  A search engine maintains local copies of different web pages to provide
quick search results. This local cache is kept up-to-date by a web crawler that
frequently visits these different pages to track changes in them. Ideally, the
local copy should be updated as soon as a page changes on the web. However,
finite bandwidth availability and server restrictions limit how frequently
different pages can be crawled. This brings forth the following optimization
problem: maximize the freshness of the local cache subject to the crawling
frequencies being within prescribed bounds. While tractable algorithms do exist
to solve this problem, these either assume the knowledge of exact page change
rates or use inefficient methods such as MLE for estimating the same. We
address this issue here.
  We provide three novel schemes for online estimation of page change rates,
all of which have extremely low running times per iteration. The first is based
on the law of large numbers and the second on stochastic approximation. The
third is an extension of the second and includes a heavy-ball momentum term.
All these schemes only need partial information about the page change process,
i.e., they only need to know if the page has changed or not since the last
crawled instance. Our main theoretical results concern asymptotic convergence
and convergence rates of these three schemes. In fact, our work is the first to
show convergence of the original stochastic heavy-ball method when neither the
gradient nor the noise variance is uniformly bounded. We also provide some
numerical experiments (based on real and synthetic data) to demonstrate the
superiority of our proposed estimators over existing ones such as MLE. We
emphasize that our algorithms are also readily applicable to the
synchronization of databases and network inventory management.
