How much Data do We Need? Sequential Data Collection for Stochastic Programming

• URL: http://arxiv.org/abs/2607.10207v1
• Date: Sat, 11 Jul 2026 08:37:57 GMT
• Title: How much Data do We Need? Sequential Data Collection for Stochastic Programming
• Abstract summary: We study an optimal stopping problem for sequential data collection in data-driven optimization.<n>We propose a benefit-driven stopping framework that balances information gain and sampling cost.<n>Results show that benefit-driven stopping rules can substantially reduce unnecessary data collection.
• Score: 4.522310554705239
• License: http://creativecommons.org/licenses/by-nc-nd/4.0/
• Abstract: Data-driven optimization often requires collecting data to estimate uncertain model parameters before solving the underlying decision problem. In practice, however, data acquisition may incur non-negligible costs, making it critical to determine when to stop additional data collection. In this paper, we study an optimal stopping problem for sequential data collection in stochastic optimization under parameter uncertainty. We propose a benefit-driven stopping framework that balances information gain and sampling cost. We model the unknown distribution parameter within a Bayesian learning framework and update beliefs sequentially as new observations are collected. At each iteration, the decision maker evaluates the expected marginal benefit of additional data relative to the unit sampling cost and determines whether to continue sampling or stop and implement the optimization decision. Based on this framework, we develop several stopping policies. The proposed policies are evaluated through a newsvendor problem with exponentially distributed demand. Numerical experiments compare the policies with fixed-budget and hindsight benchmark strategies. The results show that benefit-driven stopping rules can substantially reduce unnecessary data collection while achieving near-optimal decision performance, demonstrating the effectiveness of adaptive stopping in data-driven optimization.

Related papers

• Learning Polyhedral Conformal Sets for Robust Optimization [10.504036065018216]
  We propose a decision-aware conformal framework that learns uncertainty sets tailored to robust optimization objectives.<n>Our approach parameterizes a flexible family of polyhedral sets via data-driven hyperplanes and learns their geometry by directly minimizing the induced robust loss.<n>We provide finite-sample coverage guarantees and bounds on the sub-optimality gap to an oracle decision.
  arXiv  Detail & Related papers  (2026-05-08T21:39:41Z)
• Robust Assortment Optimization from Observational Data [32.720761309403436]
  We propose a framework for data-driven assortment optimization that accounts for potential distributional shifts in customer choice behavior.<n>Our approach models potential preference shift from a nominal choice model that generates data and seeks to maximize worst-case expected revenue.
  arXiv  Detail & Related papers  (2026-02-11T09:57:16Z)
• A Principled Approach to Randomized Selection under Uncertainty: Applications to Peer Review and Grant Funding [61.86327960322782]
  We propose a principled framework for randomized decision-making based on interval estimates of the quality of each item.<n>We introduce MERIT, an optimization-based method that maximizes the worst-case expected number of top candidates selected.<n>We prove that MERIT satisfies desirable axiomatic properties not guaranteed by existing approaches.
  arXiv  Detail & Related papers  (2025-06-23T19:59:30Z)
• OPO: Making Decision-Focused Data Acquisition Decisions [0.0]
  We propose a model for making data acquisition decisions for variables in contextual optimisation problems.<n>We solve the data acquisition problem with well-defined constraints by learning a surrogate linear objective function.<n>We ablate the problem with a number of training modalities and demonstrate that the differentiable optimisation approach outperforms random search strategies.
  arXiv  Detail & Related papers  (2025-04-21T12:41:35Z)
• Online Data Collection for Efficient Semiparametric Inference [41.49486724979923]
  We present two online data collection policies, Explore-then-Commit and Explore-then-Greedy, that use the parameter estimates at a given time to optimally allocate the remaining budget in the future steps. We prove that both policies achieve zero regret (assessed by MSE) relative to an oracle policy.
  arXiv  Detail & Related papers  (2024-11-05T15:40:53Z)
• Truncating Trajectories in Monte Carlo Policy Evaluation: an Adaptive Approach [51.76826149868971]
  Policy evaluation via Monte Carlo simulation is at the core of many MC Reinforcement Learning (RL) algorithms. We propose as a quality index a surrogate of the mean squared error of a return estimator that uses trajectories of different lengths. We present an adaptive algorithm called Robust and Iterative Data collection strategy Optimization (RIDO)
  arXiv  Detail & Related papers  (2024-10-17T11:47:56Z)
• Diffusion Models as Constrained Samplers for Optimization with Unknown Constraints [55.39203337683045]
  We propose to perform optimization within the data manifold using diffusion models.<n>Depending on the differentiability of the objective function, we propose two different sampling methods.<n>Our method achieves better or comparable performance with previous state-of-the-art baselines.
  arXiv  Detail & Related papers  (2024-02-28T03:09:12Z)
• Experiment Planning with Function Approximation [49.50254688629728]
  We study the problem of experiment planning with function approximation in contextual bandit problems. We propose two experiment planning strategies compatible with function approximation. We show that a uniform sampler achieves competitive optimality rates in the setting where the number of actions is small.
  arXiv  Detail & Related papers  (2024-01-10T14:40:23Z)
• Optimizing Data Collection for Machine Learning [87.37252958806856]
  Modern deep learning systems require huge data sets to achieve impressive performance. Over-collecting data incurs unnecessary present costs, while under-collecting may incur future costs and delay. We propose a new paradigm for modeling the data collection as a formal optimal data collection problem.
  arXiv  Detail & Related papers  (2022-10-03T21:19:05Z)
• Debiasing In-Sample Policy Performance for Small-Data, Large-Scale Optimization [4.554894288663752]
  We propose a novel estimator of the out-of-sample performance of a policy in data-driven optimization. Unlike cross-validation, our approach avoids sacrificing data for a test set. We prove our estimator performs well in the small-data, largescale regime.
  arXiv  Detail & Related papers  (2021-07-26T19:00:51Z)
• Sparse Feature Selection Makes Batch Reinforcement Learning More Sample Efficient [62.24615324523435]
  This paper provides a statistical analysis of high-dimensional batch Reinforcement Learning (RL) using sparse linear function approximation. When there is a large number of candidate features, our result sheds light on the fact that sparsity-aware methods can make batch RL more sample efficient.
  arXiv  Detail & Related papers  (2020-11-08T16:48:02Z)

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.