114,436 research outputs found
Kernels over Sets of Finite Sets using RKHS Embeddings, with Application to Bayesian (Combinatorial) Optimization
We focus on kernel methods for set-valued inputs and their application to
Bayesian set optimization, notably combinatorial optimization. We investigate
two classes of set kernels that both rely on Reproducing Kernel Hilbert Space
embeddings, namely the ``Double Sum'' (DS) kernels recently considered in
Bayesian set optimization, and a class introduced here called ``Deep
Embedding'' (DE) kernels that essentially consists in applying a radial kernel
on Hilbert space on top of the canonical distance induced by another kernel
such as a DS kernel. We establish in particular that while DS kernels typically
suffer from a lack of strict positive definiteness, vast subclasses of DE
kernels built upon DS kernels do possess this property, enabling in turn
combinatorial optimization without requiring to introduce a jitter parameter.
Proofs of theoretical results about considered kernels are complemented by a
few practicalities regarding hyperparameter fitting. We furthermore demonstrate
the applicability of our approach in prediction and optimization tasks, relying
both on toy examples and on two test cases from mechanical engineering and
hydrogeology, respectively. Experimental results highlight the applicability
and compared merits of the considered approaches while opening new perspectives
in prediction and sequential design with set inputs
Deep Kernels for Optimizing Locomotion Controllers
Sample efficiency is important when optimizing parameters of locomotion
controllers, since hardware experiments are time consuming and expensive.
Bayesian Optimization, a sample-efficient optimization framework, has recently
been widely applied to address this problem, but further improvements in sample
efficiency are needed for practical applicability to real-world robots and
high-dimensional controllers. To address this, prior work has proposed using
domain expertise for constructing custom distance metrics for locomotion. In
this work we show how to learn such a distance metric automatically. We use a
neural network to learn an informed distance metric from data obtained in
high-fidelity simulations. We conduct experiments on two different controllers
and robot architectures. First, we demonstrate improvement in sample efficiency
when optimizing a 5-dimensional controller on the ATRIAS robot hardware. We
then conduct simulation experiments to optimize a 16-dimensional controller for
a 7-link robot model and obtain significant improvements even when optimizing
in perturbed environments. This demonstrates that our approach is able to
enhance sample efficiency for two different controllers, hence is a fitting
candidate for further experiments on hardware in the future.Comment: (Rika Antonova and Akshara Rai contributed equally
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