Brief

Researchers have developed a novel method called neural slack variables to enforce functional inequality constraints like monotonicity and convexity within neural networks. This approach transforms constraint enforcement into a regression problem by integrating the primary network with a jointly trained auxiliary network. The auxiliary network acts as a target for the primary network's constraint quantities, ensuring feasibility and regularity. This technique has demonstrated superior performance over traditional penalty and primal-dual methods, achieving zero measured violations on monotonicity and convexity test cases and enabling arbitrage-free learning of volatility surfaces in quantitative finance. AI