Learning efficiently with approximate inference via dual losses

Many structured prediction tasks involve complex models where inference is computationally intractable, but where it can be well approximated using a linear programming relaxation. Previous approaches for learning for structured prediction (e.g., cutting-plane, subgradient methods, perceptron) repeatedly make predictions for some of the data points. These approaches are computationally demanding because each prediction involves solving a linear program to optimally. We present a scalable algorithm for learning for structured prediction. The main idea is to instead solve the dual of the structured prediction loss. We formulate the learning task as a convex minimization over both the weights and the dual variables corresponding to each data point. As a result, we can begin to optimize the weights even before completely solving any of the individual prediction problems. We show how the dual variables can be efficiently optimized using co-ordinate descent. Our algorithm is competitive with state-of-the-art methods such as stochastic subgradient and cutting-plane.