arXiv subjects

Will Ma

Publications and source records attributed to Will Ma.

At least 19 recordsLinked to original sources

arXiv2026

Sequential Offering in On-Demand Platforms: On the Optimality of Greedy Ranking

On-demand platforms face the fundamental challenge of fulfilling time-sensitive jobs with independent workers who may decline offers. To minimize delays and unfulfilled jobs, platforms frequently raise the offered wage sequentially following each rejection. However, the interaction between these dynamic price adjustments and the specific sequence in which workers are approached has been overlooked. In particular, if the best-suited workers (e.g., closest to the job) are also ranked earliest in the sequence, then those workers would see the lowest offered wages and may decline, leading to poor system outcomes where less-suited workers end up seeing the raised wages and accepting the job. We study the sequential offering problem to maximize expected welfare or platform profit by jointly optimizing the ranking of workers and the pricing trajectory. Surprisingly, our main result establishes that if the reservation wage distribution exhibits a non-increasing and convex density function (e.g., Uniform, Exponential), welfare is maximized by greedy ranking and wages optimized via backward induction. For arbitrary distributions, we prove that greedy ranking achieves a tight $n/(2n - 1)$ fraction of the prophet benchmark. Numerical results for settings beyond the distributional assumptions find welfare losses well below those allowed by the universal guarantee, even in families where greedy is provably suboptimal. This suggests that rather than sending initial "low ball'' offers to worse matches, platforms should stick with greedy ranking and optimize the wage offerings by appropriately taking the continuation value of the downstream offers into consideration.

cs.GT↗

arXiv2026

Which Pairs to Compare for LLM Post-Training?

Preference-based post-training has become a central paradigm for aligning language models. A common data-collection strategy is to generate a small set of completions for each prompt and label the resulting comparison pairs. However, human preference labels are often much more expensive than generating additional completions, suggesting a different use of the same labeling budget: generate a larger pool of completions, but label only the most informative comparison pairs. This paper studies which pairs should be compared in preference-based post-training. We formulate comparison curation as a sampling-design problem and evaluate designs by the quality of the final policy under the preference-based post-training objective. We instantiate this framework for Direct Preference Optimization (DPO), analyzing how the choice of labeled pairs propagates through DPO training to downstream policy performance. Our main results provide matching upper and lower bounds on the post-training optimality gap of the DPO-trained policy. The bounds show that comparison selection affects downstream performance through a single design-dependent information matrix, which links label allocation to parameter estimation error and policy suboptimality. This yields an explicit optimization criterion for budgeted comparison curation and motivates practical sampling designs for selecting informative pairs from large generated completion pools. Experiments on synthetic settings and language-model post-training benchmarks show that the proposed designs consistently improve sample efficiency over common comparison-selection heuristics.

cs.AI↗

arXiv2026

DeepStock: Reinforcement Learning with Policy Regularizations for Inventory Management

Deep Reinforcement Learning (DRL) provides a general-purpose methodology for training inventory policies that can leverage big data and compute. However, off-the-shelf implementations of DRL have seen mixed success, often plagued by high sensitivity to the hyperparameters used during training. In this paper, we show that by imposing policy regularizations, grounded in classical inventory concepts such as "Base Stock", we can significantly accelerate hyperparameter tuning and improve the final performance of several DRL methods. We report details from a 100% deployment of DRL with policy regularizations on Alibaba's e-commerce platform, Tmall. We also include extensive synthetic experiments, which show that policy regularizations reshape the narrative on what is the best DRL method for inventory management.

cs.LG↗

arXiv2026

Experimental Assortments for Choice Estimation and Nest Identification

What assortments (subsets of items) should be offered, to collect data for estimating a choice model over $n$ total items? We propose a structured, non-adaptive experiment design requiring only $O(\log n)$ distinct assortments, each offered repeatedly, that consistently outperforms randomized and other heuristic designs across an extensive numerical benchmark that estimates multiple different choice models under a variety of (possibly mis-specified) ground truths. We then focus on Nested Logit choice models, which cluster items into "nests" of close substitutes. Whereas existing Nested Logit estimation procedures assume the nests to be known and fixed, we present a new algorithm to identify nests based on collected data, which when used in conjunction with our experiment design, guarantees correct identification of nests under any Nested Logit ground truth. Our experiment design was deployed to collect data from over 70 million users at Dream11, an Indian fantasy sports platform that offers different types of betting contests, with rich substitution patterns between them. We identify nests based on the collected data, which lead to better out-of-sample choice prediction than ex-ante clustering from contest features. Our identified nests are ex-post justifiable to Dream11 management.

