arXiv subjects

Jinglong Zhao

Publications and source records attributed to Jinglong Zhao.

12 recordsLinked to original sources

arXiv2026

Optimal Control Variates for Survey Sampling and Causal Inference

We propose a family of control variate estimators for variance reduction in design-based survey sampling and causal inference, with and without interference. In these settings, inverse probability weighting (IPW) estimators are widely used, but may have large variance when sampling, treatment, or exposure probabilities are small. Building on the observation that several common estimators, including the Hajek estimator, the normalized estimator, the augmented inverse probability weighting (AIPW) estimator, and the targeted maximum likelihood estimator (TMLE), all correct the Horvitz-Thompson estimator by canceling part of its randomness, we provide a unified interpretation of these estimators as special cases of a general control variate estimator. We then construct optimal control variates that can reduce the finite sample variance compared to these common estimators. We parameterize the proposed control variates by their bases and characterize the optimal bases through a stochastic optimization formulation. In survey sampling and causal inference without interference, the optimal bases are characterized by leading eigenvectors of matrices that depend on both the design-based sampling structure and the model-based outcome uncertainty. In causal inference under network interference, the optimal bases solve a nonconvex quadratic optimization problem; we provide a $\frac{1}{2}$-approximate solution and an alternating local search heuristic. We apply the control variate estimators to the Swiss Environmental Panel survey data and the Chinese social network data, and conduct extensive simulations to show that the proposed control variate estimators can achieve substantial variance reduction.

econ.EM↗

arXiv2026

FrontierOR: Benchmarking LLMs' Capacity for Efficient Algorithm Design in Large-Scale Optimization

Large language models (LLMs) are increasingly used for optimization modeling and solver-code generation, yet practical operations research and optimization problems often require a harder capability: designing scalable algorithms that exploit problem structure and outperform direct formulation-and-solve baselines. Existing benchmarks are limited to small or simplified examples far below real-world scale and complexity. We introduce FrontierOR, among the first benchmarks to systematically evaluate LLM-based efficient algorithm design for realistic large-scale optimization problems. FrontierOR includes 180 tasks derived from methodologically diverse papers published in top-tier operations research venues, each with standardized instances and a hidden, expert-verified evaluation suite. We evaluate seven LLMs spanning frontier, cost-effective, and open-source models both in one-shot and test-time evolution settings. The results reveal that frontier models still struggle to move from executable formulations to efficient optimization algorithms: the strongest one-shot model outperforms Gurobi in only 31% of cases in both solution quality and computational efficiency, and even strong coding agents with test-time evolution achieve only 50% on selected hard tasks. FrontierOR establishes a practical evaluation platform for LLM-based optimization algorithm design, which enables future LLMs and agents to be systematically tested on whether they can move beyond correct formulation toward a feasible, high-quality, and efficient algorithm. Code and data are publicly released at https://github.com/Minw913/FrontierOR.

cs.AI↗

arXiv2025

Efficient Inference Using Large Language Models with Limited Human Data: Fine-Tuning then Rectification

Driven by recent advances in artificial intelligence (AI), a growing literature has demonstrated the potential for using large language models (LLMs) as scalable surrogates to generate human-like responses in many business applications. Two common approaches to improve the performance of LLMs include: fine-tuning, which aligns LLMs more closely with human responses, and rectification, which corrects biases in LLM outputs. In this paper, we develop a two-stage framework that combines fine-tuning and rectification, and optimally allocates limited labeled samples across the two stages. Unlike the conventional objective that minimizes the mean squared prediction errors, we propose to minimize the variance of the prediction errors as the fine-tuning objective, which is optimal for the downstream rectification stage. Building on this insight, we leverage the scaling law of fine-tuning to optimally allocate the limited labeled human data between the fine-tuning and rectification stages. Our empirical analysis validates the fine-tuning scaling law and confirms that our proposed optimal allocation rule reliably identifies the optimal sample allocation. We demonstrate substantial efficiency gains in estimation and inference performance relative to fine-tuning or rectification alone, or to employing the standard mean-squared error objective within the fine-tuning then rectification framework, resulting in significant cost savings for reliable business decisions.

cs.LG↗

arXiv2024

Experimental Design For Causal Inference Through An Optimization Lens

The study of experimental design offers tremendous benefits for answering causal questions across a wide range of applications, including agricultural experiments, clinical trials, industrial experiments, social experiments, and digital experiments. Although valuable in such applications, the costs of experiments often drive experimenters to seek more efficient designs. Recently, experimenters have started to examine such efficiency questions from an optimization perspective, as experimental design problems are fundamentally decision-making problems. This perspective offers a lot of flexibility in leveraging various existing optimization tools to study experimental design problems. This manuscript thus aims to examine the foundations of experimental design problems in the context of causal inference as viewed through an optimization lens.

