46 research outputs found
Practical Bayesian Optimization for Variable Cost Objectives
We propose a novel Bayesian Optimization approach for black-box functions
with an environmental variable whose value determines the tradeoff between
evaluation cost and the fidelity of the evaluations. Further, we use a novel
approach to sampling support points, allowing faster construction of the
acquisition function. This allows us to achieve optimization with lower
overheads than previous approaches and is implemented for a more general class
of problem. We show this approach to be effective on synthetic and real world
benchmark problems.Comment: 8 pages, 7 figure
Unscented Bayesian Optimization for Safe Robot Grasping
We address the robot grasp optimization problem of unknown objects
considering uncertainty in the input space. Grasping unknown objects can be
achieved by using a trial and error exploration strategy. Bayesian optimization
is a sample efficient optimization algorithm that is especially suitable for
this setups as it actively reduces the number of trials for learning about the
function to optimize. In fact, this active object exploration is the same
strategy that infants do to learn optimal grasps. One problem that arises while
learning grasping policies is that some configurations of grasp parameters may
be very sensitive to error in the relative pose between the object and robot
end-effector. We call these configurations unsafe because small errors during
grasp execution may turn good grasps into bad grasps. Therefore, to reduce the
risk of grasp failure, grasps should be planned in safe areas. We propose a new
algorithm, Unscented Bayesian optimization that is able to perform sample
efficient optimization while taking into consideration input noise to find safe
optima. The contribution of Unscented Bayesian optimization is twofold as if
provides a new decision process that drives exploration to safe regions and a
new selection procedure that chooses the optimal in terms of its safety without
extra analysis or computational cost. Both contributions are rooted on the
strong theory behind the unscented transformation, a popular nonlinear
approximation method. We show its advantages with respect to the classical
Bayesian optimization both in synthetic problems and in realistic robot grasp
simulations. The results highlights that our method achieves optimal and robust
grasping policies after few trials while the selected grasps remain in safe
regions.Comment: conference pape
Anomaly Detection and Removal Using Non-Stationary Gaussian Processes
This paper proposes a novel Gaussian process approach to fault removal in
time-series data. Fault removal does not delete the faulty signal data but,
instead, massages the fault from the data. We assume that only one fault occurs
at any one time and model the signal by two separate non-parametric Gaussian
process models for both the physical phenomenon and the fault. In order to
facilitate fault removal we introduce the Markov Region Link kernel for
handling non-stationary Gaussian processes. This kernel is piece-wise
stationary but guarantees that functions generated by it and their derivatives
(when required) are everywhere continuous. We apply this kernel to the removal
of drift and bias errors in faulty sensor data and also to the recovery of EOG
artifact corrupted EEG signals.Comment: 9 pages, 14 figure
Theoretical Analysis of Bayesian Optimisation with Unknown Gaussian Process Hyper-Parameters
Bayesian optimisation has gained great popularity as a tool for optimising
the parameters of machine learning algorithms and models. Somewhat ironically,
setting up the hyper-parameters of Bayesian optimisation methods is notoriously
hard. While reasonable practical solutions have been advanced, they can often
fail to find the best optima. Surprisingly, there is little theoretical
analysis of this crucial problem in the literature. To address this, we derive
a cumulative regret bound for Bayesian optimisation with Gaussian processes and
unknown kernel hyper-parameters in the stochastic setting. The bound, which
applies to the expected improvement acquisition function and sub-Gaussian
observation noise, provides us with guidelines on how to design hyper-parameter
estimation methods. A simple simulation demonstrates the importance of
following these guidelines.Comment: 16 pages, 1 figur