  Web crawling is the problem of keeping a cache of webpages fresh, i.e.,
having the most recent copy available when a page is requested. This problem is
usually coupled with the natural restriction that the bandwidth available to
the web crawler is limited. The corresponding optimization problem was solved
optimally by Azar et al. [2018] under the assumption that, for each webpage,
both the elapsed time between two changes and the elapsed time between two
requests follow a Poisson distribution with known parameters. In this paper, we
study the same control problem but under the assumption that the change rates
are unknown a priori, and thus we need to estimate them in an online fashion
using only partial observations (i.e., single-bit signals indicating whether
the page has changed since the last refresh). As a point of departure, we
characterise the conditions under which one can solve the problem with such
partial observability. Next, we propose a practical estimator and compute
confidence intervals for it in terms of the elapsed time between the
observations. Finally, we show that the explore-and-commit algorithm achieves
an $\mathcal{O}(\sqrt{T})$ regret with a carefully chosen exploration horizon.
Our simulation study shows that our online policy scales well and achieves
close to optimal performance for a wide range of the parameters.
