arXiv subjects

David Simchi-Levi

Publications and source records attributed to David Simchi-Levi.

At least 55 records · Page 3Linked to original sources

arXiv2026

PPI-SVRG: Unifying Prediction-Powered Inference and Variance Reduction for Semi-Supervised Optimization

We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates -- PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the neighborhood size. When predictions are perfect, we recover SVRG exactly. When predictions degrade, convergence remains stable but reaches a larger neighborhood. Experiments confirm the theory: PPI-SVRG reduces MSE by 43--52\% under label scarcity on mean estimation benchmarks and improves test accuracy by 2.7--2.9 percentage points on MNIST with only 10\% labeled data.

cs.LG↗

arXiv2026

Best Arm Identification with LLM Judges and Limited Human

We study fixed-confidence best-arm identification (BAI) where a cheap but potentially biased proxy (e.g., LLM judge) is available for every sample, while an expensive ground-truth label can only be acquired selectively when using a human for auditing. Unlike classical multi-fidelity BAI, the proxy is biased (arm- and context-dependent) and ground truth is selectively observed. Consequently, standard multi-fidelity methods can mis-select the best arm, and uniform auditing, though accurate, wastes scarce resources and is inefficient. We prove that without bias correction and propensity adjustment, mis-selection probability may not vanish (even with unlimited proxy data). We then develop an estimator for the mean of each arm that combines proxy scores with inverse-propensity-weighted residuals and form anytime-valid confidence sequences for that estimator. Based on the estimator and confidence sequence, we propose an algorithm that adaptively selects and audits arms. The algorithm concentrates audits on unreliable contexts and close arms and we prove that a plug-in Neyman rule achieves near-oracle audit efficiency. Numerical experiments confirm the theoretical guarantees and demonstrate the superior empirical performance of the proposed algorithm.

cs.LG↗

arXiv2026

Designing Information Delays in Supply Chains

This paper studies how a downstream retailer in a decentralized two-tier supply chain can implicitly transmit demand information to an upstream supplier through the structure of its order stream in the absence of an explicit information-sharing mechanism. We distinguish our work from prior work by introducing the notion of information delay and by linking optimal implicit information sharing to the group delay of the retailer's ordering transfer function. We show that pure delay is strictly suboptimal, while fractional-delay mechanisms can reshape the order autocorrelation to improve supplier forecastability and reduce system-wide inventory costs. Using Hardy-space factorization, we develop a tractable family of invertible ARMA policies that approximates the theoretically optimal (but non-rational) limiting filter derived by Caldentey et al. (2025) and preserves its informational delay properties. This construction yields sharp guidance on how policy complexity, as measured by the degrees of the ARMA policies, impacts supply chain costs. We further extend the analysis to memory-constrained suppliers and characterize how the complexity of the retailer's policy should scale with the supplier's finite forecasting window, highlighting when, perhaps counterintuitively, increasing policy complexity can become counterproductive.

math.OC↗

arXiv2025

Nonparametric Regression in Dirichlet Spaces: A Random Obstacle Approach

In this paper, we consider nonparametric estimation over general Dirichlet metric measure spaces. Unlike the more commonly studied reproducing kernel Hilbert space, whose elements may be defined pointwise, a Dirichlet space typically only contain equivalence classes, i.e. its elements are only unique almost everywhere. This lack of pointwise definition presents significant challenges in the context of nonparametric estimation, for example the classical ridge regression problem is ill-posed. In this paper, we develop a new technique for renormalizing the ridge loss by replacing pointwise evaluations with certain \textit{local means} around the boundaries of obstacles centered at each data point. The resulting renormalized empirical risk functional is well-posed and even admits a representer theorem in terms of certain equilibrium potentials, which are truncated versions of the associated Green function, cut-off at a data-driven threshold. We demonstrate that the renormalized ridge estimator is rate-optimal, and derive an adaptive upper bound on its convergence rate that highlights the interplay between the analytic, geometric, and probabilistic properties of the Dirichlet form. Our framework notably does not require the smoothness of the underlying space, and is applicable to both manifold and fractal settings. To the best of our knowledge, this is the first paper to obtain optimal, out-of-sample convergence guarantees in the framework of general metric measure Dirichlet spaces.

math.ST↗

arXiv2025

Perturbing the Derivative: Wild Refitting for Model-Free Evaluation of Machine Learning Models under Bregman Losses

