Gaussian Processes with State-Dependent Noise for Stochastic Control
- URL: http://arxiv.org/abs/2305.16229v1
- Date: Thu, 25 May 2023 16:36:57 GMT
- Title: Gaussian Processes with State-Dependent Noise for Stochastic Control
- Authors: Marcel Menner, Karl Berntorp
- Abstract summary: The residual model uncertainty of a dynamical system is learned using a Gaussian Process (GP)
The two GPs are interdependent and are thus learned jointly using an iterative algorithm.
- Score: 2.842794675894731
- License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
- Abstract: This paper considers a stochastic control framework, in which the residual
model uncertainty of the dynamical system is learned using a Gaussian Process
(GP). In the proposed formulation, the residual model uncertainty consists of a
nonlinear function and state-dependent noise. The proposed formulation uses a
posterior-GP to approximate the residual model uncertainty and a prior-GP to
account for state-dependent noise. The two GPs are interdependent and are thus
learned jointly using an iterative algorithm. Theoretical properties of the
iterative algorithm are established. Advantages of the proposed state-dependent
formulation include (i) faster convergence of the GP estimate to the unknown
function as the GP learns which data samples are more trustworthy and (ii) an
accurate estimate of state-dependent noise, which can, e.g., be useful for a
controller or decision-maker to determine the uncertainty of an action.
Simulation studies highlight these two advantages.
Related papers
- Robust Gaussian Processes via Relevance Pursuit [17.39376866275623]
We propose and study a GP model that achieves robustness against sparse outliers by inferring data-point-specific noise levels.
We show, surprisingly, that the model can be parameterized such that the associated log marginal likelihood is strongly concave in the data-point-specific noise variances.
arXiv Detail & Related papers (2024-10-31T17:59:56Z) - Variational Nonlinear Kalman Filtering with Unknown Process Noise
Covariance [24.23243651301339]
This paper presents a solution for identification of nonlinear state estimation and model parameters based on the approximate Bayesian inference principle.
The performance of the proposed method is verified on radar target tracking applications by both simulated and real-world data.
arXiv Detail & Related papers (2023-05-06T03:34:39Z) - Robust Control for Dynamical Systems With Non-Gaussian Noise via Formal
Abstractions [59.605246463200736]
We present a novel controller synthesis method that does not rely on any explicit representation of the noise distributions.
First, we abstract the continuous control system into a finite-state model that captures noise by probabilistic transitions between discrete states.
We use state-of-the-art verification techniques to provide guarantees on the interval Markov decision process and compute a controller for which these guarantees carry over to the original control system.
arXiv Detail & Related papers (2023-01-04T10:40:30Z) - Probabilities Are Not Enough: Formal Controller Synthesis for Stochastic
Dynamical Models with Epistemic Uncertainty [68.00748155945047]
Capturing uncertainty in models of complex dynamical systems is crucial to designing safe controllers.
Several approaches use formal abstractions to synthesize policies that satisfy temporal specifications related to safety and reachability.
Our contribution is a novel abstraction-based controller method for continuous-state models with noise, uncertain parameters, and external disturbances.
arXiv Detail & Related papers (2022-10-12T07:57:03Z) - 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) - Robust and Adaptive Temporal-Difference Learning Using An Ensemble of
Gaussian Processes [70.80716221080118]
The paper takes a generative perspective on policy evaluation via temporal-difference (TD) learning.
The OS-GPTD approach is developed to estimate the value function for a given policy by observing a sequence of state-reward pairs.
To alleviate the limited expressiveness associated with a single fixed kernel, a weighted ensemble (E) of GP priors is employed to yield an alternative scheme.
arXiv Detail & Related papers (2021-12-01T23:15:09Z) - Probabilistic robust linear quadratic regulators with Gaussian processes [73.0364959221845]
Probabilistic models such as Gaussian processes (GPs) are powerful tools to learn unknown dynamical systems from data for subsequent use in control design.
We present a novel controller synthesis for linearized GP dynamics that yields robust controllers with respect to a probabilistic stability margin.
arXiv Detail & Related papers (2021-05-17T08:36:18Z) - Adversarial Robustness Guarantees for Gaussian Processes [22.403365399119107]
Gaussian processes (GPs) enable principled computation of model uncertainty, making them attractive for safety-critical applications.
We present a framework to analyse adversarial robustness of GPs, defined as invariance of the model's decision to bounded perturbations.
We develop a branch-and-bound scheme to refine the bounds and show, for any $epsilon > 0$, that our algorithm is guaranteed to converge to values $epsilon$-close to the actual values in finitely many iterations.
arXiv Detail & Related papers (2021-04-07T15:14:56Z) - 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) - Transport Gaussian Processes for Regression [0.22843885788439797]
We propose a methodology to construct processes, which include GPs, warped GPs, Student-t processes and several others.
Our approach is inspired by layers-based models, where each proposed layer changes a specific property over the generated process.
We validate the proposed model through experiments with real-world data.
arXiv Detail & Related papers (2020-01-30T17:44:21Z)
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.