Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Gaussian Process Optimization with Adaptive Sketching: Scalable and No
  Regret   Gaussian processes (GP) are a well studied Bayesian approach for the
optimization of black-box functions. Despite their effectiveness in simple
problems, GP-based algorithms hardly scale to high-dimensional functions, as
their per-iteration time and space cost is at least quadratic in the number of
dimensions $d$ and iterations $t$. Given a set of $A$ alternatives to choose
from, the overall runtime $O(t^3A)$ is prohibitive. In this paper we introduce
BKB (budgeted kernelized bandit), a new approximate GP algorithm for
optimization under bandit feedback that achieves near-optimal regret (and hence
near-optimal convergence rate) with near-constant per-iteration complexity and
remarkably no assumption on the input space or covariance of the GP.
  We combine a kernelized linear bandit algorithm (GP-UCB) with randomized
matrix sketching based on leverage score sampling, and we prove that randomly
sampling inducing points based on their posterior variance gives an accurate
low-rank approximation of the GP, preserving variance estimates and confidence
intervals. As a consequence, BKB does not suffer from variance starvation, an
important problem faced by many previous sparse GP approximations. Moreover, we
show that our procedure selects at most $\tilde{O}(d_{eff})$ points, where
$d_{eff}$ is the effective dimension of the explored space, which is typically
much smaller than both $d$ and $t$. This greatly reduces the dimensionality of
the problem, thus leading to a $O(TAd_{eff}^2)$ runtime and $O(A d_{eff})$
space complexity.

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The categories of this paper are: atom-ph
36
The categories of this paper are: cmp-lg
6
The categories of this paper are: astro-ph
15
The categories of this paper are: nucl-ex
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The categories of this paper are: q-fin
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The categories of this paper are: alg-geom
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: supr-con