stat.ME↗

arXiv2026

AI Agents for Inventory Control: Human-LLM-OR Complementarity

Inventory control is a fundamental operations problem in which ordering decisions are traditionally guided by theoretically grounded operations research (OR) algorithms. However, such algorithms often rely on rigid modeling assumptions and can perform poorly when demand distributions shift or relevant contextual information is unavailable. Recent advances in large language models (LLMs) have generated interest in AI agents that can reason flexibly and incorporate rich contextual signals, but it remains unclear how best to incorporate LLM-based methods into traditional decision-making pipelines. We study how OR algorithms, LLMs, and humans can interact and complement each other in a multi-period inventory control setting. We construct InventoryBench, a benchmark of over 1,000 inventory instances spanning both synthetic and real-world demand data, designed to stress-test decision rules under demand shifts, seasonality, and uncertain lead times. Through this benchmark, we find that OR-augmented LLM methods outperform either method in isolation, suggesting that these methods are complementary rather than substitutes. We further investigate the role of humans through a controlled classroom experiment that embeds LLM recommendations into a human-in-the-loop decision pipeline. Contrary to prior findings that human-AI collaboration can degrade performance, we show that, on average, human-AI teams achieve higher profits than either humans or AI agents operating alone. Beyond this population-level finding, we formalize an individual-level complementarity effect and derive a distribution-free lower bound on the fraction of individuals who benefit from AI collaboration; empirically, we find this fraction to be substantial.

cs.AI↗

arXiv2026

LLM-SAA: LLM-persona Generated Distributions for Decision-making

LLMs can generate a wealth of data, ranging from simulated personas imitating human valuations and preferences, to demand forecasts based on world knowledge. But how well do such LLM-generated distributions support downstream decision-making? For example, when pricing a new product, a firm could prompt an LLM to simulate how much consumers are willing to pay based on a product description, but how useful is the resulting distribution for optimizing the price? We refer to this approach as LLM-SAA, in which an LLM is used to construct an estimated distribution and the decision is then optimized under that distribution. In this paper, we study metrics to evaluate the quality of these LLM-generated distributions, based on the decisions they induce. Taking three canonical decision-making problems (assortment optimization, pricing, and newsvendor) as examples, we find that LLM-generated distributions are practically useful, especially in low-data regimes. We also show that decision-agnostic metrics such as Wasserstein distance can be misleading when evaluating these distributions for decision-making.

cs.LG↗

arXiv2026

Optimal Bayesian Stopping for Efficient Inference of Consistent LLM Answers

A simple strategy for improving LLM accuracy, especially in math and reasoning problems, is to sample multiple responses and submit the answer most consistently reached. In this paper we leverage Bayesian prior information to save on sampling costs, stopping once sufficient consistency is reached. Although the exact posterior is computationally intractable, we further introduce an efficient "L-aggregated" stopping policy that tracks only the L-1 most frequent answer counts. Theoretically, we prove that L=3 is all you need: this coarse approximation is sufficient to achieve asymptotic optimality, and strictly dominates prior-free baselines, while having a fast posterior computation. Empirically, this identifies the most consistent (i.e., mode) LLM answer using fewer samples, and can achieve similar answer accuracy while cutting the number of LLM calls (i.e., saving on LLM inference costs) by up to 50%.

