Negotiation is a fundamental strategic interaction in management science, characterized by agents attempting to reach agreements while protecting private information, such as reservation costs and hidden valuations. A prevalent yet complex scenario involves a single seller negotiating concurrently with multiple buyers, each possessing heterogeneous, private budgets. In such settings, constrained by a limited number of communication turns, the seller must balance exploring the broader market to discover the highest valuation with concentrating sufficient turns on a single target buyer to secure the best possible outcome. Our analysis reveals a significant gap in standard Large Language Models (LLMs): while these models are linguistically proficient, they fail to act as effective economic decision-makers. Specifically, they exhibit a failure to explore the buyer pool, often fixating on the current highest bid rather than strategically investigating the market to discover latent high valuations. In this paper, we propose a specialized training recipe using Reinforcement Learning from Verifiable Rewards (RLVR). By anchoring the reward function to objective economic outcomes, the strategic balance between market discovery and surplus extraction emerges natively through the learning process. Our results demonstrate that the trained seller undergoes a multi-stage strategic evolution, learning to leverage price anchoring and strategic probing to identify more profitable counterparties. The agent extracts a substantially higher surplus than frontier models by both improving its persuasive bargaining skills and consistently closing deals with high-value buyers. Finally, we show that our seller strategies generalize robustly to unseen buyer negotiation styles and budget distributions.

This technical note studies the reliability limits of LLM-based multi-agent planning as a delegated decision problem. We model the LLM-based multi-agent architecture as a finite acyclic decision network in which multiple stages process shared model-context information, communicate through language interfaces with limited capacity, and may invoke human review. We show that, without new exogenous signals, any delegated network is decision-theoretically dominated by a centralized Bayes decision maker with access to the same information. In the common-evidence regime, this implies that optimizing over multi-agent directed acyclic graphs under a finite communication budget can be recast as choosing a budget-constrained stochastic experiment on the shared signal. We also characterize the loss induced by communication and information compression. Under proper scoring rules, the gap between the centralized Bayes value and the value after communication admits an expected posterior divergence representation, which reduces to conditional mutual information under logarithmic loss and to expected squared posterior error under the Brier score. These results characterize the fundamental reliability limits of delegated LLM planning. Experiments with LLMs on a controlled problem set further demonstrate these characterizations.

Operations Research practitioners routinely debug infeasible models through an iterative process: analyzing Irreducible Infeasible Subsystems (IIS), identifying constraint conflicts, and systematically repairing formulations until feasibility is achieved. Yet existing LLM benchmarks evaluate OR as one-shot translationgiven a problem description, generate solver code-ignoring this diagnostic loop entirely. We introduce two benchmarks that place the solver in the evaluation loop. OR-Debug-Bench evaluates iterative self-correction through 5,000+ problems spanning 9 error types; each repair action triggers solver re-execution and IIS recomputation, providing deterministic, verifiable feedback. OR-Bias-Bench evaluates behavioral rationality through 2,000 newsvendor instances (1,000 ID + 1,000 OOD), measuring systematic deviations from closed-form optimal policies. Across 26 models and 12,000+ samples, we find that domain-specific RLVR training enables an 8B model to surpass frontier APIs: 95.3% vs 86.2% recovery rate (+9.1%), 62.4% vs 47.8% diagnostic accuracy (+14.6%), and 2.25 vs 3.78 steps to resolution (1.7× faster). On OR-Bias-Bench, curriculum training achieves the only negative ID→OOD bias drift among models evaluated (-9.6%), reducing systematic bias by 48% (from 20.0% to 10.4%). These results demonstrate that process-level evaluation with verifiable oracles enables targeted training that outperforms scale.

