Identifying similar keywords, known as broad matches, is an important task in online advertising that has become a standard feature on all major keyword advertising platforms. Effective broad matching leads to improvements in both relevance and monetization, while increasing advertisers' reach and making campaign management easier. In this paper, we present a learning-based approach to broad matching that is based on exploiting implicit feedback in the form of advertisement clickthrough logs. Our method can utilize arbitrary similarity functions by incorporating them as features. We present an online learning algorithm, Amnesiac Averaged Perceptron, that is highly efficient yet able to quickly adjust to the rapidly-changing distributions of bidded keywords, advertisements and user behavior. Experimental results obtained from (1) historical logs and (2) live trials on a large-scale advertising platform demonstrate the effectiveness of the proposed algorithm and the overall success of our approach in identifying high-quality broad match mappings.