Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Accelerating Optimization and Reinforcement Learning with
  Quasi-Stochastic Approximation   The ODE method has been a workhorse for algorithm design and analysis since
the introduction of the stochastic approximation. It is now understood that
convergence theory amounts to establishing robustness of Euler approximations
for ODEs, while theory of rates of convergence requires finer analysis. This
paper sets out to extend this theory to quasi-stochastic approximation, based
on algorithms in which the "noise" is based on deterministic signals. The main
results are obtained under minimal assumptions: the usual Lipschitz conditions
for ODE vector fields, and it is assumed that there is a well defined
linearization near the optimal parameter $\theta^*$, with Hurwitz linearization
matrix $A^*$.
  The main contributions are summarized as follows:
  (i) If the algorithm gain is $a_t=g/(1+t)^\rho$ with $g>0$ and
$\rho\in(0,1)$, then the rate of convergence of the algorithm is $1/t^\rho$.
There is also a well defined "finite-$t$" approximation: \[
a_t^{-1}\{\Theta_t-\theta^*\}=\bar{Y}+\Xi^{\mathrm{I}}_t+o(1) \] where
$\bar{Y}\in\mathbb{R}^d$ is a vector identified in the paper, and
$\{\Xi^{\mathrm{I}}_t\}$ is bounded with zero temporal mean.
  (ii) With gain $a_t = g/(1+t)$ the results are not as sharp: the rate of
convergence $1/t$ holds only if $I + g A^*$ is Hurwitz.
  (iii) Based on the Ruppert-Polyak averaging of stochastic approximation, one
would expect that a convergence rate of $1/t$ can be obtained by averaging: \[
\Theta^{\text{RP}}_T=\frac{1}{T}\int_{0}^T \Theta_t\,dt \] where the estimates
$\{\Theta_t\}$ are obtained using the gain in (i). The preceding sharp bounds
imply that averaging results in $1/t$ convergence rate if and only if
$\bar{Y}=\sf 0$. This condition holds if the noise is additive, but appears to
fail in general.
  (iv) The theory is illustrated with applications to gradient-free
optimization and policy gradient algorithms for reinforcement learning.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
32
The categories of this paper are: atom-ph
20
The categories of this paper are: acc-phys
6
The categories of this paper are: astro-ph
11
The categories of this paper are: hep-lat
14
The categories of this paper are: math-ph
13
The categories of this paper are: quant-ph
34
The categories of this paper are: chem-ph
31
The categories of this paper are: ao-sci
24
The categories of this paper are: dg-ga
18
The categories of this paper are: econ