Pairwise human-preference platforms such as Chatbot Arena have become central to large language model (LLM) evaluation, yet reliable task-specific ranking remains challenging. Global leaderboards mask task heterogeneity, while ranking each fine-grained task independently is unstable under sparse, imbalanced comparisons. We propose a low-rank framework for task-specific LLM ranking from sparse pairwise comparisons, modeling the task-by-model ability matrix Θ^⋆∈ℝ^d_t × d_m as low rank so that information is shared across related tasks while task-specific differences are preserved. We first develop a max-norm (ℓ_∞) accurate estimator for the latent scores, combining a convex initializer with alternating-minimization refinement, and prove task-wise top-K recovery guarantees under sparse sampling. Our main contribution is an uncertainty quantification framework for task-specific ranking. We construct cross-fitted one-step debiased estimators for fixed score contrasts – such as the task-specific ability gap between two models – yielding asymptotically valid confidence intervals that attain the semiparametric efficiency bound. We then extend the inference to the high-dimensional ranking regime, where per-task ranks and top-K membership are determined by many dependent score-gap hypotheses. Using Gaussian and multiplier-bootstrap calibration, we obtain simultaneous confidence sets for per-task ranks and valid top-K membership tests across many tasks and models. Experiments on synthetic data and Chatbot Arena show that low-rank sharing improves sample efficiency over independent task-wise Bradley-Terry estimation and produces tighter, better-calibrated ranking certificates, with the largest gains in the sparse regime typical of real LLM benchmarks.

Operations Research practitioners debug infeasible models through an iterative process: inspecting Irreducible Infeasible Subsystems ( IIS), identifying constraint conflicts, and repairing formulations until feasibility is restored. Existing LLM benchmarks mostly treat OR as one-shot translation from problem descriptions to solver code, omitting this diagnostic loop. We formalize infeasible-model repair as a solver-in-the-loop Markov Decision Process in which each action triggers solver re-execution and IIS recomputation, yielding deterministic, verifiable feedback. We introduce ORLoopBench, a benchmark suite with two components: OR-Debug-Bench releases 5,362 LP/MILP repair instances, while OR-Bias-Bench evaluates closed-form operational decision rationality across inventory settings. Solver-verified RLVR training enables an 8B model to surpass frontier APIs on LP repair (95.3

Generative artificial intelligence (GenAI) is shifting from conversational assistants toward agentic systems—autonomous decision-making systems that sense, decide, and act within operational workflows. This shift creates an autonomy paradox: as GenAI systems are granted greater operational autonomy, they should, by design, embody more formal structure, more explicit constraints, and stronger tail-risk discipline. We argue that stochastic generative models can be fragile in operational domains unless paired with mechanisms that provide verifiable feasibility, robustness to distribution shift, and stress testing under high-consequence scenarios. To address this challenge, we develop a conceptual framework for assured autonomy grounded in operations research (OR), built on two complementary approaches. First, flow-based generative models frame generation as deterministic transport characterized by an ordinary differential equation, enabling auditability, constraint-aware generation, and connections to optimal transport, robust optimization, and sequential decision control. Second, operational safety is formulated through an adversarial robustness lens: decision rules are evaluated against worst-case perturbations within uncertainty or ambiguity sets, making unmodeled risks part of the design. This framework clarifies how increasing autonomy shifts OR’s role from solver to guardrail to system architect, with responsibility for control logic, incentive protocols, monitoring regimes, and safety boundaries. These elements define a research agenda for assured autonomy in safety-critical, reliability-sensitive operational domains.

We study semi-supervised stochastic optimization when labeled data is scarce but predictions from pre-trained models are available. PPI and SVRG both reduce variance through control variates – PPI uses predictions, SVRG uses reference gradients. We show they are mathematically equivalent and develop PPI-SVRG, which combines both. Our convergence bound decomposes into the standard SVRG rate plus an error floor from prediction uncertainty. The rate depends only on loss geometry; predictions affect only the neighborhood size. When predictions are perfect, we recover SVRG exactly. When predictions degrade, convergence remains stable but reaches a larger neighborhood. Experiments confirm the theory: PPI-SVRG reduces MSE by 43–52% under label scarcity on mean estimation benchmarks and improves test accuracy by 2.7–2.9 percentage points on MNIST with only 10% labeled data.

