arXiv subjects

Shengyu Cao

Publications and source records attributed to Shengyu Cao.

5 recordsLinked to original sources

arXiv2026

A Solicit-Then-Suggest Model of Agentic Purchasing

E-commerce is shifting from search-based shopping to agentic purchasing. Rather than relying on keywords, AI shopping agents learn customer preferences through targeted multi-round conversations and then recommend a tailored set of products. We develop a solicit-then-suggest framework to study this setting. In a d-dimensional preference space, an agent conducts m rounds of solicitation to refine its belief about the customer's ideal product, then recommends k products from which the customer chooses. Our analysis identifies the key economic tradeoff. Under a Gaussian prior, we establish an uncertainty decomposition: solicitation depth and assortment breadth are substitutes, with total prior uncertainty split between what solicitation resolves and what assortment breadth hedges. The two instruments improve match quality at very different rates. Expected loss decreases on the order of 1/m with solicitation depth, but only on the order of k^(-2/d) with assortment breadth, reflecting a curse of dimensionality. Thus, a few well-designed questions can achieve what would otherwise require far more recommendations. We also characterize the optimal policy. The optimal assortment forms a Voronoi partition, assigning each product to the posterior region it best serves. With a single recommended product, the optimal solicitation follows a water-filling rule that equalizes posterior uncertainty across dimensions. With multiple products, the optimum may allocate less precision to dimensions that the assortment can hedge. This single-product water-filling rule also yields a general approximation guarantee for larger assortments, and the gap vanishes as dimension grows. Beyond the Gaussian case, the uncertainty decomposition and substitutability between solicitation depth and assortment breadth continue to hold for non-Gaussian priors.

cs.GT↗

arXiv2026

Supracompetitive Pricing Under AI Monoculture

When competing sellers delegate pricing to a shared AI model, such as a large language model, correlated recommendations combined with performance-driven updates aggregating seller feedback raise a key question: can standard AI deployment practices inadvertently produce supracompetitive pricing? We develop a stylized duopoly model in which two sellers receive pricing recommendations from a shared AI characterized by two parameters: a propensity parameter capturing the model's tendency to set high prices and an output-fidelity parameter measuring alignment between this tendency and actual outputs, with propensity updated via periodic retraining on observed outcomes. We find that configuring AI models for robustness and reproducibility can lead to supracompetitive pricing via a phase transition. Below a critical output-fidelity threshold, competitive pricing is the unique stable outcome. Above it, the model exhibits bistability: both competitive and supracompetitive pricing are locally stable, with the realized outcome determined by the model's initial propensity. Supracompetitive pricing raises average prices, but occasional low-price recommendations complicate detection. With perfect output fidelity, full price coordination emerges from any interior initial propensity. For finite training batches of size $b$, when the initial propensity lies in the supracompetitive basin, the probability of supracompetitive pricing approaches 1 as $b$ increases, with the region of indeterminate outcomes shrinking at rate $O(1/\sqrt{b})$. Any factor reducing alignment between the model's propensity and sellers' actual pricing, whether through diversifying AI providers, introducing recommendation noise, or reducing seller adherence, pushes the market toward competitive outcomes.

econ.TH↗

arXiv2025

Optimal Partition for Multi-Type Queueing System

We study an optimal server partition and customer assignment problem for an uncapacitated FCFS queueing system with heterogeneous types of customers. Each type of customers is associated with a Poisson arrival, a certain service time distribution, and a unit waiting cost. The goal is to minimize the expected total waiting cost by partitioning the server into sub-queues, each with a smaller service capacity, and routing customer types probabilistically. First, we show that by properly partitioning the queue, it is possible to reduce the expected waiting costs by an arbitrarily large ratio. Then, we show that for any given server partition, the optimal customer assignment admits a certain geometric structure, enabling an efficient algorithm to find the optimal assignment. Such an optimal structure also applies when minimizing the expected sojourn time. Finally, we consider the joint partition-assignment optimization problem. The customer assignment under the optimal server partition admits a stronger structure. Specifically, if the first two moments of the service time distributions satisfy certain properties, it is optimal to deterministically assign customer types with consecutive service rates to the same sub-queue. This structure allows for more efficient algorithms. Overall, the common rule of thumb to partition customers into continuous segments ranked by service rates could be suboptimal, and our work is the first to comprehensively study the queue partition problem based on customer types.

math.OC↗

arXiv2023

Best Arm Identification in Batched Multi-armed Bandit Problems

Recently multi-armed bandit problem arises in many real-life scenarios where arms must be sampled in batches, due to limited time the agent can wait for the feedback. Such applications include biological experimentation and online marketing. The problem is further complicated when the number of arms is large and the number of batches is small. We consider pure exploration in a batched multi-armed bandit problem. We introduce a general linear programming framework that can incorporate objectives of different theoretical settings in best arm identification. The linear program leads to a two-stage algorithm that can achieve good theoretical properties. We demonstrate by numerical studies that the algorithm also has good performance compared to certain UCB-type or Thompson sampling methods.

stat.ML↗

arXiv2022

Extreme ratio between spectral and Frobenius norms of nonnegative tensors

One of the fundamental problems in multilinear algebra, the minimum ratio between the spectral and Frobenius norms of tensors, has received considerable attention in recent years. While most values are unknown for real and complex tensors, the asymptotic order of magnitude and tight lower bounds have been established. However, little is known about nonnegative tensors. In this paper, we present an almost complete picture of the ratio for nonnegative tensors. In particular, we provide a tight lower bound that can be achieved by a wide class of nonnegative tensors under a simple necessary and sufficient condition, which helps to characterize the extreme tensors and obtain results such as the asymptotic order of magnitude. We show that the ratio for symmetric tensors is no more than that for general tensors multiplied by a constant depending only on the order of tensors, hence determining the asymptotic order of magnitude for real, complex, and nonnegative symmetric tensors. We also find that the ratio is in general different to the minimum ratio between the Frobenius and nuclear norms for nonnegative tensors, a sharp contrast to the case for real tensors and complex tensors.

math.NA↗