Approximate bilevel programming via pareto optimization for imputation and control of optimization and equilibrium models

摘要: We consider the problem of imputing function that describes an optimization or equilibrium process from noisy partial observations nearly optimal (possibly non-cooperative) decisions. generalize existing inverse and variational inequality problems to construct a novel class multi-objective problems: approximate bilevel programs. In this class, “ill” nature complementary condition prevalent in programming is avoided, residual functions commonly used for design analysis iterative procedures, are powerful tool study solutions problems. particular, we show duality gaps provide stronger bounds than l p norms KKT residuals. The weighted criterion method some sense equivalent formulations case full observations. Our approach allows solve under unifying framework, via block coordinate descent, demonstrated on 1) consumer utility estimation pricing 2) latency inference road network Los Angeles.