In large language model (LLM) serving, each request accumulates persistent graphics processing unit (GPU) memory during service as its key-value cache grows with every generated token. Under high concurrency, aggregate memory usage therefore increases endogenously over time: the service process itself creates future capacity pressure. When memory capacity is exceeded, systems evict active requests, discarding cached state and restarting them later, which wastes computation and reduces throughput. We develop a discrete-time dynamical model of memory-constrained LLM inference that captures admission, memory growth, and eviction under continuous batching. In the saturated-input regime, the system admits both eviction-free fixed points and limit cycles with evictions. For homogeneous workloads, we show that the eviction-free equilibrium is unstable and that, except for a Lebesgue-measure-zero exact-capture set, the system converges to a unique worst-case limit cycle that is asymptotically stable outside this exceptional set, with throughput losses as large as 50%. For heterogeneous workloads, we prove a stability criterion in the two-class common-input setting and explain how the survival-polynomial mechanism generalizes to multiple classes and heterogeneous-input lengths. Under an input-dominated scaling regime, coprime decoding lengths stabilize the eviction-free equilibrium, while non-coprime lengths create synchronized modes that drive instability. These results characterize when workload heterogeneity desynchronizes completions and helps stabilize memory-constrained serving. More broadly, we identify service-induced congestion as a structural instability mechanism and derive scheduling design principles for sustaining high throughput.

Designing service systems requires selecting among alternative configurations – choosing the best chatbot variant, the optimal routing policy, or the most effective quality control procedure. In many service systems, the primary evidence of performance quality is textual – customer support transcripts, complaint narratives, compliance review reports – rather than the scalar measurements assumed by classical optimization methods. Large language models (LLMs) can read such textual evidence and produce standardized quality scores, but these automated judges exhibit systematic biases that vary across alternatives and evaluation instances. Human expert review remains accurate but costly. We study how to identify the best service configuration with high confidence while minimizing expensive human audits, given that automated evaluation is cheap but biased. We formalize this as a sequential decision problem where a biased proxy score is observed for every evaluation, and a verified outcome can be acquired selectively at additional cost. We prove that LLM-only selection fails under arm-dependent bias, and that naive selective-audit estimators can be asymptotically biased. We develop an estimator combining proxy scores with inverse-propensity-weighted residuals and construct anytime-valid confidence sequences. Our algorithm, PP-LUCB, jointly decides which alternatives to evaluate and whether to request human audits, concentrating reviews where the LLM judge is least reliable. We prove correctness and establish instance-dependent cost bounds showing near-optimal efficiency. On a customer support ticket classification task, our algorithm correctly identifies the best model in 40/40 trials while achieving 90% audit cost reduction.

With the rapid advancement of generative AI (GenAI), mechanism design adapted to its unique characteristics poses new theoretical and practical challenges. Unlike traditional goods, content from one domain can enhance the training and performance of GenAI models in other domains. For example, OpenAI's video generation model Sora (Liu et al., 2024b) relies heavily on image data to improve video generation quality. In this work, we study nonlinear procurement mechanism design under data transferability, where online platforms employ both human creators and GenAI to satisfy cross-domain content demand. We propose optimal mechanisms that maximize either platform revenue or social welfare and identify the specific properties of GenAI that make such high-dimensional design problems tractable. Our analysis further reveals which domains face stronger competitive pressure and which tend to experience overproduction. Moreover, the growing role of data intermediaries, including labeling companies such as Scale AI and creator organizations such as The Wall Street Journal, introduces a third layer into the traditional platform-creator structure. We show that this three-layer market can result in a lose-lose outcome, reducing both platform revenue and social welfare, as large pre-signed contracts distort creators' incentives and lead to inefficiencies in the data market. These findings suggest a need for government regulation of the GenAI data ecosystem, and our theoretical insights are further supported by numerical simulations.

