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This paper presents RAYEN, a framework to impose hard convex constraints onthe output or latent variable of a neural network. RAYEN guarantees that, forany input or any weights of the network, the constraints are satisfied at alltimes. Compared to other approaches, RAYEN does not perform acomputationally-expensive orthogonal projection step onto the feasible set,does not rely on soft constraints (which do not guarantee the satisfaction ofthe constraints at test time), does not use conservative approximations of thefeasible set, and does not perform a potentially slow inner gradient descentcorrection to enforce the constraints. RAYEN supports any combination oflinear, convex quadratic, second-order cone (SOC), and linear matrix inequality(LMI) constraints, achieving a very small computational overhead compared tounconstrained networks. For example, it is able to impose 1K quadraticconstraints on a 1K-dimensional variable with an overhead of less than 8 ms,and an LMI constraint with 300x300 dense matrices on a 10K-dimensional variablein less than 12 ms. When used in neural networks that approximate the solutionof constrained optimization problems, RAYEN achieves computation times between20 and 7468 times faster than state-of-the-art algorithms, while guaranteeingthe satisfaction of the constraints at all times and obtaining a cost veryclose to the optimal one.

RAYEN: Imposition of Hard Convex Constraints on Neural Networks