We study the excess risk evaluation of classical penalized empirical risk minimization (ERM) with Bregman losses. We show that by leveraging the idea of wild refitting, one can efficiently upper bound the excess risk through the so-called "wild optimism," without relying on the global structure of the underlying function class. This property makes our approach inherently model-free. Unlike conventional analysis, our framework operates with just one dataset and black-box access to the training procedure. The method involves randomized Rademacher symmetrization and constructing artificially modified outputs by perturbation in the derivative space with appropriate scaling, upon which we retrain a second predictor for excess risk estimation. We establish high-probability performance guarantee under the fixed design setting, demonstrating that wild refitting under Bregman losses, with an appropriately chosen wild noise scale, yields a valid upper bound on the excess risk. Thus, our work is promising for theoretically evaluating modern opaque ML models, such as deep neural networks and generative models, where the function class is too complex for classical learning theory and empirical process techniques.

stat.ML↗

arXiv2025

Beyond Covariance Matrix: The Statistical Complexity of Private Linear Regression

We study the statistical complexity of private linear regression under an unknown, potentially ill-conditioned covariate distribution. Somewhat surprisingly, under privacy constraints the intrinsic complexity is \emph{not} captured by the usual covariance matrix but rather its $L_1$ analogues. Building on this insight, we establish minimax convergence rates for both the central and local privacy models and introduce an Information-Weighted Regression method that attains the optimal rates. As application, in private linear contextual bandits, we propose an efficient algorithm that achieves rate-optimal regret bounds of order $\sqrt{T}+\frac{1}α$ and $\sqrt{T}/α$ under joint and local $α$-privacy models, respectively. Notably, our results demonstrate that joint privacy comes at almost no additional cost, addressing the open problems posed by Azize and Basu (2024).

cs.LG↗

arXiv2025

Regret Distribution in Stochastic Bandits: Optimal Trade-off between Expectation and Tail Risk

We study the optimal trade-off between expectation and tail risk for regret distribution in the stochastic multi-armed bandit model. We fully characterize the interplay among three desired properties for policy design: worst-case optimality, instance-dependent consistency, and light-tailed risk. New policies are proposed to characterize the optimal regret tail probability for any regret threshold. In particular, we discover an intrinsic gap of the optimal tail rate depending on whether the time horizon $T$ is known a priori or not. Interestingly, when it comes to the purely worst-case scenario, this gap disappears. Our results reveal insights on how to design policies that balance between efficiency and safety, and highlight extra insights on policy robustness with regard to policy hyper-parameters and model mis-specification. We also conduct a simulation study to validate our theoretical insights and provide practical amendment to our policies. Finally, we discuss extensions of our results to (i) general sub-exponential environments and (ii) general stochastic linear bandits. Furthermore, we find that a special case of our policy design surprisingly coincides with what was adopted in AlphaGo Monte Carlo Tree Search. Our theory provides high-level insights to why their engineered solution is successful and should be advocated in complex decision-making environments.

stat.ML↗

arXiv2025

Solve Smart, Not Often: Policy Learning for Costly MILP Re-solving

A common challenge in real-time operations is deciding whether to re-solve an optimization problem or continue using an existing solution. While modern data platforms may collect information at high frequencies, many real-time operations require repeatedly solving computationally intensive optimization problems formulated as Mixed-Integer Linear Programs (MILPs). Determining when to re-solve is, therefore, an economically important question. This problem poses several challenges: 1) How to characterize solution optimality and solving cost; 2) How to detect environmental changes and select beneficial samples for solving the MILP; 3) Given the large time horizon and non-MDP structure, vanilla reinforcement learning (RL) methods are not directly applicable and tend to suffer from value function explosion. Existing literature largely focuses on heuristics, low-data settings, and smooth objectives, with little focus on common NP-hard MILPs. We propose a framework called Proximal Policy Optimization with Change Point Detection (POC), which systematically offers a solution for balancing performance and cost when deciding appropriate re-solving times. Theoretically, we establish the relationship between the number of re-solves and the re-solving cost. To test our framework, we assemble eight synthetic and real-world datasets, and show that POC consistently outperforms existing baselines by 2%-17%. As a side benefit, our work fills the gap in the literature by introducing real-time MILP benchmarks and evaluation criteria.

