  In this work, we study the problem of learning a single model for multiple
domains. Unlike the conventional machine learning scenario where each domain
can have the corresponding model, multiple domains (i.e., applications/users)
may share the same machine learning model due to maintenance loads in cloud
computing services. For example, a digit-recognition model should be applicable
to hand-written digits, house numbers, car plates, etc. Therefore, an ideal
model for cloud computing has to perform well at each applicable domain. To
address this new challenge from cloud computing, we develop a framework of
robust optimization over multiple domains. In lieu of minimizing the empirical
risk, we aim to learn a model optimized to the adversarial distribution over
multiple domains. Hence, we propose to learn the model and the adversarial
distribution simultaneously with the stochastic algorithm for efficiency.
Theoretically, we analyze the convergence rate for convex and non-convex
models. To our best knowledge, we first study the convergence rate of learning
a robust non-convex model with a practical algorithm. Furthermore, we
demonstrate that the robustness of the framework and the convergence rate can
be further enhanced by appropriate regularizers over the adversarial
distribution. The empirical study on real-world fine-grained visual
categorization and digits recognition tasks verifies the effectiveness and
efficiency of the proposed framework.
