Zuo-jun Max Shen

Donghao Ying, Mengzi Amy Guo, Hyunin Lee et al. · berkeley

We study Concave Constrained Markov Decision Processes (Concave CMDPs) where both the objective and constraints are defined as concave functions of the state-action occupancy measure. We propose the Variance-Reduced Primal-Dual Policy Gradient Algorithm (VR-PDPG), which updates the primal variable via policy gradient ascent and the dual variable via projected sub-gradient descent. Despite the challenges posed by the loss of additivity structure and the nonconcave nature of the problem, we establish the global convergence of VR-PDPG by exploiting a form of hidden concavity. In the exact setting, we prove an $O(T^{-1/3})$ convergence rate for both the average optimality gap and constraint violation, which further improves to $O(T^{-1/2})$ under strong concavity of the objective in the occupancy measure. In the sample-based setting, we demonstrate that VR-PDPG achieves an $\widetilde{O}(ε^{-4})$ sample complexity for $ε$-global optimality. Moreover, by incorporating a diminishing pessimistic term into the constraint, we show that VR-PDPG can attain a zero constraint violation without compromising the convergence rate of the optimality gap. Finally, we validate the effectiveness of our methods through numerical experiments.

Hansheng Jiang, Zuo-Jun Max Shen, Junyu Liu

Quantum computing is expected to have transformative influences on many domains, but its practical deployments on industry problems are underexplored. We focus on applying quantum computing to operations management problems in industry, and in particular, supply chain management. Many problems in supply chain management involve large state and action spaces and pose computational challenges on classic computers. We develop a quantized policy iteration algorithm to solve an inventory control problem and demonstrative its effectiveness. We also discuss in-depth the hardware requirements and potential challenges on implementing this quantum algorithm in the near term. Our simulations and experiments are powered by \texttt{IBM Qiskit} and the \texttt{qBraid} system.

Yonatan Mintz, Zuo-Jun Max Shen, Anil Aswani

Most cities in India do not have water distribution networks that provide water throughout the entire day. As a result, it is common for homes and apartment buildings to utilize water storage systems that are filled during a small window of time in the day when the water distribution network is active. However, these water storage systems do not have disinfection capabilities, and so long durations of storage (i.e., as few as four days) of the same water leads to substantial increases in the amount of bacteria and viruses in that water. This paper considers the stochastic control problem of deciding how much water to store each day in the system, as well as deciding when to completely empty the water system, in order to tradeoff: the financial costs of the water, the health costs implicit in long durations of storing the same water, the potential for a shortfall in the quantity of stored versus demanded water, and water wastage from emptying the system. To solve this problem, we develop a new Binary Dynamic Search (BiDS) algorithm that is able to use binary search in one dimension to compute the value function of stochastic optimal control problems with controlled resets to a single state and with constraints on the maximum time span in between resets of the system.

Ilgin Dogan, Zuo-Jun Max Shen, Anil Aswani

Motivated by a number of real-world applications from domains like healthcare and sustainable transportation, in this paper we study a scenario of repeated principal-agent games within a multi-armed bandit (MAB) framework, where: the principal gives a different incentive for each bandit arm, the agent picks a bandit arm to maximize its own expected reward plus incentive, and the principal observes which arm is chosen and receives a reward (different than that of the agent) for the chosen arm. Designing policies for the principal is challenging because the principal cannot directly observe the reward that the agent receives for their chosen actions, and so the principal cannot directly learn the expected reward using existing estimation techniques. As a result, the problem of designing policies for this scenario, as well as similar ones, remains mostly unexplored. In this paper, we construct a policy that achieves a low regret (i.e., square-root regret up to a log factor) in this scenario for the case where the agent has perfect-knowledge about its own expected rewards for each bandit arm. We design our policy by first constructing an estimator for the agent's expected reward for each bandit arm. Since our estimator uses as data the sequence of incentives offered and subsequently chosen arms, the principal's estimation can be regarded as an analogy of online inverse optimization in MAB's. Next we construct a policy that we prove achieves a low regret by deriving finite-sample concentration bounds for our estimator. We conclude with numerical simulations demonstrating the applicability of our policy to real-life setting from collaborative transportation planning.