stat.ME↗

arXiv2023

Adaptive Neyman Allocation

In the experimental design literature, Neyman allocation refers to the practice of allocating units into treated and control groups, potentially in unequal numbers proportional to their respective standard deviations, with the objective of minimizing the variance of the treatment effect estimator. This widely recognized approach increases statistical power in scenarios where the treated and control groups have different standard deviations, as is often the case in social experiments, clinical trials, marketing research, and online A/B testing. However, Neyman allocation cannot be implemented unless the standard deviations are known in advance. Fortunately, the multi-stage nature of the aforementioned applications allows the use of earlier stage observations to estimate the standard deviations, which further guide allocation decisions in later stages. In this paper, we introduce a competitive analysis framework to study this multi-stage experimental design problem. We propose a simple adaptive Neyman allocation algorithm, which almost matches the information-theoretic limit of conducting experiments. We provide theory for estimation and inference using data collected from our adaptive Neyman allocation algorithm. We demonstrate the effectiveness of our adaptive Neyman allocation algorithm using both online A/B testing data from a social media site and synthetic data.

stat.ME↗

arXiv2023

Estimating Effects of Long-Term Treatments

Estimating the effects of long-term treatments through A/B testing is challenging. Treatments, such as updates to product functionalities, user interface designs, and recommendation algorithms, are intended to persist within the system for a long duration of time after their initial launches. However, due to the constraints of conducting long-term experiments, practitioners often rely on short-term experimental results to make product launch decisions. It remains open how to accurately estimate the effects of long-term treatments using short-term experimental data. To address this question, we introduce a longitudinal surrogate framework that decomposes the long-term effects into functions based on user attributes, short-term metrics, and treatment assignments. We outline identification assumptions, estimation strategies, inferential techniques, and validation methods under this framework. Empirically, we demonstrate that our approach outperforms existing solutions by using data from two real-world experiments, each involving more than a million users on WeChat, one of the world's largest social networking platforms.

econ.EM↗

arXiv2022

Pigeonhole Design: Balancing Sequential Experiments from an Online Matching Perspective

Practitioners and academics have long appreciated the benefits of covariate balancing when they conduct randomized experiments. For web-facing firms running online A/B tests, however, it still remains challenging in balancing covariate information when experimental subjects arrive sequentially. In this paper, we study an online experimental design problem, which we refer to as the "Online Blocking Problem." In this problem, experimental subjects with heterogeneous covariate information arrive sequentially and must be immediately assigned into either the control or the treated group. The objective is to minimize the total discrepancy, which is defined as the minimum weight perfect matching between the two groups. To solve this problem, we propose a randomized design of experiment, which we refer to as the "Pigeonhole Design." The pigeonhole design first partitions the covariate space into smaller spaces, which we refer to as pigeonholes, and then, when the experimental subjects arrive at each pigeonhole, balances the number of control and treated subjects for each pigeonhole. We analyze the theoretical performance of the pigeonhole design and show its effectiveness by comparing against two well-known benchmark designs: the match-pair design and the completely randomized design. We identify scenarios when the pigeonhole design demonstrates more benefits over the benchmark design. To conclude, we conduct extensive simulations using Yahoo! data to show a 10.2% reduction in variance if we use the pigeonhole design to estimate the average treatment effect.

stat.ME↗

arXiv2021

Synthetic Controls for Experimental Design

This article studies experimental design in settings where the experimental units are large aggregate entities (e.g., markets), and only one or a small number of units can be exposed to the treatment. In such settings, randomization of the treatment may result in treated and control groups with very different characteristics at baseline, inducing biases. We propose a variety of experimental non-randomized synthetic control designs (Abadie, Diamond and Hainmueller, 2010, Abadie and Gardeazabal, 2003) that select the units to be treated, as well as the untreated units to be used as a control group. Average potential outcomes are estimated as weighted averages of the outcomes of treated units for potential outcomes with treatment, and weighted averages the outcomes of control units for potential outcomes without treatment. We analyze the properties of estimators based on synthetic control designs and propose new inferential techniques. We show that in experimental settings with aggregate units, synthetic control designs can substantially reduce estimation biases in comparison to randomization of the treatment.