Across business and social science applications, outcomes are often missing in ways that depend on the unobserved outcomes themselves. In service systems, for example, whether a customer submits a rating depends on the rating they would have provided. Such missing-not-at-random (MNAR) mechanisms make population quantities difficult to identify without strong assumptions on the observation process. Meanwhile, rich unstructured data, such as customer interaction histories, are increasingly available and can be used to construct structured measurements using tools such as large language models (LLMs). In this work, we develop an assumption-lean partial identification framework that uses such measurements as weak shadow variables, defined as outcome-informative proxies that are conditionally independent of missingness given the true outcome and observed covariates. Importantly, they need not accurately predict missing outcomes or satisfy the completeness requirement in the classical shadow variable literature. For identification, we characterize sharp bounds on population quantities through a pair of linear programs. For estimation and inference, we propose a localized penalized estimator that remains feasible under sampling error, and a subsampling algorithm for constructing confidence intervals. In semi-synthetic experiments using real customer-service dialogues, weak-shadow-variable intervals are about 89% narrower than those without auxiliary information, while their midpoints have around 41% lower estimation error than classical MNAR methods.

Reinforcement learning (RL) in large environments often suffers from severe computational bottlenecks, as conventional regret minimization algorithms require repeated, costly calls to planning and statistical estimation oracles. While recent advances have explored offline oracle-efficient algorithms, their computational complexity typically scales with the cardinality of the state and action spaces, rendering them intractable for large-scale or continuous environments. In this paper, we address this fundamental limitation by studying offline oracle-efficient episodic RL through the lens of log-barrier and log-determinant regularization. Specifically, for tabular Markov Decision Processes (MDPs), we propose a novel algorithm that achieves the optimal Õ(√(T)) regret bound while requiring only O(Hloglog T) calls to both the offline statistical estimation and planning oracles when T is known and O(Hlog T) calls when T is unknown. Crucially, this oracle complexity is entirely independent of the size of the state and action spaces. This strict independence drastically reduces the planning oracle complexity, representing a substantial improvement over existing offline oracle-efficient algorithms (Qian et al., 2024). Furthermore, we demonstrate the versatility of our framework by generalizing the algorithm to linear MDPs featuring infinite state spaces and arbitrary action spaces. We prove that this generalized approach successfully attains meaningful sub-linear regret. Consequently, our work yields the first doubly oracle-efficient (i.e., efficient with respect to both statistical estimation and policy optimization) regret minimization algorithm capable of solving MDPs with infinite state and action spaces, significantly expanding the boundaries of computationally tractable RL.

Classical chaining controls an indexed stochastic process through a single worst-case bound and can therefore obscure substantial variation across the index set. We develop the first simultaneous pointwise majorization theory for Banach-valued processes with finite-metric mixed-tail increments. Suppose that an anchored process (Z_t)_t∈ T satisfies, for some integer m≥1, pseudo-metrics d_1,…,d_m, and orders α_1,…,α_m>0, ℙ{Z_t-Z_s>∑_j=1^m u^1/α_jd_j(s,t)}≤ 2e^-u,s,t∈ T. For ambient priors μ_1,…,μ_m, let v_j(t):=d_j(t,t_0), Φ_j(t):=∫_0^4v_j(t)(log1/μ_j(B_d_j(t,r)))^1/α_jdr. We prove that, ∀ δ∈(0,1), with probability at least 1-δ, simultaneously for all t∈ T, Z_t≤ C_m,∑_j=1^m{Φ_j(t)+v_j(t)(log(e/δ))^1/α_j}. Here :=(α_1,…,α_m) and C_m, depend only on m and these tail orders. The result subsumes single-metric sub-Weibull processes of every positive order as the case m=1. In the Gaussian setting, it sharpens the pointwise upper bound of by eliminating the logarithmic terms generated by dyadic peeling. The proof retains the index-wise costs of measure-generated admissible chains and synchronizes the regimes through a nested common refinement. Finally, we apply our theorems to stationary diffusion empirical processes and decoupled Gaussian chaos to obtain simultaneous pointwise envelope bounds, which can further be applied to other statistics problems.