Ilgin Dogan, Zuo-Jun Max Shen, Anil Aswani

In practice, incentive providers (i.e., principals) often cannot observe the reward realizations of incentivized agents, which is in contrast to many principal-agent models that have been previously studied. This information asymmetry challenges the principal to consistently estimate the agent's unknown rewards by solely watching the agent's decisions, which becomes even more challenging when the agent has to learn its own rewards. This complex setting is observed in various real-life scenarios ranging from renewable energy storage contracts to personalized healthcare incentives. Hence, it offers not only interesting theoretical questions but also wide practical relevance. This paper explores a repeated adverse selection game between a self-interested learning agent and a learning principal. The agent tackles a multi-armed bandit (MAB) problem to maximize their expected reward plus incentive. On top of the agent's learning, the principal trains a parallel algorithm and faces a trade-off between consistently estimating the agent's unknown rewards and maximizing their own utility by offering adaptive incentives to lead the agent. For a non-parametric model, we introduce an estimator whose only input is the history of principal's incentives and agent's choices. We unite this estimator with a proposed data-driven incentive policy within a MAB framework. Without restricting the type of the agent's algorithm, we prove finite-sample consistency of the estimator and a rigorous regret bound for the principal by considering the sequential externality imposed by the agent. Lastly, our theoretical results are reinforced by simulations justifying applicability of our framework to green energy aggregator contracts.

Junyu Liu, Hansheng Jiang, Zuo-Jun Max Shen

Energy cost is increasingly crucial in the modern computing industry with the wide deployment of large-scale machine learning models and language models. For the firms that provide computing services, low energy consumption is important both from the perspective of their own market growth and the government's regulations. In this paper, we study the energy benefits of quantum computing vis-a-vis classical computing. Deviating from the conventional notion of quantum advantage based solely on computational complexity, we redefine advantage in an energy efficiency context. Through a Cournot competition model constrained by energy usage, we demonstrate quantum computing firms can outperform classical counterparts in both profitability and energy efficiency at Nash equilibrium. Therefore quantum computing may represent a more sustainable pathway for the computing industry. Moreover, we discover that the energy benefits of quantum computing economies are contingent on large-scale computation. Based on real physical parameters, we further illustrate the scale of operation necessary for realizing this energy efficiency advantage.

Beichen Wan, Mo Liu, Paul Grigas et al.

We consider the sequential experimental design problem in the predict-then-optimize paradigm. In this paradigm, the outputs of the prediction model are used as coefficient vectors in a downstream linear optimization problem. Traditional sequential experimental design aims to control the input variables (features) so that the improvement in prediction accuracy from each experimental outcome (label) is maximized. However, in the predict-then-optimize setting, performance is ultimately evaluated based on the decision loss induced by the downstream optimization, rather than by prediction error. This mismatch between prediction accuracy and decision loss renders traditional decision-blind designs inefficient. To address this issue, we propose a directional-based metric to quantify predictive uncertainty. This metric does not require solving an optimization oracle and is therefore computationally tractable. We show that the resulting sequential design criterion enjoys strong consistency and convergence guarantees. Under a broad class of distributions, we demonstrate that our directional uncertainty-based design attains an earlier stopping time than decision-blind designs. This advantage is further supported by real-world experiments on an LLM job allocation problem.

Lingjie Zhao, Xue Yu, Yongzhi Qi et al.

As the pursuit of synergy between Artificial Intelligence (AI) and Operations Research (OR) gains momentum in handling complex inventory systems, a critical challenge persists: how to effectively reconcile AI's adaptive perception with OR's structural rigor. To bridge this gap, we propose a novel OR-Guided "Pretrain-then-Reinforce" framework. To provide structured guidance, we propose a simulation-augmented OR model that generates high-quality reference decisions, implicitly capturing complex business constraints and managerial preferences. Leveraging these OR-derived decisions as foundational training labels, we design a domain-informed deep learning foundation model to establish foundational decision-making capabilities, followed by a reinforcement learning (RL) fine-tuning stage. Uniquely, we position RL as a deep alignment mechanism that enables the AI agent to internalize the optimality principles of OR, while simultaneously leveraging exploration for general policy refinement and allowing expert guidance for scenario-specific adaptation (e.g., promotional events). Validated through extensive numerical experiments and a field deployment at JD.com augmented by a Difference-in-Differences (DiD) analysis, our model significantly outperforms incumbent industrial practices, delivering real-world gains of a 5.27-day reduction in turnover and a 2.29% increase in in-stock rates, alongside a 29.95% decrease in holding costs. Contrary to the prevailing trend of brute-force model scaling, our study demonstrates that a lightweight, domain-informed model can deliver state-of-the-art performance and robust transferability when guided by structured OR logic. This approach offers a scalable and cost-effective paradigm for intelligent supply chain management, highlighting the value of deeply aligning AI with OR.

