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Recent research has proposed neural architectures for solving combinatorialproblems in structured output spaces. In many such problems, there may existmultiple solutions for a given input, e.g. a partially filled Sudoku puzzle mayhave many completions satisfying all constraints. Further, we are ofteninterested in finding any one of the possible solutions, without any preferencebetween them. Existing approaches completely ignore this solution multiplicity.In this paper, we argue that being oblivious to the presence of multiplesolutions can severely hamper their training ability. Our contribution is twofold. First, we formally define the task of learning one-of-many solutions forcombinatorial problems in structured output spaces, which is applicable forsolving several problems of interest such as N-Queens, and Sudoku. Second, wepresent a generic learning framework that adapts an existing prediction networkfor a combinatorial problem to handle solution multiplicity. Our framework usesa selection module, whose goal is to dynamically determine, for every input,the solution that is most effective for training the network parameters in anygiven learning iteration. We propose an RL based approach to jointly train theselection module with the prediction network. Experiments on three differentdomains, and using two different prediction networks, demonstrate that ourframework significantly improves the accuracy in our setting, obtaining up to21 pt gain over the baselines.

Neural Learning of One-of-Many Solutions for Combinatorial Problems in Structured Output Spaces