Robust Distributed Training of Linear Classifiers Based on Divergence Minimization Principle

We study a distributed training of a linear classifier in which the data is separated into many shards and each worker only has access to its own shard. The goal of this distributed training is to utilize the data of all shards to obtain a wellperforming linear classifier. The iterative parameter mixture (IPM) framework (Mann et al., 2009) is a state-of-the-art distributed learning framework that has a strong theoretical guarantee when the data is clean. However, contamination on shards, which sometimes arises in real world environments, largely deteriorates the performances of the distributed training. To remedy the negative effect of the contamination, we propose a divergence minimization principle for the weight determination in IPM. From this principle, we can naturally derive the Beta-IPM scheme, which leverages the power of robust estimation based on the beta divergence. A mistake/loss bound analysis indicates the advantage of our Beta-IPM in contaminated environments. Experiments with various datasets revealed that, even when 80% of the shards are contaminated, Beta-IPM can suppress the influence of the contamination.