cs.LG↗

arXiv2025

Online Resource Allocation with Average Budget Constraints

We consider the problem of online resource allocation with average budget constraints. At each time point the decision maker makes an irrevocable decision of whether to accept or reject a request before the next request arrives with the goal to maximize the cumulative rewards. In contrast to existing literature requiring the total resource consumption is below a certain level, we require the average resource consumption per accepted request does not exceed a given threshold. This problem can be casted as an online knapsack problem with exogenous random budget replenishment, and can find applications in various fields such as online anomaly detection, sequential advertising, and per-capita public service providers. We start with general arrival distributions and show that a simple policy achieves a $O(\sqrt{T})$ regret. We complement the result by showing that such a regret growing rate is in general not improvable. We then shift our focus to discrete arrival distributions. We find that many existing re-solving heuristics in the online resource allocation literature, albeit achieve bounded loss in canonical settings, may incur a $Ω(\sqrt{T})$ or even a $Ω(T)$ regret. With the observation that canonical policies tend to be too optimistic and over accept arrivals, we propose a novel policy that incorporates budget safety buffers. It turns out that a little more safety can greatly enhance efficiency -- small additional logarithmic buffers suffice to reduce the regret from $Ω(\sqrt{T})$ or even $Ω(T)$ to $O(\ln^2 T)$. From a practical perspective, we extend the policy to the scenario with continuous arrival distributions, time-dependent information structures, as well as unknown $T$. We conduct both synthetic experiments and empirical applications on a time series data of New York City taxi passengers to validate the performance of our proposed policies.

stat.ME↗

arXiv2025

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↗

arXiv2025

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↗

arXiv2025

Improving the Estimation of Lifetime Effects in A/B Testing via Treatment Locality

Utilizing randomized experiments to evaluate the effect of short-term treatments on the short-term outcomes has been well understood and become the golden standard in industrial practice. However, as service systems become increasingly dynamical and personalized, much focus is shifting toward maximizing long-term outcomes, such as customer lifetime value, through lifetime exposure to interventions. Our goal is to assess the impact of treatment and control policies on long-term outcomes from relatively short-term observations, such as those generated by A/B testing. A key managerial observation is that many practical treatments are local, affecting only targeted states while leaving other parts of the policy unchanged. This paper rigorously investigates whether and how such locality can be exploited to improve estimation of long-term effects in Markov Decision Processes (MDPs), a fundamental model of dynamic systems. We first develop optimal inference techniques for general A/B testing in MDPs and establish corresponding efficiency bounds. We then propose methods to harness the localized structure by sharing information on the non-targeted states. Our new estimator can achieve a linear reduction with the number of test arms for a major part of the variance without sacrificing unbiasedness. It also matches a tighter variance lower bound that accounts for locality. Furthermore, we extend our framework to a broad class of differentiable estimators, which encompasses many widely used approaches in practice. We show that all such estimators can benefit from variance reduction through information sharing without increasing their bias. Together, these results provide both theoretical foundations and practical tools for conducting efficient experiments in dynamic service systems with local treatments.

stat.ME↗

arXiv2025

Large Language Models for Supply Chain Decisions

Supply Chain Management requires addressing a variety of complex decision-making challenges, from sourcing strategies to planning and execution. Over the last few decades, advances in computation and information technologies have enabled the transition from manual, intuition and experience-based decision-making, into more automated and data-driven decisions using a variety of tools that apply optimization techniques. These techniques use mathematical methods to improve decision-making. Unfortunately, business planners and executives still need to spend considerable time and effort to (i) understand and explain the recommendations coming out of these technologies; (ii) analyze various scenarios and answer what-if questions; and (iii) update the mathematical models used in these tools to reflect current business environments. Addressing these challenges requires involving data science teams and/or the technology providers to explain results or make the necessary changes in the technology and hence significantly slows down decision making. Motivated by the recent advances in Large Language Models (LLMs), we report how this disruptive technology can democratize supply chain technology - namely, facilitate the understanding of tools' outcomes, as well as the interaction with supply chain tools without human-in-the-loop. Specifically, we report how we apply LLMs to address the three challenges described above, thus substantially reducing the time to decision from days and weeks to minutes and hours as well as dramatically increasing planners' and executives' productivity and impact.