stat.ML↗

arXiv2025

Personalized Promotions in Practice: Dynamic Allocation and Reference Effects

Partnering with a large online retailer, we consider the problem of sending daily personalized promotions to a userbase of over 20 million customers. We propose an efficient policy for determining, every day, the promotion that each customer should receive (10%, 12%, 15%, 17%, or 20% off), while respecting global allocation constraints. This policy was successfully deployed to see a 4.5% revenue increase during an A/B test, by better targeting promotion-sensitive customers and also learning intertemporal patterns across customers. We also consider theoretically modeling the intertemporal state of the customer. The data suggests a simple new combinatorial model of pricing with reference effects, where the customer remembers the best promotion they saw over the past $\ell$ days as the "reference value", and is more likely to purchase if this value is poor. We tightly characterize the structure of optimal policies for maximizing long-run average revenue under this model -- they cycle between offering poor promotion values $\ell$ times and offering good values once.

cs.GT↗

arXiv2025

SynthIPD: training-free synthetic individual patient data generation

Individual patient data (IPD) are essential for statistical inference in clinical research. However, privacy concerns, high data-sharing costs, and restrictive access often make IPD unavailable. Conventional synthetic data generation usually relies on black box models such as generative adversial networks. These methods, however, requires a large piece of IPD for model training, may be ungeneralizable and lacks interpretability. This paper introduces an assumption-lean, three-step methodology for generating synthetic IPD with survival endpoints only based on published clinical trial articles. The method mainly leverages Kaplan-Meier (KM) curves with at-risk/censoring information and subgroup-level summary statistics. It digitizes the KM curve using Scalable Vector Graphics (SVG) beyond pixel accuracy and then generates synthetic covariates based on the statistics. We illustrate the method's potential through $2$ detailed case studies and simulation studies. The method offers important implications, enabling high-fidelity IPD generation to support evidence-based medical decisions.

stat.AP↗

arXiv2025

Potential-Based Greedy Matching for Dynamic Delivery Pooling

We study the dynamic pooling of multiple orders into a single trip, a strategy widely adopted by online delivery platforms. When an order has to be dispatched, the platform must determine which (if any) of the available orders to pool it with, weighing the immediate efficiency gains against the uncertain, differential benefits of holding each order for future pooling opportunities. In this paper, we demonstrate the effectiveness of using the delivery distance as a proxy for opportunity cost via a potential-based greedy algorithm (PB). The algorithm is simple, pooling each departing job with the available job that maximizes the immediate savings in travel distance minus "half its delivery distance", which we call the potential of the available job. Theoretically, we show that PB achieves vanishing worst-case regret per job as market density increases, whereas a naive greedy policy suffers constant regret. We further show that the potential approximates the true opportunity cost of dispatching a job, in a stochastic setting with sufficient density. Finally, we conduct extensive numerical experiments on both synthetic data and real-world data from the Meituan platform. Despite being forecast-agnostic, PB consistently outperforms greedy heuristics that rely on historical data. Moreover, PB achieves performance comparable to computationally-intensive batching heuristics, which themselves also benefit from incorporating the potential to further improve their performance or drastically reduce computational costs.

cs.DS↗

arXiv2025

Forward-backward Contention Resolution Schemes for Fair Rationing

We use contention resolution schemes (CRS) to derive algorithms for the fair rationing of a single resource when agents have stochastic demands. We aim to provide ex-ante guarantees on the level of service provided to each agent, who may measure service in different ways (Type-I, II, or III), calling for CRS under different feasibility constraints (rank-1 matroid or knapsack). We are particularly interested in two-order CRS where the agents are equally likely to arrive in a known forward order or its reverse, which is motivated by online rationing at food banks. In particular, we derive a two-order CRS for rank-1 matroids with guarantee $1/(1+e^{-1/2})\approx 0.622$, which we prove is tight. This improves upon the $1/2$ guarantee that is best-possible under a single order (Alaei, SIAM J. Comput. 2014), while achieving separation with the $1-1/e\approx 0.632$ guarantee that is possible for random-order CRS (Lee and Singla, ESA 2018). Because CRS guarantees imply prophet inequalities, this also beats the two-order prophet inequality with ratio $(\sqrt{5}-1)/2\approx 0.618$ from (Arsenis, SODA 2021), which was tight for single-threshold policies. Rank-1 matroids suffice to provide guarantees under Type-II or III service, but Type-I service requires knapsack. Accordingly, we derive a two-order CRS for knapsack with guarantee $1/3$, improving upon the $1/(3+e^{-2})\approx 0.319$ guarantee that is best-possible under a single order (Jiang et al., SODA 2022). To our knowledge, $1/3$ provides the best-known guarantee for knapsack CRS even in the offline setting. Finally, we provide an upper bound of $1/(2+e^{-1})\approx 0.422$ for two-order knapsack CRS, strictly smaller than the upper bound of $(1-e^{-2})/2\approx0.432$ for random-order knapsack CRS.