Yongzhi Qi, Hao Hu, Dazhou Lei et al.

Time series neural networks perform exceptionally well in real-world applications but encounter challenges such as limited scalability, poor generalization, and suboptimal zero-shot performance. Inspired by large language models, there is interest in developing large time series models (LTM) to address these issues. However, current methods struggle with training complexity, adapting human feedback, and achieving high predictive accuracy. We introduce TimeHF, a novel pipeline for creating LTMs with 6 billion parameters, incorporating human feedback. We use patch convolutional embedding to capture long time series information and design a human feedback mechanism called time-series policy optimization. Deployed in JD.com's supply chain, TimeHF handles automated replenishment for over 20,000 products, improving prediction accuracy by 33.21% over existing methods. This work advances LTM technology and shows significant industrial benefits.

Yongzhi Qi, Jiaheng Yin, Jianshen Zhang et al.

In supply chain management, planning is a critical concept. The movement of physical products across different categories, from suppliers to warehouse management, to sales, and logistics transporting them to customers, entails the involvement of many entities. It covers various aspects such as demand forecasting, inventory management, sales operations, and replenishment. How to collect relevant data from an e-commerce platform's perspective, formulate long-term plans, and dynamically adjust them based on environmental changes, while ensuring interpretability, efficiency, and reliability, is a practical and challenging problem. In recent years, the development of AI technologies, especially the rapid progress of large language models, has provided new tools to address real-world issues. In this work, we construct a Supply Chain Planning Agent (SCPA) framework that can understand domain knowledge, comprehend the operator's needs, decompose tasks, leverage or create new tools, and return evidence-based planning reports. We deploy this framework in JD.com's real-world scenario, demonstrating the feasibility of LLM-agent applications in the supply chain. It effectively reduced labor and improved accuracy, stock availability, and other key metrics.

Yunhao Liang, Pujun Zhang, Yuan Qu et al.

The pretrain-transfer paradigm, which underpins the success of large language models (LLMs), has demonstrated the immense power of creating foundation models that learn generalizable representations from vast datasets. However, extending this paradigm to Operations Research (OR) problems on graph structures remains challenging due to the fundamental conflict between the statistical flexibility of language and the strict combinatorial constraints of graphs. To bridge this gap, we introduce the Graph Foundation Model (GFM), the first framework capable of solving all distance-based optimization problems on graph structures. By introducing the LLM-like self-supervised pre-training paradigm on the paths generated from random walks in the graph, GFM is compelled to internalize the graph's complex topological and combinatorial rules, where the connectivity of the structure itself can be treated as the supervisory signal. Unlike existing neural methods that learn complex and task-specific solving policies, our approach leverages the pre-trained GFM as a foundational model of the graph's intrinsic structure, which in turn enables a simple generative heuristic to tackle a diverse range of optimization challenges effectively. Comprehensive experiments on networks ranging from 20 to 893 nodes demonstrate that GFM achieves competitive performance against specialized solvers across a variety of distinct optimization task classes, while maintaining significantly faster inference times. Our work establishes a new paradigm of adapting the pretrain-transfer framework to graph optimization, opening the door for applying foundation model innovations to OR.

Yunhao Liang, Yuan Qu, Jingyuan Yang et al.

Coordinating multiple large language models (LLMs) to solve complex tasks collaboratively poses a fundamental trade-off between the computation costs and collective performance compared with individual model. We introduce a novel, game-theoretically grounded reinforcement learning (RL) framework, the Multi-Agent Cooperation Sequential Public Goods Game (MAC-SPGG), to systematically incentivize cooperation in multi-LLM ensembles. In MAC-SPGG, LLM agents move in sequence, observing predecessors' outputs and updating beliefs to condition their own contributions. By redesigning the public-goods reward, effortful contributions become the unique Subgame Perfect Nash Equilibrium (SPNE), which eliminates free-riding under traditional SPGG or PGG. Its sequential protocol replaces costly round-based information exchanges with a streamlined decision flow, cutting communication overhead while retaining strategic depth. We prove the existence and uniqueness of the SPNE under realistic parameters, and empirically show that MAC-SPGG-trained ensembles outperform single-agent baselines, chain-of-thought prompting, and other cooperative methods, even achieving comparable performance to large-scale models across reasoning, math, code generation, and NLP tasks. Our results highlight the power of structured, incentive-aligned MAC-SPGG cooperation for scalable and robust multi-agent language generation.

