Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the convergence, lock-in probability and sample complexity of
  stochastic approximation   It is shown that under standard hypotheses, if stochastic approximation
iterates remain tight, they converge with probability one to what their o.d.e.
limit suggests. A simple test for tightness (and therefore a.s. convergence) is
provided. Further, estimates on lock-in probability, i.e., the probability of
convergence to a specific attractor of the o.d.e. limit given that the iterates
visit its domain of attraction, and sample complexity, i.e., the number of
steps needed to be within a prescribed neighborhood of the desired limit set
with a prescribed probability, are also provided. The latter improve
significantly upon existing results in that they require a much weaker
condition on the martingale difference noise.

36
The categories of this paper are: cmp-lg
31
The categories of this paper are: ao-sci
37
The categories of this paper are: supr-con
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
0
The categories of this paper are: hep-ph
13
The categories of this paper are: quant-ph
33
The categories of this paper are: plasm-ph
4
The categories of this paper are: cond-mat