cs.DS↗

arXiv2024

Fair Secretaries with Unfair Predictions

Algorithms with predictions is a recent framework for decision-making under uncertainty that leverages the power of machine-learned predictions without making any assumption about their quality. The goal in this framework is for algorithms to achieve an improved performance when the predictions are accurate while maintaining acceptable guarantees when the predictions are erroneous. A serious concern with algorithms that use predictions is that these predictions can be biased and, as a result, cause the algorithm to make decisions that are deemed unfair. We show that this concern manifests itself in the classical secretary problem in the learning-augmented setting -- the state-of-the-art algorithm can have zero probability of accepting the best candidate, which we deem unfair, despite promising to accept a candidate whose expected value is at least $\max\{\Omega (1) , 1 - O(\epsilon)\}$ times the optimal value, where $\epsilon$ is the prediction error. We show how to preserve this promise while also guaranteeing to accept the best candidate with probability $\Omega(1)$. Our algorithm and analysis are based on a new "pegging" idea that diverges from existing works and simplifies/unifies some of their results. Finally, we extend to the $k$-secretary problem and complement our theoretical analysis with experiments.

cs.LG↗

arXiv2024

Survey of Data-driven Newsvendor: Unified Analysis and Spectrum of Achievable Regrets

In the Newsvendor problem, the goal is to guess the number that will be drawn from some distribution, with asymmetric consequences for guessing too high vs. too low. In the data-driven version, the distribution is unknown, and one must work with samples from the distribution. Data-driven Newsvendor has been studied under many variants: additive vs. multiplicative regret, high probability vs. expectation bounds, and different distribution classes. This paper studies all combinations of these variants, filling in many gaps in the literature and simplifying many proofs. In particular, we provide a unified analysis based on the notion of clustered distributions, which in conjunction with our new lower bounds, shows that the entire spectrum of regrets between $1/\sqrt{n}$ and $1/n$ can be possible. Simulations on commonly-used distributions demonstrate that our notion is the "correct" predictor of empirical regret across varying data sizes.

stat.ML↗

arXiv2024

Randomized Rounding Approaches to Online Allocation, Sequencing, and Matching

Randomized rounding is a technique that was originally used to approximate hard offline discrete optimization problems from a mathematical programming relaxation. Since then it has also been used to approximately solve sequential stochastic optimization problems, overcoming the curse of dimensionality. To elaborate, one first writes a tractable linear programming relaxation that prescribes probabilities with which actions should be taken. Rounding then designs a (randomized) online policy that approximately preserves all of these probabilities, with the challenge being that the online policy faces hard constraints, whereas the prescribed probabilities only have to satisfy these constraints in expectation. Moreover, unlike classical randomized rounding for offline problems, the online policy's actions unfold sequentially over time, interspersed by uncontrollable stochastic realizations that affect the feasibility of future actions. This tutorial provides an introduction for using randomized rounding to design online policies, through four self-contained examples representing fundamental problems in the area: online contention resolution, stochastic probing, stochastic knapsack, and stochastic matching.

cs.DS↗

arXiv2024

Online Matching and Contention Resolution for Edge Arrivals with Vanishing Probabilities

