Title: The Primal-Dual Newsvendor for Network Inventory

Abstract: Classic inventory management considers holding stock of a single product in a single location to meet uncertain demand. The resulting newsvendor model, with its intuitive solution balancing overage and underage costs, is essential for operations managers seeking to set appropriate inventory levels. Modern businesses, however, typically operate large inventory networks, where stocks are pooled across products and locations in order to better match supply with demand. Two examples from practice are assemble-to-order (ATO) networks, which stock inventory of common resources that are used to assemble end products on-demand, and flexible fulfillment networks, which stock inventory in multiple storage locations in order to flexibly fulfill demand arriving from different customer regions. The classic newsvendor model provides little guidance for these network settings, especially when practical realities like fixed costs, batch ordering, and integer constraints are taken into account. Our approach to this problem uses linear programming to reinterpret the classic newsvendor solution from a primal-dual perspective, then leverages this perspective to design efficient algorithms for general inventory networks. This approach provides an intuitive solution that balances overage and underage costs across the network, as well as a constant factor approximation guarantee relative to optimal. In particular, we achieve the best known factor for both problems we study: 1.58 for ATO, and 4 for flexible fulfillment networks (reduced from 1.8 and 8, respectively, in the current literature). Further, as a purely combinatorial primal-dual algorithm, our approach avoids solving any linear programs and so is quite fast in practice, but still provides instance specific guarantees by constructing both primal and dual solutions.

Title: Selling Advantages: Externality-Based Upgrades for Digital Goods under Income Effects

Abstract: Many digital products, such as video games or social media, have a social component that allows firms to sell paid upgrades whose value derives from giving buyers an advantage over other users. While such externality-based upgrades are often inexpensive to design, they impose negative externalities on the remaining users and degrade their experience. We analytically study the trade-off between externality-based and externality-free upgrade features in the design of digital goods when users are vertically differentiated by income effects. We show that the classical result that offering a single, externality-free version is optimal does not extend to settings with nonlinear income effects. Moreover, even when user costs are linear, it can be optimal to offer upgrades consisting of externality-based features. However, if such features are offered, optimal versioning also requires offering a version that includes all externality-free features and none that are externality-based, as well as a low-quality, free base version to mitigate negative externalities. Our results provide guidance for the design of digital goods in markets where user interactions or income effects are present.

Title: Decentralized Multi-product Pricing: Diagonal Dominance, Nash Equilibrium, and Price of Anarchy

Abstract: Decentralized decision making in multi-product firms can lead to efficiency losses when autonomous decision makers fail to internalize cross-product demand interactions. This paper quantifies the magnitude of such losses by analyzing the Price of Anarchy in a pricing game in which each decision maker independently sets prices to maximize its own product-level revenue. We model demand using a linear system that captures both substitution and complementarity effects across products. We first establish existence and uniqueness of a pure-strategy Nash equilibrium under economically standard diagonal dominance conditions. Our main contribution is the derivation of a tight worst-case lower bound on the ratio between decentralized revenue and the optimal centralized revenue. We show that this efficiency loss is governed by a single scalar parameter, denoted by μ, which measures the aggregate strength of cross-price effects relative to own-price sensitivities. We further refine the analysis by providing an instance-exact characterization of efficiency loss based on the spectral properties of the demand interaction matrix. Together, these results offer a quantitative framework for assessing the trade-off between centralized pricing and decentralized autonomy in multi-product firms.

Title: A Computational Method for Solving the Stochastic Joint Replenishment Problem in High Dimensions

Abstract: We consider a discrete-time formulation for a class of high-dimensional stochastic joint replenishment problems. First, we approximate the problem by a continuous-time impulse control problem. Exploiting connections among the impulse control problem, backward stochastic differential equations (BSDEs) with jumps, and the stochastic target problem, we develop a novel, simulation-based computational method that relies on deep neural networks to solve the impulse control problem. Based on that solution, we propose an implementable inventory control policy for the original (discrete-time) stochastic joint replenishment problem, and test it against the best available benchmarks in a series of test problems. For the problems studied thus far, our method matches or beats the best benchmark we could find, and it is computationally feasible up to at least 50 dimensions—that is, 50 stock-keeping units (SKUs).

Title: Statistical Inference for Markov Chains with Known Structure

Abstract: For Markov chains arising in many operations settings, such as in queueing systems and inventory systems, the chain's stochastic recursion representation is known except for the distribution of the iid "driving noise" variables. We refer to such chains, which can have a general state space, as SKUD chains: "structure known, unknown distribution." Given a dataset of driving noise samples, and for a nonparametric model of the driving noise distribution, we study statistically efficient estimation of equilibrium and non-equilibrium expectation performance measures for SKUD chains. Such expectations can be viewed as functionals of the driving noise distribution, and we develop a semiparametric efficiency framework to characterize consistent, asymptotically minimum variance estimation. We then study the properties of plug-in estimation, where the empirical driving noise distribution is plugged into the functional of interest, which also corresponds to driving the chain using the empirical distribution. Interestingly, we show that plug-in estimation suffers from fundamental issues when the population driving noise distribution is continuous, which contrasts with the discreteness of the empirical driving noise distribution. Notably, the empirically driven chain is not φ-irreducible unless the population chain has an accessible atom. Moreover, when the state space is infinite, plug-in estimation can be inconsistent for equilibrium expectations, even when an accessible atom exists, as well as for non-equilibrium expectations. We characterize when plug-in estimation enjoys consistency, asymptotic normality, and statistical efficiency, and in such settings, we develop consistent asymptotic variance estimators to enable inference. We also develop alternative sampling procedures for efficient estimation and inference, which resolve the issues of plug-in estimation.

