Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Two-Timescale Stochastic Gradient Descent in Continuous Time with
  Applications to Joint Online Parameter Estimation and Optimal Sensor
  Placement   In this paper, we establish the almost sure convergence of two-timescale
stochastic gradient descent algorithms in continuous time under general noise
and stability conditions, extending well known results in discrete time. We
analyse algorithms with additive noise and those with non-additive noise. In
the non-additive case, our analysis is carried out under the assumption that
the noise is a continuous-time Markov process, controlled by the algorithm
states. The algorithms we consider can be applied to a broad class of bilevel
optimisation problems. We study one such problem in detail, namely, the problem
of joint online parameter estimation and optimal sensor placement for a
partially observed diffusion process. We demonstrate how this can be formulated
as a bilevel optimisation problem, and propose a solution in the form of a
continuous-time, two-timescale, stochastic gradient descent algorithm.
Furthermore, under suitable conditions on the latent signal, the filter, and
the filter derivatives, we establish almost sure convergence of the online
parameter estimates and optimal sensor placements to the stationary points of
the asymptotic log-likelihood and asymptotic filter covariance, respectively.
We also provide numerical examples, illustrating the application of the
proposed methodology to a partially observed Bene\v{s} equation, and a
partially observed stochastic advection-diffusion equation.

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The categories of this paper are: bayes-an
12
The categories of this paper are: nucl-th
6
The categories of this paper are: astro-ph
30
The categories of this paper are: q-alg
36
The categories of this paper are: cmp-lg
20
The categories of this paper are: acc-phys
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
31
The categories of this paper are: ao-sci
1
The categories of this paper are: cs
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: eess
8
The categories of this paper are: hep-ex
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The categories of this paper are: adap-org