We study the performance of sequential contention resolution and matching algorithms on random graphs with vanishing edge probabilities. When the edges of the graph are processed in an adversarially-chosen order, we derive a new OCRS that is $0.382$-selectable, attaining the "independence benchmark" from the literature under the vanishing edge probabilities assumption. Complementary to this positive result, we show that no OCRS can be more than $0.390$-selectable, significantly improving upon the upper bound of $0.428$ from the literature. We also derive negative results that are specialized to bipartite graphs or subfamilies of OCRS's. Meanwhile, when the edges of the graph are processed in a uniformly random order, we show that the simple greedy contention resolution scheme which accepts all active and feasible edges is $1/2$-selectable. This result is tight due to a known upper bound. Finally, when the algorithm can choose the processing order, we show that a slight tweak to the random order -- give each vertex a random priority and process edges in lexicographic order -- results in a strictly better contention resolution scheme that is $1-\ln(2-1/e)\approx0.510$-selectable. Our positive results also apply to online matching on $1$-uniform random graphs with vanishing (non-identical) edge probabilities, extending and unifying some results from the random graphs literature.

cs.DS↗

arXiv2024

Sample Complexity of Posted Pricing for a Single Item

Selling a single item to $n$ self-interested buyers is a fundamental problem in economics, where the two objectives typically considered are welfare maximization and revenue maximization. Since the optimal mechanisms are often impractical and do not work for sequential buyers, posted pricing mechanisms, where fixed prices are set for the item for different buyers, have emerged as a practical and effective alternative. This paper investigates how many samples are needed from buyers' value distributions to find near-optimal posted prices, considering both independent and correlated buyer distributions, and welfare versus revenue maximization. We obtain matching upper and lower bounds (up to logarithmic factors) on the sample complexity for all these settings.

cs.GT↗

arXiv2024

VC Theory for Inventory Policies

There has been growing interest in applying reinforcement learning (RL) to inventory management, either by optimizing over temporal transitions or by learning directly from full historical demand trajectories. This contrasts sharply with classical data-driven approaches, which first estimate demand distributions from past data and then compute well-structured optimal policies via dynamic programming. This paper considers a hybrid approach that combines trajectory-based RL with policy regularization imposing base-stock and $(s, S) $ structures. We provide generalization guarantees for this combined approach for several well-known classes in a $T$-period dynamic inventory model, using tools from the celebrated Vapnik-Chervonenkis (VC) theory, such as the Pseudo-dimension and Fat-shattering dimension. Our results have implications for regret against the best-in-class policies, and allow for an arbitrary distribution over demand sequences, which makes no assumptions such as independence across time. Surprisingly, we prove that the class of policies defined by $T$ non-stationary base-stock levels exhibits a generalization error that does not grow with $T$, whereas the two-parameter $(s, S)$ policy class has a generalization error growing logarithmically with $T$. Overall, our analysis leverages specific inventory structures within the learning theory framework, and improves sample complexity guarantees even compared to existing results assuming independent demands.

stat.ML↗

arXiv2024

Online Contention Resolution Schemes for Network Revenue Management and Combinatorial Auctions

We study the Network Revenue Management (NRM) and Online Combinatorial Auctions (OCA) problems, in which products composed of up to L resources are allocated in an online fashion. We take a randomized rounding approach to these problems, employing the modern tool of Online Contention Resolution Schemes (OCRS) and their random-order analogues (RCRS). However in NRM and OCA, there can be negative correlation in different products being demanded, making the standard definitions of OCRS/RCRS inapplicable. This motivates a new definition of random-element OCRS/RCRS, in which batches of elements arrive, and at most one element in each batch is demanded. We first establish a simple random-element OCRS for achieving the well-known guarantee of 1/(1+L). We then prove that this guarantee is a fundamental barrier---it is tight for all prime-power values of L, using a construction based on finite affine planes. Next, we break this barrier in several settings: the standard OCRS setting, on L-partite hypergraphs, and in the RCRS setting. The first setting importantly establishes a separation between standard and random-element OCRS, showing that the negative correlation between elements being demanded in random-element OCRS can actually worsen guarantees. We also establish a separation between standard and random-element RCRS. Although the general formulations of NRM and OCA require random-element OCRS, we also identify special cases in which standard OCRS or RCRS suffice. This includes establishing new reductions from NRM with Poisson arrivals to standard OCRS, and NRM with time-homogeneous Poisson arrivals to standard RCRS.

cs.GT↗