale systems. The proposed implementation consists of three steps: (A) from high-dimensional agent-based simulations, machine learning (in particular, non-linear manifold learning (DMs)) We exploit the Equation-free approach to perform numerical bifurcation analysis of the emergent dynamics. We design data-driven embedded wash-out controllers that drive the agent-based simulators to their intrinsic, imprecisely known, emergent open-loop unstable steady-states.
  arXiv  Detail & Related papers  (2022-07-12T18:16:22Z)
• Anomaly Detection of Time Series with Smoothness-Inducing Sequential Variational Auto-Encoder [59.69303945834122]
  We present a Smoothness-Inducing Sequential Variational Auto-Encoder (SISVAE) model for robust estimation and anomaly detection of time series. Our model parameterizes mean and variance for each time-stamp with flexible neural networks. We show the effectiveness of our model on both synthetic datasets and public real-world benchmarks.
  arXiv  Detail & Related papers  (2021-02-02T06:15:15Z)
• Gaussian Process-based Min-norm Stabilizing Controller for Control-Affine Systems with Uncertain Input Effects and Dynamics [90.81186513537777]
  We propose a novel compound kernel that captures the control-affine nature of the problem. We show that this resulting optimization problem is convex, and we call it Gaussian Process-based Control Lyapunov Function Second-Order Cone Program (GP-CLF-SOCP)
  arXiv  Detail & Related papers  (2020-11-14T01:27:32Z)
• Control as Hybrid Inference [62.997667081978825]
  We present an implementation of CHI which naturally mediates the balance between iterative and amortised inference. We verify the scalability of our algorithm on a continuous control benchmark, demonstrating that it outperforms strong model-free and model-based baselines.
  arXiv  Detail & Related papers  (2020-07-11T19:44:09Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.