Title: What Data Enables Optimal Decisions? A Study of Data Informativeness in Optimization Under Uncertainty

Abstract: We study the fundamental question of how informative a dataset is for solving a given decision-making task. In our setting, a dataset provides partial information about unknown parameters of an optimization task. Focusing on linear programs with uncertainty in the cost vector, we characterize theoretically when a dataset is sufficient to recover an optimal decision. We show how task structure and uncertainty shape data requirements and provide algorithms for principled task-aware data selection.

Title: A Causal Framework for Proxy Gaming and Goal Drift in Sequential AI Decision Systems

Abstract: Digital platforms increasingly rely on AI systems that predict human behavior in order to optimize user engagement, sales, and related performance metrics. Under some conditions, however, systems designed to predict behavior can drift toward shaping it in harmful ways. This work proposes a structural causal modeling framework for analyzing that transition as a form of proxy gaming and instrumental goal drift. The framework clarifies how optimization against behavioral proxies, especially in feedback-rich environments, can lead closed-loop systems to manipulate users in ways that improve measured outcomes while undermining user welfare or autonomy. Viewing reinforcement learning through a causal lens, I further examine mechanisms through which such systems may progress from prediction to behavior modification or other misaligned outcomes. The analysis contributes a causal perspective on specification error in AI-enabled decision systems, clarifies when predictive optimization becomes manipulative intervention, and identifies implications for the design, monitoring, and governance of platform policies.

Title: How Long Does it Take to Sell Your Products?

Abstract: We study the pricing problem of a seller with finite inventory over a finite sales horizon. Customers arrive according to a Poisson process and have valuations drawn from short-tailed, light-tailed, or heavy-tailed distributions, corresponding to the standard classes in Extreme Value Theory.  Our focus is on the normalized time required to sell k out of q products in an asymptotic regime in which the sales horizon becomes large. Under static pricing, we show that for short-tailed and light-tailed valuations, the time required to sell k products converges to zero, both in distribution and in expectation. For heavy-tailed valuations, by contrast, the limiting distribution is non-degenerate but exhibits a positive probability of unsold inventory. Under dynamic pricing, we show that the time of the kth sale converges to an expression involving products of Beta random variables whose parameters are determined by the tail class of the valuation distribution. In the light-tailed case, this reduces to the kth order statistic of a uniform distribution, implying that sales are asymptotically optimally balanced over the available horizon. For short-tailed and heavy-tailed valuations, the corresponding distributions are shifted slightly earlier and later, respectively, within the sales horizon.  In addition, we show that sales times admit a natural interpretation on a logarithmic time scale, derive comparative statics, and demonstrate that, in general, static pricing cannot be said to be uniformly faster or slower than dynamic pricing.  Our results address the question of what constitutes the "right time" to sell a product and provide practitioners with insights into expected sales patterns, which may contribute to greater compliance and trust in pricing software.

Title: A Theoretical Framework for Auxiliary-Loss-Free Load Balancing of Sparse Mixture-of-Experts in Large-Scale AI Models

Abstract: In large-scale AI training, Sparse Mixture-of-Experts (s-MoE) layers enable scaling by activating only a small subset of experts per token. An operational challenge in this design is load balancing: routing tokens to minimize the number of idle experts, which is important for the efficient utilization of costly GPUs and for the thorough training of architecture parameters across all experts. We provide a theoretical framework for analyzing the Auxiliary-Loss-Free Load Balancing (ALF-LB) procedure by casting it as a primal-dual method using a single-shot, constant-time update per training iteration for solving an assignment problem. First, in a stylized deterministic setting, our framework yields several insightful structural properties: (i) a monotonic improvement condition for the Lagrangian objective, (ii) a preference rule that moves tokens from overloaded to underloaded experts, and (iii) an approximate-balancing guarantee. Then, we incorporate the stochastic and dynamic nature of AI training using a generalized online optimization formulation. In the online setting, we derive a strong convexity property of the objective that leads to a logarithmic expected regret bound under certain step-size choices. Additionally, we present real experiments on 1B-parameter DeepSeekMoE models to complement our theoretical findings. Together, these results build a principled framework for analyzing the Auxiliary-Loss-Free Load Balancing of s-MoE in AI models.