Reporter：JunyiLiu
Abstract：In this talk, we focus on a class of stochastic optimization problems that minimize the conditionally expected cost given a new covariate feature. In real-world OR applications, without the prior knowledge of the conditional probability distribution, it is hard to obtain scenarios under the covariate feature of interest. To deal with this challenge, we propose a data-driven piecewise affine decision rule (PADR) method based on historical data pairs. We provide the first non-asymptotic consistency of the data-driven PADR-based method for a broad class of decision-making problems under a minimal Lipschitz continuity assumption of the optimal decision rule. To solve the PADR-based empirical risk minimization problem with a coupled nonconvex and nondifferentiable structure, we develop an enhanced stochastic majorization minimization algorithm and provide the first non-asymptotic convergence rate in terms of directional stationarity. Numerical results for both convex and nonconvex stochastic optimization problems with various nonlinear generating models indicates the superiority of the proposed data-driven method compared with the state-of-the-art data-driven methods.
