Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling

• URL: http://arxiv.org/abs/2505.18327v1
• Date: Fri, 23 May 2025 19:33:08 GMT
• Title: Online Statistical Inference of Constrained Stochastic Optimization via Random Scaling
• Authors: Xinchen Du, Wanrong Zhu, Wei Biao Wu, Sen Na,
• Abstract summary: We develop an online inference procedure for constrained optimization using Sketched Sequential Quadratic Programming (SSQP)<n>As a direct generalization of sketched Newton methods, SSQP approximates the objective with a quadratic model and the constraints with a linear model at each step, then applies a sketching solver to in solve the resulting subproblem.<n>In particular, we construct a test statistic based on SSQP iterates whose limiting distribution is free of any unknown parameters.
• Score: 17.9255078650875
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Constrained stochastic nonlinear optimization problems have attracted significant attention for their ability to model complex real-world scenarios in physics, economics, and biology. As datasets continue to grow, online inference methods have become crucial for enabling real-time decision-making without the need to store historical data. In this work, we develop an online inference procedure for constrained stochastic optimization by leveraging a method called Sketched Stochastic Sequential Quadratic Programming (SSQP). As a direct generalization of sketched Newton methods, SSQP approximates the objective with a quadratic model and the constraints with a linear model at each step, then applies a sketching solver to inexactly solve the resulting subproblem. Building on this design, we propose a new online inference procedure called random scaling. In particular, we construct a test statistic based on SSQP iterates whose limiting distribution is free of any unknown parameters. Compared to existing online inference procedures, our approach offers two key advantages: (i) it enables the construction of asymptotically valid confidence intervals; and (ii) it is matrix-free, i.e. the computation involves only primal-dual SSQP iterates $(\boldsymbol{x}_t, \boldsymbol{\lambda}_t)$ without requiring any matrix inversions. We validate our theory through numerical experiments on nonlinearly constrained regression problems and demonstrate the superior performance of our random scaling method over existing inference procedures.

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