Online Parameter Estimation for Safety-Critical Systems with Gaussian Processes

• URL: http://arxiv.org/abs/2002.07870v1
• Date: Tue, 18 Feb 2020 20:38:00 GMT
• Title: Online Parameter Estimation for Safety-Critical Systems with Gaussian Processes
• Authors: Mouhyemen Khan and Abhijit Chatterjee
• Abstract summary: We present a Bayesian optimization framework based on Gaussian processes (GPs) for online parameter estimation. It uses an efficient search strategy over a response surface in the parameter space for finding the global optima with minimal function evaluations. We demonstrate our technique on an actuated planar pendulum and safety-critical quadrotor in simulation with changing parameters.
• Score: 6.122161391301866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Parameter estimation is crucial for modeling, tracking, and control of complex dynamical systems. However, parameter uncertainties can compromise system performance under a controller relying on nominal parameter values. Typically, parameters are estimated using numerical regression approaches framed as inverse problems. However, they suffer from non-uniqueness due to existence of multiple local optima, reliance on gradients, numerous experimental data, or stability issues. Addressing these drawbacks, we present a Bayesian optimization framework based on Gaussian processes (GPs) for online parameter estimation. It uses an efficient search strategy over a response surface in the parameter space for finding the global optima with minimal function evaluations. The response surface is modeled as correlated surrogates using GPs on noisy data. The GP posterior predictive variance is exploited for smart adaptive sampling. This balances the exploration versus exploitation trade-off which is key in reaching the global optima under limited budget. We demonstrate our technique on an actuated planar pendulum and safety-critical quadrotor in simulation with changing parameters. We also benchmark our results against solvers using interior point method and sequential quadratic program. By reconfiguring the controller with new optimized parameters iteratively, we drastically improve trajectory tracking of the system versus the nominal case and other solvers.

Related papers

• Accelerated zero-order SGD under high-order smoothness and overparameterized regime [79.85163929026146]
  We present a novel gradient-free algorithm to solve convex optimization problems. Such problems are encountered in medicine, physics, and machine learning. We provide convergence guarantees for the proposed algorithm under both types of noise.
  arXiv  Detail & Related papers  (2024-11-21T10:26:17Z)
• Scaling Exponents Across Parameterizations and Optimizers [94.54718325264218]
  We propose a new perspective on parameterization by investigating a key assumption in prior work. Our empirical investigation includes tens of thousands of models trained with all combinations of threes. We find that the best learning rate scaling prescription would often have been excluded by the assumptions in prior work.
  arXiv  Detail & Related papers  (2024-07-08T12:32:51Z)
• A Unified Gaussian Process for Branching and Nested Hyperparameter Optimization [19.351804144005744]
  In deep learning, tuning parameters with conditional dependence are common in practice. New GP model accounts for the dependent structure among input variables through a new kernel function. High prediction accuracy and better optimization efficiency are observed in a series of synthetic simulations and real data applications of neural networks.
  arXiv  Detail & Related papers  (2024-01-19T21:11:32Z)
• A Framework for History-Aware Hyperparameter Optimisation in Reinforcement Learning [8.659973888018781]
  A Reinforcement Learning (RL) system depends on a set of initial conditions that affect the system's performance. We propose a framework based on integrating complex event processing and temporal models, to alleviate these trade-offs. We tested the proposed approach in a 5G mobile communications case study that uses DQN, a variant of RL, for its decision-making.
  arXiv  Detail & Related papers  (2023-03-09T11:30:40Z)
• Surrogate modeling for Bayesian optimization beyond a single Gaussian process [62.294228304646516]
  We propose a novel Bayesian surrogate model to balance exploration with exploitation of the search space. To endow function sampling with scalability, random feature-based kernel approximation is leveraged per GP model. To further establish convergence of the proposed EGP-TS to the global optimum, analysis is conducted based on the notion of Bayesian regret.
  arXiv  Detail & Related papers  (2022-05-27T16:43:10Z)
• Auto-Tuned Sim-to-Real Transfer [143.44593793640814]
  Policies trained in simulation often fail when transferred to the real world. Current approaches to tackle this problem, such as domain randomization, require prior knowledge and engineering. We propose a method for automatically tuning simulator system parameters to match the real world.
  arXiv  Detail & Related papers  (2021-04-15T17:59:55Z)
• 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)
• Variable selection for Gaussian process regression through a sparse projection [0.802904964931021]
  This paper presents a new variable selection approach integrated with Gaussian process (GP) regression. The choice of tuning parameters and the accuracy of the estimation are evaluated with the simulation some chosen benchmark approaches.
  arXiv  Detail & Related papers  (2020-08-25T01:06:10Z)
• Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications [5.660384137948734]
  The proposed algorithm converges to the correct distribution with a controllable bias under mild conditions. We show that the proposed algorithm canally converge to the correct distribution with a controllable bias under mild conditions.
  arXiv  Detail & Related papers  (2020-06-29T20:57:20Z)
• Parameterized MDPs and Reinforcement Learning Problems -- A Maximum Entropy Principle Based Framework [2.741266294612776]
  We present a framework to address a class of sequential decision making problems. Our framework features learning the optimal control policy with robustness to noisy data.
  arXiv  Detail & Related papers  (2020-06-17T04:08:35Z)
• 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.