Weformulate the decoding process asanoptimization problem which allows for multiple attributesweaimtocontrol tobeeasilyincorporated asdifferentiable constraints to the optimization. By relaxing this discrete optimization to a continuous one, we make use of Lagrangian multipliers and gradient-descent based techniques to generate the desired text.

Stochastic approximation is a foundation for many algorithms found in machine learning and optimization.

Such problems arise, for example, in reinforcement learning, engineering design, and manufacturing.

Smooth convex optimization problems over polytopes are an important class of problems that appear in many settings, such as low-rank matrix completion [1],structured supervised learning [2,3],electrical flowsovergraphs [4],video co-localization in computer vision [5], traffic assignment problems [6], and submodular function minimization [7].