A dual method for solving the nonlinear structured prediction problem

Abstract

In this paper, we present a perceptron-based algorithm and have developed a dual formulation to solve the nonlinear structured prediction problem, which we called Dual Structured Incremental Margin Algorithm (DSIMA). The proposed formulation allows the introduction of kernel functions enabling the efficient solution of nonlinear problems. In order to verify the correctness and applicability of the algorithm, we consider an inverse approach to the path planning problem. The problem mapped on a grid environment can be solved by a search process that essentially depends on the definition of the transition costs between states. In this context, we develop and apply a learning algorithm that is able to perform the reverse path, i.e., the prediction of these costs in a direct space for the linear form. However, considering the nonlinear form, the problem is solved in a space of high dimension and where it is possible to learn a path instead of the transition costs. This learning problem is usually formulated as a convex optimization problem of maximum margin. Several tests to solve the costs prediction problem were carried out and the results compared to other structured prediction techniques. The proposed algorithm demonstrated greater efficiency in terms of computational effort and quality of prediction.