Firms that price perishable resources – airline seats, hotel rooms, seasonal inventory – now routinely use demand predictions, but these predictions vary widely in quality. Under hard capacity constraints, acting on an inaccurate prediction can irreversibly deplete inventory needed for future periods. We study how prediction uncertainty propagates into dynamic pricing decisions with linear demand, stochastic noise, and finite capacity. A certified demand forecast with known error bound ε^0 specifies where the system should operate: it shifts regret from O(√(T)) to O(log T) when ε^0 ≲ T^-1/4, and we prove this threshold is tight. A misspecified surrogate model – biased but correlated with true demand – cannot set prices directly but reduces learning variance by a factor of (1-ρ^2) through control variates. The two mechanisms compose: the forecast determines the regret regime; the surrogate tightens estimation within it. All algorithms rest on a boundary attraction mechanism that stabilizes pricing near degenerate capacity boundaries without requiring non-degeneracy assumptions. Experiments confirm the phase transition threshold, the variance reduction from surrogates, and robustness across problem instances.

Modern supply chain operations can require coordinating replenishment across thousands of heterogeneous items under correlated stochastic demand, heterogeneous lead times, and shared fixed ordering costs, yielding observation spaces exceeding 10^4 dimensions. At this scale, rolling-horizon stochastic mixed-integer linear programs (MILPs) become prohibitively slow, while standard reinforcement learning (RL) methods face increasingly challenging credit assignment in high-dimensional action spaces. We introduce OR-Transformer, a deep reinforcement learning framework for joint replenishment under stochastic demand, with an item-permutation-equivariant Transformer architecture and pathwise-gradient training through the inventory dynamics. Across problem sizes up to 1,024 inventory items, OR-Transformer increasingly outperforms learning-based and rolling-horizon MILP baselines as scale grows. It also reduces online decision-making time by over 4 million times relative to MILP solvers, enabling real-time, large-scale deep RL in supply chain operations.

Modern experiments, including evaluations of AI-enabled services and platform interventions, often depart from independent and identically distributed (i.i.d.) sampling because assignments may be adaptive, balanced across covariates, or subject to rollout constraints such as exposure, fairness, and budget limits. This paper studies the efficiency benchmark for estimating causal targets in such sequential experiments. We show that every non-anticipating design induces an average propensity score, and we establish a semiparametric lower bound: for regular locally unbiased estimators, attainable precision is bounded by the i.i.d. efficiency benchmark evaluated at this induced score. The average propensity score thereby serves as a common benchmark and design target, allowing sequential experimental design to be viewed as choosing or learning an efficient allocation rule, with operational constraints entering through the admissible set when present. We then develop implementable batched adaptive designs that approach this benchmark through two complementary mechanisms. The first uses regression adjustment based on efficient influence functions; for general smooth estimands it attains the benchmark under standard nuisance-rate conditions, while for linear functionals of outcome means it achieves a sharp second-order rate. The second uses adaptive covariate balancing to attain the same benchmark through the assignment mechanism, enabling simple moment-based estimation. Both routes require only a small number of policy updates, making them compatible with delayed feedback and easier to monitor in operational deployments. Numerical experiments and an empirical study of AI medical-assistant evaluation demonstrate the practical efficiency gains, including in multi-treatment settings. Overall, the paper provides a unified framework for characterizing and designing efficient sequential experiments.

We study whether stochastic nonconvex optimization can be reduced to ordinary static regret minimization in online convex optimization in a black-box manner. For smooth nonconvex objectives, our reduction maintains a predictable gradient tracker, while a black-box online learner selects a preconditioner that determines how this tracker is transformed into the update direction. The learner receives linear convex losses and is evaluated against a single fixed comparator over one undiscounted online game. For a β-smooth objective with range bounded by M and an unbiased stochastic-gradient oracle with variance bounded by σ^2, we establish 1/T∑_t=1^T 𝔼[∇ f(x_t)_2^2] ≲σ√(Mβ)/√(T) + √(Mβ) ℛ_T(𝒜,I_d)/T + Mβ/T. Consequently, any black-box OCO algorithm with ℛ_T(𝒜,I_d)=O(√(T)) recovers the classical O(1/√(T)) convergence rate. We further show that the same black-box framework extends beyond the smooth setting to Lipschitz nonconvex objectives without Lipschitz continuous gradients. Importantly, this extension continues to rely only on an ordinary static-regret guarantee and requires no stronger notion of online regret. When the OCO oracle admits square-root static regret, the resulting conversion achieves the optimal O(T^-2/7) convergence rate for the corresponding Goldstein stationary point. These results resolve the open problem posed by Chen and Hazan (2024). More broadly, our framework separates optimizer design into gradient prediction and online preconditioner selection, providing a principled perspective on how adaptive optimization methods such as AdaGrad and Shampoo may be understood through static regret and applied in nonconvex optimization.

