Statistical Inference for Weighted Sample Average Approximation in Contextual Stochastic Optimization

• URL: http://arxiv.org/abs/2503.12747v2
• Date: Wed, 26 Mar 2025 14:15:54 GMT
• Title: Statistical Inference for Weighted Sample Average Approximation in Contextual Stochastic Optimization
• Authors: Yanyuan Wang, Xiaowei Zhang,
• Abstract summary: Contextual optimization provides a framework for decision-making under uncertainty incorporating contextual information through covariates.<n>We first establish central limit theorems for wSAA estimates of optimal values when problems can be solved exactly.<n>We then investigate practical scenarios with computational budget constraints, revealing a fundamental tradeoff between statistical accuracy and computational cost as sample sizes increase.
• Score: 1.4565642534804486
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Contextual stochastic optimization provides a framework for decision-making under uncertainty incorporating observable contextual information through covariates. We analyze statistical inference for weighted sample average approximation (wSAA), a widely-used method for solving contextual stochastic optimization problems. We first establish central limit theorems for wSAA estimates of optimal values when problems can be solved exactly, characterizing how estimation uncertainty scales with covariate sample size. We then investigate practical scenarios with computational budget constraints, revealing a fundamental tradeoff between statistical accuracy and computational cost as sample sizes increase. Through central limit theorems for budget-constrained wSAA estimates, we precisely characterize this statistical-computational tradeoff. We also develop "over-optimizing" strategies for solving wSAA problems that ensure valid statistical inference. Extensive numerical experiments on both synthetic and real-world datasets validate our theoretical findings.

