Jian-qiang Hu

Mingjie Hu, Jian-Qiang Hu, Enlu Zhou

Data acquisition efficiency is a central challenge in deploying reinforcement learning in business and healthcare operations, where interactions are costly, slow, and often involve humans in the loop. This paper develops a unified large deviations framework for data acquisition in infinite-horizon reinforcement learning. We introduce the exponential decay rate of the policy-selection error probability as a principled efficiency metric and derive a variational characterization of this rate via large deviations theory for Markov chains, yielding a nested optimization problem. Based on this characterization, we formalize two complementary notions of optimality in terms of the optimal solution of the nested problem. Because the resulting program is implicit and generally intractable, we propose a tractable convex relaxation with explicit constraints. We then develop a lazy one-step projected subgradient method to solve the relaxed problem and use its iterates to construct an adaptive data acquisition policy. We prove that the resulting reinforcement learning algorithm is near-robustly optimal under our optimality criterion, up to a constant factor. Finally, we extend the framework to linear function approximation to improve scalability, and numerical experiments support the effectiveness of the proposed approach.

Xiangyu Yang, Feng Xu, Jian-Qiang Hu et al.

Firms increasingly rely on dynamic pricing to respond to evolving customer demand, yet in many applications they observe only the revenue generated by a single posted price in each period. At the same time, market conditions may shift gradually or abruptly due to changes in customer preferences, competition, or external shocks. These features create two intertwined challenges: learning the revenue--demand relationship from limited feedback and adapting pricing decisions to a changing environment. We study how a seller can learn and earn effectively under these constraints, without assuming a specific parametric form for demand. We develop a learning framework that updates prices using revenue-based gradient approximations constructed from one observation per period. To address environmental changes, we incorporate a restarting mechanism that periodically refreshes the learning process so that outdated information is discounted. When the degree of nonstationarity is unknown, we further introduce a meta-learning layer to adaptively hedge across multiple restarting schedules. We provide performance guarantees for our approach, showing how cumulative revenue loss relative to a fully informed benchmark depends on both the time horizon and the magnitude of market variation. Simulation experiments using synthetic and real-world data illustrate the effectiveness of the proposed procedures.

Mingjie Hu, Siyang Gao, Jian-qiang Hu et al.

Large language models (LLMs) have significant potential to improve operational efficiency in operations management. Deploying these models requires specifying a policy that governs response quality, shapes user experience, and influences operational value. In this research, we treat LLMs as stochastic simulators and propose a pairwise comparison-based adaptive simulation experiment framework for identifying the optimal policy from a finite set of candidates. We consider two policy spaces: an unstructured space with no parametric assumption, and a structured space in which the data are generated from a preference model. For both settings, we characterize the fundamental data requirements for identifying the optimal policy with high probability. In the unstructured case, we derive a closed-form expression for the optimal sampling proportions, together with a clear operational interpretation. In the structured case, we formulate a regularized convex program to compute the optimal proportions. We then develop an adaptive experimental procedure, termed LLM-PO, for both policy spaces, and prove that it identifies the optimal policy with the desired statistical guarantee while asymptotically attaining the fundamental data requirements. Numerical experiments demonstrate that LLM-PO consistently outperforms benchmark methods and improves LLM performance.