  We study large-scale classification problems in changing environments where a
small part of the dataset is modified, and the effect of the data modification
must be quickly incorporated into the classifier. When the entire dataset is
large, even if the amount of the data modification is fairly small, the
computational cost of re-training the classifier would be prohibitively large.
In this paper, we propose a novel method for efficiently incorporating such a
data modification effect into the classifier without actually re-training it.
The proposed method provides bounds on the unknown optimal classifier with the
cost only proportional to the size of the data modification. We demonstrate
through numerical experiments that the proposed method provides sufficiently
tight bounds with negligible computational costs, especially when a small part
of the dataset is modified in a large-scale classification problem.