Hansheng Jiang, Chunlin Sun, Zuo-Jun Max Shen

We consider a network inventory system motivated by one-way, on-demand vehicle sharing services. Under uncertain and correlated network demand, the service operator periodically repositions vehicles to match a fixed supply with spatial customer demand while minimizing costs. Finding an optimal repositioning policy in such a general inventory network is analytically and computationally challenging. We introduce a base-stock repositioning policy as a multidimensional generalization of the classical inventory rule to $n$ locations, and we establish its asymptotic optimality under two practically relevant regimes. We present exact reformulations that enable efficient computation of the best base-stock policy in an offline setting with historical data. In the online setting, we illustrate the challenges of learning with censored data in networked systems through a regret lower bound analysis and by demonstrating the suboptimality of alternative algorithmic approaches. We propose a Surrogate Optimization and Adaptive Repositioning algorithm and prove that it attains an optimal regret of $O(n^{2.5} \sqrt{T})$, which matches the regret lower bound in $T$ with polynomial dependence on $n$. Our work highlights the critical role of inventory repositioning in the viability of shared mobility businesses and illuminates the inherent challenges posed by data and network complexity. Our results demonstrate that simple, interpretable policies, such as the state-independent base-stock policies we analyze, can provide significant practical value and achieve near-optimal performance.

Shuo Sun, Meng Qi, Zuo-Jun Max Shen

In this work, we consider an online robust Markov Decision Process (MDP) where we have the information of finitely many prototypes of the underlying transition kernel. We consider an adaptively updated ambiguity set of the prototypes and propose an algorithm that efficiently identifies the true underlying transition kernel while guaranteeing the performance of the corresponding robust policy. To be more specific, we provide a sublinear regret of the subsequent optimal robust policy. We also provide an early stopping mechanism and a worst-case performance bound of the value function. In numerical experiments, we demonstrate that our method outperforms existing approaches, particularly in the early stage with limited data. This work contributes to robust MDPs by considering possible prior information about the underlying transition probability and online learning, offering both theoretical insights and practical algorithms for improved decision-making under uncertainty.

Mo Liu, Paul Grigas, Heyuan Liu et al.

We develop the first active learning method for contextual linear optimization. Specifically, we introduce a label acquisition algorithm that sequentially decides whether to request the ``labels'' of feature samples from an unlabeled data stream, where the labels correspond to the coefficients of the objective in the linear optimization. Our method is the first to be directly informed by the decision loss induced by the predicted coefficients, referred to as the Smart Predict-then-Optimize (SPO) loss. Motivated by the structure of the SPO loss, our algorithm adopts a margin-based criterion utilizing the concept of distance to degeneracy. In particular, we design an efficient active learning algorithm with theoretical excess risk (i.e., generalization) guarantees. We derive upper bounds on the label complexity, defined as the number of samples whose labels are acquired to achieve a desired small level of SPO risk. These bounds show that our algorithm has a much smaller label complexity than the naive supervised learning approach that labels all samples, particularly when the SPO loss is minimized directly on the collected data. To address the discontinuity and nonconvexity of the SPO loss, we derive label complexity bounds under tractable surrogate loss functions. Under natural margin conditions, these bounds also outperform naive supervised learning. Using the SPO+ loss, a specialized surrogate of the SPO loss, we establish even tighter bounds under separability conditions. Finally, we present numerical evidence showing the practical value of our algorithms in settings such as personalized pricing and the shortest path problem.