In user-agent interaction scenarios such as recommendation, brainstorming, and code suggestion, Large Language Models (LLMs) often generate sets of candidate recommendations where the objective is to maximize the collective utility of the entire set rather than individual candidates independently. However, existing reinforcement learning post-training paradigms, such as Group Relative Policy Optimization (GRPO), typically assign the same set-level scalar reward to every candidate in the set. This leads to noisy training signals where poor candidates free-ride on the high reward produced by a single strong peer, resulting in suboptimal exploration. To address this, we propose Shapley-Enhanced GRPO (ShapE-GRPO). By leveraging the permutation-invariant nature of set-level utility, we derive a Shapley-enhanced formulation from cooperative game theory to decompose set-level rewards into granular, candidate-specific signals. We show that our formulation preserves the fundamental axioms of the Shapley value while remaining computationally efficient with polynomial-time complexity. Empirically, ShapE-GRPO consistently outperforms standard GRPO across diverse datasets with accelerated convergence during training.

We study resource-constrained dynamic pricing when the seller seeks revenue and valid inference about demand at a price fixed before the selling season. Depletion can remove every feasible price near the target, so randomization over the remaining prices need not preserve identification. We propose an inference-aware re-solving policy that checks target support before observing the current covariates and implements the fluid target load with a logged pricing mixture. In an affine binding-capacity family, target mass t^-γ yields information T^1-γ, interval radius T^-(1-γ)/2, and regret O(log T+T^1-γ) against the initial fluid optimum. In the same affine family, learned barycentric re-solving retains a target-local component of constant mass and, with polynomial error spending of exponent greater than one, achieves a linear information clock and O(log T) regret; slack-capacity local pricing gives the same orders. An exact-input smooth-frontier extension gives root-T inference and O(log^2T) regret. Physical exclusion rules out uniformly shrinking intervals, while target mass of order 1/t alone yields bounded information. The policy reports an interval only after its prespecified support and information checks pass.

Problem Definition. Supply chain optimization models frequently become infeasible because of modeling errors. Diagnosis and repair require scarce OR expertise: analysts must interpret solver diagnostics, trace root causes across echelons, and fix formulations without sacrificing operational soundness. Whether AI agents can perform this task remains untested. Methodology/Results. OptiRepair splits this task into a domain-agnostic feasibility phase (iterative IIS-guided repair of any LP) and a domain-specific validation phase (five rationality checks grounded in inventory theory). We test 22 API models from 7 families on 976 multi-echelon supply chain problems and train two 8B-parameter models using self-taught reasoning with solver-verified rewards. The trained models reach 81.7% Rational Recovery Rate (RRR) -- the fraction of problems resolved to both feasibility and operational rationality -- versus 42.2% for the best API model and 21.3% on average. The gap concentrates in Phase 1 repair: API models average 27.6% recovery rate versus 97.2% for trained models. Managerial Implications. Two gaps separate current AI from reliable model repair: solver interaction (API models restore only 27.6% of infeasible formulations) and operational rationale (roughly one in four feasible repairs violate supply chain theory). Each requires a different intervention: solver interaction responds to targeted training; operational rationale requires explicit specification as solver-verifiable checks. For organizations adopting AI in operational planning, formalizing what "rational" means in their context is the higher-return investment.