A Neural RDE approach for continuous-time non-Markovian stochastic control problems

• URL: http://arxiv.org/abs/2306.14258v1
• Date: Sun, 25 Jun 2023 14:30:33 GMT
• Title: A Neural RDE approach for continuous-time non-Markovian stochastic control problems
• Authors: Melker Hoglund, Emilio Ferrucci, Camilo Hernandez, Aitor Muguruza Gonzalez, Cristopher Salvi, Leandro Sanchez-Betancourt, Yufei Zhang
• Abstract summary: We propose a novel framework for continuous-time non-Markovian control problems by means of neural rough differential equations (Neural RDEs) Non-Markovianity naturally arises in control problems due to the time delay effects in the system coefficients or the driving noises. By modelling the control process as the solution of a Neural RDE driven by the state process, we show that the control-state joint dynamics are governed by an uncontrolled, augmented Neural RDE.
• Score: 4.155942878350882
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a novel framework for solving continuous-time non-Markovian stochastic control problems by means of neural rough differential equations (Neural RDEs) introduced in Morrill et al. (2021). Non-Markovianity naturally arises in control problems due to the time delay effects in the system coefficients or the driving noises, which leads to optimal control strategies depending explicitly on the historical trajectories of the system state. By modelling the control process as the solution of a Neural RDE driven by the state process, we show that the control-state joint dynamics are governed by an uncontrolled, augmented Neural RDE, allowing for fast Monte-Carlo estimation of the value function via trajectories simulation and memory-efficient backpropagation. We provide theoretical underpinnings for the proposed algorithmic framework by demonstrating that Neural RDEs serve as universal approximators for functions of random rough paths. Exhaustive numerical experiments on non-Markovian stochastic control problems are presented, which reveal that the proposed framework is time-resolution-invariant and achieves higher accuracy and better stability in irregular sampling compared to existing RNN-based approaches.

Related papers

• Trajectory Flow Matching with Applications to Clinical Time Series Modeling [77.58277281319253]
  Trajectory Flow Matching (TFM) trains a Neural SDE in a simulation-free manner, bypassing backpropagation through the dynamics. We demonstrate improved performance on three clinical time series datasets in terms of absolute performance and uncertainty prediction.
  arXiv  Detail & Related papers  (2024-10-28T15:54:50Z)
• A Simulation-Free Deep Learning Approach to Stochastic Optimal Control [12.699529713351287]
  We propose a simulation-free algorithm for the solution of generic problems in optimal control (SOC) Unlike existing methods, our approach does not require the solution of an adjoint problem.
  arXiv  Detail & Related papers  (2024-10-07T16:16:53Z)
• Neural ODEs as Feedback Policies for Nonlinear Optimal Control [1.8514606155611764]
  We use Neural ordinary differential equations (Neural ODEs) to model continuous time dynamics as differential equations parametrized with neural networks. We propose the use of a neural control policy posed as a Neural ODE to solve general nonlinear optimal control problems.
  arXiv  Detail & Related papers  (2022-10-20T13:19:26Z)
• Continuous-Time Modeling of Counterfactual Outcomes Using Neural Controlled Differential Equations [84.42837346400151]
  Estimating counterfactual outcomes over time has the potential to unlock personalized healthcare. Existing causal inference approaches consider regular, discrete-time intervals between observations and treatment decisions. We propose a controllable simulation environment based on a model of tumor growth for a range of scenarios.
  arXiv  Detail & Related papers  (2022-06-16T17:15:15Z)
• A Priori Denoising Strategies for Sparse Identification of Nonlinear Dynamical Systems: A Comparative Study [68.8204255655161]
  We investigate and compare the performance of several local and global smoothing techniques to a priori denoise the state measurements. We show that, in general, global methods, which use the entire measurement data set, outperform local methods, which employ a neighboring data subset around a local point.
  arXiv  Detail & Related papers  (2022-01-29T23:31:25Z)
• A Theoretical Overview of Neural Contraction Metrics for Learning-based Control with Guaranteed Stability [7.963506386866862]
  This paper presents a neural network model of an optimal contraction metric and corresponding differential Lyapunov function. Its innovation lies in providing formal robustness guarantees for learning-based control frameworks.
  arXiv  Detail & Related papers  (2021-10-02T00:28:49Z)
• Neural ODE Processes [64.10282200111983]
  We introduce Neural ODE Processes (NDPs), a new class of processes determined by a distribution over Neural ODEs. We show that our model can successfully capture the dynamics of low-dimensional systems from just a few data-points.
  arXiv  Detail & Related papers  (2021-03-23T09:32:06Z)
• 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)
• Neural Stochastic Contraction Metrics for Learning-based Control and Estimation [13.751135823626493]
  The NSCM framework allows autonomous agents to approximate optimal stable control and estimation policies in real-time. It outperforms existing nonlinear control and estimation techniques including the state-dependent Riccati equation, iterative LQR, EKF, and the neural contraction.
  arXiv  Detail & Related papers  (2020-11-06T03:04:42Z)
• Adaptive Control and Regret Minimization in Linear Quadratic Gaussian (LQG) Setting [91.43582419264763]
  We propose LqgOpt, a novel reinforcement learning algorithm based on the principle of optimism in the face of uncertainty. LqgOpt efficiently explores the system dynamics, estimates the model parameters up to their confidence interval, and deploys the controller of the most optimistic model.
  arXiv  Detail & Related papers  (2020-03-12T19:56:38Z)

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.