Meng Qi, Paul Grigas, Zuo-Jun Max Shen

Many real-world optimization problems involve uncertain parameters with probability distributions that can be estimated using contextual feature information. In contrast to the standard approach of first estimating the distribution of uncertain parameters and then optimizing the objective based on the estimation, we propose an integrated conditional estimation-optimization (ICEO) framework that estimates the underlying conditional distribution of the random parameter while considering the structure of the optimization problem. We directly model the relationship between the conditional distribution of the random parameter and the contextual features, and then estimate the probabilistic model with an objective that aligns with the downstream optimization problem. We show that our ICEO approach is asymptotically consistent under moderate regularity conditions and further provide finite performance guarantees in the form of generalization bounds. Computationally, performing estimation with the ICEO approach is a non-convex and often non-differentiable optimization problem. We propose a general methodology for approximating the potentially non-differentiable mapping from estimated conditional distribution to the optimal decision by a differentiable function, which greatly improves the performance of gradient-based algorithms applied to the non-convex problem. We also provide a polynomial optimization solution approach in the semi-algebraic case. Numerical experiments are also conducted to show the empirical success of our approach in different situations including with limited data samples and model mismatches.

Ilgin Dogan, Zuo-Jun Max Shen, Anil Aswani

The exploration/exploitation trade-off is an inherent challenge in data-driven adaptive control. Though this trade-off has been studied for multi-armed bandits (MAB's) and reinforcement learning for linear systems; it is less well-studied for learning-based control of nonlinear systems. A significant theoretical challenge in the nonlinear setting is that there is no explicit characterization of an optimal controller for a given set of cost and system parameters. We propose the use of a finite-horizon oracle controller with full knowledge of parameters as a reasonable surrogate to optimal controller. This allows us to develop policies in the context of learning-based MPC and MAB's and conduct a control-theoretic analysis using techniques from MPC- and optimization-theory to show these policies achieve low regret with respect to this finite-horizon oracle. Our simulations exhibit the low regret of our policy on a heating, ventilation, and air-conditioning model with partially-unknown cost function.

Sheng Liu, Zuo-Jun Max Shen, Xiang Ji

We study an urban bike lane planning problem based on the fine-grained bike trajectory data, which is made available by smart city infrastructure such as bike-sharing systems. The key decision is where to build bike lanes in the existing road network. As bike-sharing systems become widespread in the metropolitan areas over the world, bike lanes are being planned and constructed by many municipal governments to promote cycling and protect cyclists. Traditional bike lane planning approaches often rely on surveys and heuristics. We develop a general and novel optimization framework to guide the bike lane planning from bike trajectories. We formalize the bike lane planning problem in view of the cyclists' utility functions and derive an integer optimization model to maximize the utility. To capture cyclists' route choices, we develop a bilevel program based on the Multinomial Logit model. We derive structural properties about the base model and prove that the Lagrangian dual of the bike lane planning model is polynomial-time solvable. Furthermore, we reformulate the route choice based planning model as a mixed integer linear program using a linear approximation scheme. We develop tractable formulations and efficient algorithms to solve the large-scale optimization problem. Via a real-world case study with a city government, we demonstrate the efficiency of the proposed algorithms and quantify the trade-off between the coverage of bike trips and continuity of bike lanes. We show how the network topology evolves according to the utility functions and highlight the importance of understanding cyclists' route choices. The proposed framework drives the data-driven urban planning scheme in smart city operations management.

Jaime Carrasco, Cristobal Pais, Zuo-Jun Max Shen et al.

In practical applications, it is common that wildfire simulators do not correctly predict the evolution of the fire scar. Usually, this is caused due to multiple factors including inaccuracy in the input data such as land cover classification, moisture, improperly represented local winds, cumulative errors in the fire growth simulation model, high level of discontinuity/heterogeneity within the landscape, among many others. Therefore in practice, it is necessary to adjust the propagation of the fire to obtain better results, either to support suppression activities or to improve the performance of the simulator considering new default parameters for future events, best representing the current fire spread growth phenomenon. In this article, we address this problem through a new methodology using Derivative-Free Optimization (DFO) algorithms for adjusting the Rate of Spread (ROS) factors in a fire simulation growth model called Cell2Fire. To achieve this, we solve an error minimization optimization problem that captures the difference between the simulated and observed fire, which involves the evaluation of the simulator output in each iteration as part of a DFO framework, allowing us to find the best possible factors for each fuel present on the landscape. Numerical results for different objective functions are shown and discussed, including a performance comparison of alternative DFO algorithms.