Related papers

• ODAR: Principled Adaptive Routing for LLM Reasoning via Active Inference [60.958331943869126]
  ODAR-Expert is an adaptive routing framework that optimize the accuracy-efficiency trade-off via principled resource allocation.<n>We show strong and consistent gains, including 98.2% accuracy on MATH and 54.8% on Humanity's Last Exam.
  arXiv  Detail & Related papers  (2026-02-27T05:22:01Z)
• Principled Algorithms for Optimizing Generalized Metrics in Binary Classification [53.604375124674796]
  We introduce principled algorithms for optimizing generalized metrics, supported by $H$-consistency and finite-sample generalization bounds.<n>Our approach reformulates metric optimization as a generalized cost-sensitive learning problem.<n>We develop new algorithms, METRO, with strong theoretical performance guarantees.
  arXiv  Detail & Related papers  (2025-12-29T01:33:42Z)
• Black-box Optimization with Simultaneous Statistical Inference for Optimal Performance [18.13513199455587]
  Black-box optimization is often encountered for decision-making in complex systems management.<n>Our goal is to address the dual tasks of optimization and statistical inference for the optimal performance in an online fashion.
  arXiv  Detail & Related papers  (2025-01-14T02:37:09Z)
• Statistical Inference in Tensor Completion: Optimal Uncertainty Quantification and Statistical-to-Computational Gaps [7.174572371800217]
  This paper presents a simple yet efficient method for statistical inference of tensor linear forms using incomplete and noisy observations. It is suitable for various statistical inference tasks, including constructing confidence intervals, inference under heteroskedastic and sub-exponential noise, and simultaneous testing.
  arXiv  Detail & Related papers  (2024-10-15T03:09:52Z)
• Generalization Bounds of Surrogate Policies for Combinatorial Optimization Problems [61.580419063416734]
  A recent stream of structured learning approaches has improved the practical state of the art for a range of optimization problems. The key idea is to exploit the statistical distribution over instances instead of dealing with instances separately. In this article, we investigate methods that smooth the risk by perturbing the policy, which eases optimization and improves the generalization error.
  arXiv  Detail & Related papers  (2024-07-24T12:00:30Z)
• Stratified Prediction-Powered Inference for Hybrid Language Model Evaluation [62.2436697657307]
  Prediction-powered inference (PPI) is a method that improves statistical estimates based on limited human-labeled data.<n>We propose a method called Stratified Prediction-Powered Inference (StratPPI)<n>We show that the basic PPI estimates can be considerably improved by employing simple data stratification strategies.
  arXiv  Detail & Related papers  (2024-06-06T17:37:39Z)
• Likelihood Ratio Confidence Sets for Sequential Decision Making [51.66638486226482]
  We revisit the likelihood-based inference principle and propose to use likelihood ratios to construct valid confidence sequences. Our method is especially suitable for problems with well-specified likelihoods. We show how to provably choose the best sequence of estimators and shed light on connections to online convex optimization.
  arXiv  Detail & Related papers  (2023-11-08T00:10:21Z)
• A Note on Task-Aware Loss via Reweighing Prediction Loss by Decision-Regret [11.57423546614283]
  We propose a decision-aware version of predict-then-optimize. We reweigh the prediction error by the decision regret incurred by an (unweighted) pilot estimator of costs. We show that this approach can lead to improvements over a "predict-then-optimize" framework.
  arXiv  Detail & Related papers  (2022-11-09T18:59:35Z)
• Data-Driven Sample Average Approximation with Covariate Information [0.0]
  We study optimization for data-driven decision-making when we have observations of the uncertain parameters within the optimization model together with concurrent observations of coparametrics. We investigate three data-driven frameworks that integrate a machine learning prediction model within a programming sample average approximation (SAA) for approximating the solution to this problem.
  arXiv  Detail & Related papers  (2022-07-27T14:45:04Z)
• Off-Policy Evaluation with Policy-Dependent Optimization Response [90.28758112893054]
  We develop a new framework for off-policy evaluation with a textitpolicy-dependent linear optimization response. We construct unbiased estimators for the policy-dependent estimand by a perturbation method. We provide a general algorithm for optimizing causal interventions.
  arXiv  Detail & Related papers  (2022-02-25T20:25:37Z)
• Differential privacy and robust statistics in high dimensions [49.50869296871643]
  High-dimensional Propose-Test-Release (HPTR) builds upon three crucial components: the exponential mechanism, robust statistics, and the Propose-Test-Release mechanism. We show that HPTR nearly achieves the optimal sample complexity under several scenarios studied in the literature.
  arXiv  Detail & Related papers  (2021-11-12T06:36:40Z)
• Integrated Conditional Estimation-Optimization [6.037383467521294]
  Many real-world optimization problems uncertain parameters with probability can be estimated using contextual feature information. In contrast to the standard approach of estimating the distribution of uncertain parameters, we propose an integrated conditional estimation approach. We show that our ICEO approach is theally consistent under moderate conditions.
  arXiv  Detail & Related papers  (2021-10-24T04:49:35Z)
• Outlier-Robust Sparse Estimation via Non-Convex Optimization [73.18654719887205]
  We explore the connection between high-dimensional statistics and non-robust optimization in the presence of sparsity constraints. We develop novel and simple optimization formulations for these problems. As a corollary, we obtain that any first-order method that efficiently converges to station yields an efficient algorithm for these tasks.
  arXiv  Detail & Related papers  (2021-09-23T17:38:24Z)
• Heavy-tailed Streaming Statistical Estimation [58.70341336199497]
  We consider the task of heavy-tailed statistical estimation given streaming $p$ samples. We design a clipped gradient descent and provide an improved analysis under a more nuanced condition on the noise of gradients.
  arXiv  Detail & Related papers  (2021-08-25T21:30:27Z)
• Amortized Conditional Normalized Maximum Likelihood: Reliable Out of Distribution Uncertainty Estimation [99.92568326314667]
  We propose the amortized conditional normalized maximum likelihood (ACNML) method as a scalable general-purpose approach for uncertainty estimation. Our algorithm builds on the conditional normalized maximum likelihood (CNML) coding scheme, which has minimax optimal properties according to the minimum description length principle. We demonstrate that ACNML compares favorably to a number of prior techniques for uncertainty estimation in terms of calibration on out-of-distribution inputs.
  arXiv  Detail & Related papers  (2020-11-05T08:04:34Z)
• Instability, Computational Efficiency and Statistical Accuracy [101.32305022521024]
  We develop a framework that yields statistical accuracy based on interplay between the deterministic convergence rate of the algorithm at the population level, and its degree of (instability) when applied to an empirical object based on $n$ samples. We provide applications of our general results to several concrete classes of models, including Gaussian mixture estimation, non-linear regression models, and informative non-response models.
  arXiv  Detail & Related papers  (2020-05-22T22:30:52Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.