cs.AI↗

arXiv2025

Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective

We study a sequential contextual decision-making problem in which certain covariates are missing but can be imputed using a pre-trained AI model. From a theoretical perspective, we analyze how the presence of such a model influences the regret of the decision-making process. We introduce a novel notion called "model elasticity", which quantifies the sensitivity of the reward function to the discrepancy between the true covariate and its imputed counterpart. This concept provides a unified way to characterize the regret incurred due to model imputation, regardless of the underlying missingness mechanism. More surprisingly, we show that under the missing at random (MAR) setting, it is possible to sequentially calibrate the pre-trained model using tools from orthogonal statistical learning and doubly robust regression. This calibration significantly improves the quality of the imputed covariates, leading to much better regret guarantees. Our analysis highlights the practical value of having an accurate pre-trained model in sequential decision-making tasks and suggests that model elasticity may serve as a fundamental metric for understanding and improving the integration of pre-trained models in a wide range of data-driven decision-making problems.

cs.LG↗

arXiv2025

Constrained Online Decision-Making: A Unified Framework

Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as adaptive experimental design under safety constraints, personalized recommendation with resource limits, and dynamic pricing under fairness requirements. In this paper, we investigate a general formulation of sequential decision-making with stage-wise feasibility constraints, where at each round, the learner must select an action based on observed context while ensuring that a problem-specific feasibility criterion is satisfied. We propose a unified algorithmic framework that captures many existing constrained learning problems, including constrained bandits, active learning with label budgets, online hypothesis testing with Type I error control, and model calibration. Central to our approach is the concept of upper counterfactual confidence bounds, which enables the design of practically efficient online algorithms with strong theoretical guarantees using any offline conditional density estimation oracle. To handle feasibility constraints in complex environments, we introduce a generalized notion of the eluder dimension, extending it from the classical setting based on square loss to a broader class of metric-like probability divergences. This allows us to capture the complexity of various density function classes and characterize the utility regret incurred due to feasibility constraint uncertainty. Our result offers a principled foundation for constrained sequential decision-making in both theory and practice.

stat.ML↗

arXiv2025

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↗

arXiv2025

Contextual Online Decision Making with Infinite-Dimensional Functional Regression

Contextual sequential decision-making problems play a crucial role in machine learning, encompassing a wide range of downstream applications such as bandits, sequential hypothesis testing and online risk control. These applications often require different statistical measures, including expectation, variance and quantiles. In this paper, we provide a universal admissible algorithm framework for dealing with all kinds of contextual online decision-making problems that directly learns the whole underlying unknown distribution instead of focusing on individual statistics. This is much more difficult because the dimension of the regression is uncountably infinite, and any existing linear contextual bandits algorithm will result in infinite regret. To overcome this issue, we propose an efficient infinite-dimensional functional regression oracle for contextual cumulative distribution functions (CDFs), where each data point is modeled as a combination of context-dependent CDF basis functions. Our analysis reveals that the decay rate of the eigenvalue sequence of the design integral operator governs the regression error rate and, consequently, the utility regret rate. Specifically, when the eigenvalue sequence exhibits a polynomial decay of order $\frac{1}γ\ge 1$, the utility regret is bounded by $\tilde{\mathcal{O}}\Big(T^{\frac{3γ+2}{2(γ+2)}}\Big)$. By setting $γ=0$, this recovers the existing optimal regret rate for contextual bandits with finite-dimensional regression and is optimal under a stronger exponential decay assumption. Additionally, we provide a numerical method to compute the eigenvalue sequence of the integral operator, enabling the practical implementation of our framework.

stat.ML↗

arXiv2025

Learning to Price with Resource Constraints: From Full Information to Machine-Learned Prices

We study the dynamic pricing problem with knapsack, addressing the challenge of balancing exploration and exploitation under resource constraints. We introduce three algorithms tailored to different informational settings: a Boundary Attracted Re-solve Method for full information, an online learning algorithm for scenarios with no prior information, and an estimate-then-select re-solve algorithm that leverages machine-learned informed prices with known upper bound of estimation errors. The Boundary Attracted Re-solve Method achieves logarithmic regret without requiring the non-degeneracy condition, while the online learning algorithm attains an optimal $O(\sqrt{T})$ regret. Our estimate-then-select approach bridges the gap between these settings, providing improved regret bounds when reliable offline data is available. Numerical experiments validate the effectiveness and robustness of our algorithms across various scenarios. This work advances the understanding of online resource allocation and dynamic pricing, offering practical solutions adaptable to different informational structures.

math.OC↗