32,370 research outputs found
Differentiating the multipoint Expected Improvement for optimal batch design
This work deals with parallel optimization of expensive objective functions
which are modeled as sample realizations of Gaussian processes. The study is
formalized as a Bayesian optimization problem, or continuous multi-armed bandit
problem, where a batch of q > 0 arms is pulled in parallel at each iteration.
Several algorithms have been developed for choosing batches by trading off
exploitation and exploration. As of today, the maximum Expected Improvement
(EI) and Upper Confidence Bound (UCB) selection rules appear as the most
prominent approaches for batch selection. Here, we build upon recent work on
the multipoint Expected Improvement criterion, for which an analytic expansion
relying on Tallis' formula was recently established. The computational burden
of this selection rule being still an issue in application, we derive a
closed-form expression for the gradient of the multipoint Expected Improvement,
which aims at facilitating its maximization using gradient-based ascent
algorithms. Substantial computational savings are shown in application. In
addition, our algorithms are tested numerically and compared to
state-of-the-art UCB-based batch-sequential algorithms. Combining starting
designs relying on UCB with gradient-based EI local optimization finally
appears as a sound option for batch design in distributed Gaussian Process
optimization
Batch Bayesian Optimization via Local Penalization
The popularity of Bayesian optimization methods for efficient exploration of
parameter spaces has lead to a series of papers applying Gaussian processes as
surrogates in the optimization of functions. However, most proposed approaches
only allow the exploration of the parameter space to occur sequentially. Often,
it is desirable to simultaneously propose batches of parameter values to
explore. This is particularly the case when large parallel processing
facilities are available. These facilities could be computational or physical
facets of the process being optimized. E.g. in biological experiments many
experimental set ups allow several samples to be simultaneously processed.
Batch methods, however, require modeling of the interaction between the
evaluations in the batch, which can be expensive in complex scenarios. We
investigate a simple heuristic based on an estimate of the Lipschitz constant
that captures the most important aspect of this interaction (i.e. local
repulsion) at negligible computational overhead. The resulting algorithm
compares well, in running time, with much more elaborate alternatives. The
approach assumes that the function of interest, , is a Lipschitz continuous
function. A wrap-loop around the acquisition function is used to collect
batches of points of certain size minimizing the non-parallelizable
computational effort. The speed-up of our method with respect to previous
approaches is significant in a set of computationally expensive experiments.Comment: 11 pages, 10 figure
Efficient Neural Network Implementations on Parallel Embedded Platforms Applied to Real-Time Torque-Vectoring Optimization Using Predictions for Multi-Motor Electric Vehicles
The combination of machine learning and heterogeneous embedded platforms enables new potential for developing sophisticated control concepts which are applicable to the field of vehicle dynamics and ADAS. This interdisciplinary work provides enabler solutions -ultimately implementing fast predictions using neural networks (NNs) on field programmable gate arrays (FPGAs) and graphical processing units (GPUs)- while applying them to a challenging application: Torque Vectoring on a multi-electric-motor vehicle for enhanced vehicle dynamics. The foundation motivating this work is provided by discussing multiple domains of the technological context as well as the constraints related to the automotive field, which contrast with the attractiveness of exploiting the capabilities of new embedded platforms to apply advanced control algorithms for complex control problems. In this particular case we target enhanced vehicle dynamics on a multi-motor electric vehicle benefiting from the greater degrees of freedom and controllability offered by such powertrains. Considering the constraints of the application and the implications of the selected multivariable optimization challenge, we propose a NN to provide batch predictions for real-time optimization. This leads to the major contribution of this work: efficient NN implementations on two intrinsically parallel embedded platforms, a GPU and a FPGA, following an analysis of theoretical and practical implications of their different operating paradigms, in order to efficiently harness their computing potential while gaining insight into their peculiarities. The achieved results exceed the expectations and additionally provide a representative illustration of the strengths and weaknesses of each kind of platform. Consequently, having shown the applicability of the proposed solutions, this work contributes valuable enablers also for further developments following similar fundamental principles.Some of the results presented in this work are related to activities within the 3Ccar project, which has
received funding from ECSEL Joint Undertaking under grant agreement No. 662192. This Joint Undertaking
received support from the European Union’s Horizon 2020 research and innovation programme and Germany,
Austria, Czech Republic, Romania, Belgium, United Kingdom, France, Netherlands, Latvia, Finland, Spain, Italy,
Lithuania. This work was also partly supported by the project ENABLES3, which received funding from ECSEL
Joint Undertaking under grant agreement No. 692455-2
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