91,687 research outputs found
Zero-Order Optimization for Gaussian Process-based Model Predictive Control
By enabling constraint-aware online model adaptation, model predictive
control using Gaussian process (GP) regression has exhibited impressive
performance in real-world applications and received considerable attention in
the learning-based control community. Yet, solving the resulting optimal
control problem in real-time generally remains a major challenge, due to i) the
increased number of augmented states in the optimization problem, as well as
ii) computationally expensive evaluations of the posterior mean and covariance
and their respective derivatives. To tackle these challenges, we employ i) a
tailored Jacobian approximation in a sequential quadratic programming (SQP)
approach, and combine it with ii) a parallelizable GP inference and automatic
differentiation framework. Reducing the numerical complexity with respect to
the state dimension for each SQP iteration from to
, and accelerating GP evaluations on a graphical processing
unit, the proposed algorithm computes suboptimal, yet feasible solutions at
drastically reduced computation times and exhibits favorable local convergence
properties. Numerical experiments verify the scaling properties and investigate
the runtime distribution across different parts of the algorithm.Comment: accepted for European Journal of Control (EJC), ECC 2023 Special
Issu
Gaussian process for activity modeling and anomaly detection
Complex activity modeling and identification of anomaly is one of the most interesting and desired capabilities for automated video behavior analysis. A number of different approaches have been proposed in the past to tackle this problem. There are two main challenges for activity modeling and anomaly detection: 1) most existing approaches require sufficient data and supervision for learning; 2) the most interesting abnormal activities arise rarely and are ambiguous among typical activities, i.e. hard to be precisely defined. In this paper, we propose a novel approach to model complex activities and detect anomalies by using non-parametric Gaussian Process (GP) models in a crowded and complicated traffic scene. In comparison with parametric models such as HMM, GP models are nonparametric and have their advantages. Our GP models exploit implicit spatial-temporal dependence among local activity patterns. The learned GP regression models give a probabilistic prediction of regional activities at next time interval based on observations at present. An anomaly will be detected by comparing the actual observations with the prediction at real time. We verify the effectiveness and robustness of the proposed model on the QMUL Junction Dataset. Furthermore, we provide a publicly available manually labeled ground truth of this data set
Sequential Gaussian Processes for Online Learning of Nonstationary Functions
Many machine learning problems can be framed in the context of estimating
functions, and often these are time-dependent functions that are estimated in
real-time as observations arrive. Gaussian processes (GPs) are an attractive
choice for modeling real-valued nonlinear functions due to their flexibility
and uncertainty quantification. However, the typical GP regression model
suffers from several drawbacks: i) Conventional GP inference scales
with respect to the number of observations; ii) updating a GP model
sequentially is not trivial; and iii) covariance kernels often enforce
stationarity constraints on the function, while GPs with non-stationary
covariance kernels are often intractable to use in practice. To overcome these
issues, we propose an online sequential Monte Carlo algorithm to fit mixtures
of GPs that capture non-stationary behavior while allowing for fast,
distributed inference. By formulating hyperparameter optimization as a
multi-armed bandit problem, we accelerate mixing for real time inference. Our
approach empirically improves performance over state-of-the-art methods for
online GP estimation in the context of prediction for simulated non-stationary
data and hospital time series data
Understanding and Comparing Scalable Gaussian Process Regression for Big Data
As a non-parametric Bayesian model which produces informative predictive
distribution, Gaussian process (GP) has been widely used in various fields,
like regression, classification and optimization. The cubic complexity of
standard GP however leads to poor scalability, which poses challenges in the
era of big data. Hence, various scalable GPs have been developed in the
literature in order to improve the scalability while retaining desirable
prediction accuracy. This paper devotes to investigating the methodological
characteristics and performance of representative global and local scalable GPs
including sparse approximations and local aggregations from four main
perspectives: scalability, capability, controllability and robustness. The
numerical experiments on two toy examples and five real-world datasets with up
to 250K points offer the following findings. In terms of scalability, most of
the scalable GPs own a time complexity that is linear to the training size. In
terms of capability, the sparse approximations capture the long-term spatial
correlations, the local aggregations capture the local patterns but suffer from
over-fitting in some scenarios. In terms of controllability, we could improve
the performance of sparse approximations by simply increasing the inducing
size. But this is not the case for local aggregations. In terms of robustness,
local aggregations are robust to various initializations of hyperparameters due
to the local attention mechanism. Finally, we highlight that the proper hybrid
of global and local scalable GPs may be a promising way to improve both the
model capability and scalability for big data.Comment: 25 pages, 15 figures, preprint submitted to KB
Using Parameterized Black-Box Priors to Scale Up Model-Based Policy Search for Robotics
The most data-efficient algorithms for reinforcement learning in robotics are
model-based policy search algorithms, which alternate between learning a
dynamical model of the robot and optimizing a policy to maximize the expected
return given the model and its uncertainties. Among the few proposed
approaches, the recently introduced Black-DROPS algorithm exploits a black-box
optimization algorithm to achieve both high data-efficiency and good
computation times when several cores are used; nevertheless, like all
model-based policy search approaches, Black-DROPS does not scale to high
dimensional state/action spaces. In this paper, we introduce a new model
learning procedure in Black-DROPS that leverages parameterized black-box priors
to (1) scale up to high-dimensional systems, and (2) be robust to large
inaccuracies of the prior information. We demonstrate the effectiveness of our
approach with the "pendubot" swing-up task in simulation and with a physical
hexapod robot (48D state space, 18D action space) that has to walk forward as
fast as possible. The results show that our new algorithm is more
data-efficient than previous model-based policy search algorithms (with and
without priors) and that it can allow a physical 6-legged robot to learn new
gaits in only 16 to 30 seconds of interaction time.Comment: Accepted at ICRA 2018; 8 pages, 4 figures, 2 algorithms, 1 table;
Video at https://youtu.be/HFkZkhGGzTo ; Spotlight ICRA presentation at
https://youtu.be/_MZYDhfWeL
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