stat.ME↗

arXiv2020

Dynamic Pricing (and Assortment) under a Static Calendar

This work is motivated by our collaboration with a large consumer packaged goods (CPG) company. We have found that while the company appreciates the advantages of dynamic pricing, they deem it operationally much easier to plan out a static price calendar in advance. We investigate the efficacy of static control policies for revenue management problems whose optimal solution is inherently dynamic. In these problems, a firm has limited inventory to sell over a finite time horizon, over which heterogeneous customers stochastically arrive. We consider both pricing and assortment controls, and derive simple static policies in the form of a price calendar or a planned sequence of assortments, respectively. In the assortment planning problem, we also differentiate between the static vs. dynamic substitution models of customer demand. We show that our policies are within 1-1/e (approximately 0.63) of the optimum under stationary (IID) demand, and 1/2 of the optimum under non-stationary demand, with both guarantees approaching 1 if the starting inventories are large. We adapt the technique of prophet inequalities from optimal stopping theory to pricing and assortment problems, and our results are relative to the linear programming relaxation. Under the special case of IID single-item pricing, our results improve the understanding of irregular and discrete demand curves, by showing that a static calendar can be (1-1/e)-approximate if the prices are sorted high-to-low. Finally, we demonstrate on both data from the CPG company and synthetic data from the literature that our simple price and assortment calendars are effective.

cs.DS↗

arXiv2020

Design and Analysis of Switchback Experiments

Switchback experiments, where a firm sequentially exposes an experimental unit to random treatments, are among the most prevalent designs used in the technology sector, with applications ranging from ride-hailing platforms to online marketplaces. Although practitioners have widely adopted this technique, the derivation of the optimal design has been elusive, hindering practitioners from drawing valid causal conclusions with enough statistical power. We address this limitation by deriving the optimal design of switchback experiments under a range of different assumptions on the order of the carryover effect -- the length of time a treatment persists in impacting the outcome. We cast the optimal experimental design problem as a minimax discrete optimization problem, identify the worst-case adversarial strategy, establish structural results, and solve the reduced problem via a continuous relaxation. For switchback experiments conducted under the optimal design, we provide two approaches for performing inference. The first provides exact randomization based p-values, and the second uses a new finite population central limit theorem to conduct conservative hypothesis tests and build confidence intervals. We further provide theoretical results when the order of the carryover effect is misspecified and provide a data-driven procedure to identify the order of the carryover effect. We conduct extensive simulations to study the numerical performance and empirical properties of our results, and conclude with practical suggestions.

stat.ME↗

arXiv2019

Blind Network Revenue Management and Bandits with Knapsacks under Limited Switches

This paper studies the impact of limited switches on resource-constrained dynamic pricing with demand learning. We focus on the classical price-based blind network revenue management problem and extend our results to the bandits with knapsacks problem. In both settings, a decision maker faces stochastic and distributionally unknown demand, and must allocate finite initial inventory across multiple resources over time. In addition to standard resource constraints, we impose a switching constraint that limits the number of action changes over the time horizon. We establish matching upper and lower bounds on the optimal regret and develop computationally efficient limited-switch algorithms that achieve it. We show that the optimal regret rate is fully characterized by a piecewise-constant function of the switching budget, which further depends on the number of resource constraints. Our results highlight the fundamental role of resource constraints in shaping the statistical complexity of online learning under limited switches. Extensive simulations demonstrate that our algorithms maintain strong cumulative reward performance while significantly reducing the number of switches.

cs.LG↗

arXiv2019

The Competitive Ratio of Threshold Policies for Online Unit-density Knapsack Problems

We study a wholesale supply chain ordering problem. In this problem, the supplier has an initial stock, and faces an unpredictable stream of incoming orders, making real-time decisions on whether to accept or reject each order. What makes this wholesale supply chain ordering problem special is its ``knapsack constraint,'' that is, we do not allow partially accepting an order or splitting an order. The objective is to maximize the utilized stock. We model this wholesale supply chain ordering problem as an online unit-density knapsack problem. We study randomized threshold algorithms that accept an item as long as its size exceeds the threshold. We derive two optimal threshold distributions, the first is 0.4324-competitive relative to the optimal offline integral packing, and the second is 0.4285-competitive relative to the optimal offline fractional packing. Both results require optimizing the cumulative distribution function of the random threshold, which are challenging infinite-dimensional optimization problems. We also consider the generalization to multiple knapsacks, where an arriving item has a different size in each knapsack. We derive a 0.2142-competitive algorithm for this problem. We also show that any randomized algorithm for this problem cannot be more than 0.4605-competitive. This is the first upper bound strictly less than 0.5, which implies the intrinsic challenge of knapsack constraint. We show how to naturally implement our optimal threshold distributions in the warehouses of a Latin American chain department store. We run simulations on their order data, which demonstrate the efficacy of our proposed algorithms.

cs.DS↗