  We consider the problem of designing optimal online-ad investment strategies
for a single advertiser, who invests at multiple sponsored search sites
simultaneously, with the objective of maximizing his average revenue subject to
the advertising budget constraint. A greedy online investment scheme is
developed to achieve an average revenue that can be pushed to within
$O(\epsilon)$ of the optimal, for any $\epsilon>0$, with a tradeoff that the
temporal budget violation is $O(1/\epsilon)$. Different from many existing
algorithms, our scheme allows the advertiser to \emph{asynchronously} update
his investments on each search engine site, hence applies to systems where the
timescales of action update intervals are heterogeneous for different sites. We
also quantify the impact of inaccurate estimation of the system dynamics and
show that the algorithm is robust against imperfect system knowledge.
