Best Arm Identification with LLM Judges and Limited Human

We study fixed-confidence best-arm identification (BAI) where a cheap but potentially biased proxy (e.g., LLM judge) is available for every sample, while an expensive ground-truth label can only be acquired selectively when using a human for auditing. Unlike classical multi-fidelity BAI, the proxy is biased (arm- and context-dependent) and ground truth is selectively observed. Consequently, standard multi-fidelity methods can mis-select the best arm, and uniform auditing, though accurate, wastes scarce resources and is inefficient. We prove that without bias correction and propensity adjustment, mis-selection probability may not vanish (even with unlimited proxy data). We then develop an estimator for the mean of each arm that combines proxy scores with inverse-propensity-weighted residuals and form anytime-valid confidence sequences for that estimator. Based on the estimator and confidence sequence, we propose an algorithm that adaptively selects and audits arms. The algorithm concentrates audits on unreliable contexts and close arms and we prove that a plug-in Neyman rule achieves near-oracle audit efficiency. Numerical experiments confirm the theoretical guarantees and demonstrate the superior empirical performance of the proposed algorithm.

PPI-SVRG: Unifying Prediction-Powered Inference and Variance Reduction for Semi-Supervised Optimization

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.

Solver-in-the-Loop: MDP-Based Benchmarks for Self-Correction and Behavioral Rationality in Operations Research

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 translation -- given a problem description, generate solver code -- ignoring this diagnostic loop entirely. We introduce two benchmarks that place the \textbf{solver in the evaluation loop}. \textbf{\ORDebug{}} 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. \textbf{\ORBias{}} 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$\times$ faster). On \ORBias{}, curriculum training achieves the only negative ID$\rightarrow$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.

Assured Autonomy: How Operations Research Powers and Orchestrates Generative AI Systems

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 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.

From Confounding to Learning: Dynamic Service Fee Pricing on Third-Party Platforms

We study the pricing behavior of third-party platforms facing strategic agents. Assuming the platform is a revenue maximizer, it observes market features that generally affect demand. Since only the equilibrium price and quantity are observable, this presents a general demand learning problem under confounding. Mathematically, we develop an algorithm with optimal regret of $\Tilde{\cO}(\sqrt{T}\wedgeσ_S^{-2})$. Our results reveal that supply-side noise fundamentally affects the learnability of demand, leading to a phase transition in regret. Technically, we show that non-i.i.d. actions can serve as instrumental variables for learning demand. We also propose a novel homeomorphic construction that allows us to establish estimation bounds without assuming star-shapedness, providing the first efficiency guarantee for learning demand with deep neural networks. Finally, we demonstrate the practical applicability of our approach through simulations and real-world data from Zomato and Lyft.

Multi-agent Adaptive Mechanism Design

We study a sequential mechanism design problem in which a principal seeks to elicit truthful reports from multiple rational agents while starting with no prior knowledge of agents' beliefs. We introduce Distributionally Robust Adaptive Mechanism (DRAM), a general framework combining insights from both mechanism design and online learning to jointly address truthfulness and cost-optimality. Throughout the sequential game, the mechanism estimates agents' beliefs and iteratively updates a distributionally robust linear program with shrinking ambiguity sets to reduce payments while preserving truthfulness. Our mechanism guarantees truthful reporting with high probability while achieving $\tilde{O}(\sqrt{T})$ cumulative regret, and we establish a matching lower bound showing that no truthful adaptive mechanism can asymptotically do better. The framework generalizes to plug-in estimators, supporting structured priors and delayed feedback. To our knowledge, this is the first adaptive mechanism under general settings that maintains truthfulness and achieves optimal regret when incentive constraints are unknown and must be learned.

Beyond Majority Voting: LLM Aggregation by Leveraging Higher-Order Information

With the rapid progress of multi-agent large language model (LLM) reasoning, how to effectively aggregate answers from multiple LLMs has emerged as a fundamental challenge. Standard majority voting treats all answers equally, failing to consider latent heterogeneity and correlation across models. In this work, we design two new aggregation algorithms called Optimal Weight (OW) and Inverse Surprising Popularity (ISP), leveraging both first-order and second-order information. Our theoretical analysis shows these methods provably mitigate inherent limitations of majority voting under mild assumptions, leading to more reliable collective decisions. We empirically validate our algorithms on synthetic datasets, popular LLM fine-tuning benchmarks such as UltraFeedback and MMLU, and a real-world healthcare setting ARMMAN. Across all cases, our methods consistently outperform majority voting, offering both practical performance gains and conceptual insights for the design of robust multi-agent LLM pipelines.

Pre-Trained AI Model Assisted Online Decision-Making under Missing Covariates: A Theoretical Perspective

We study a sequential contextual decision-making problem in which certain covariates are missing but can be imputed using a pre-trained AI model. From a theoretical perspective, we analyze how the presence of such a model influences the regret of the decision-making process. We introduce a novel notion called "model elasticity", which quantifies the sensitivity of the reward function to the discrepancy between the true covariate and its imputed counterpart. This concept provides a unified way to characterize the regret incurred due to model imputation, regardless of the underlying missingness mechanism. More surprisingly, we show that under the missing at random (MAR) setting, it is possible to sequentially calibrate the pre-trained model using tools from orthogonal statistical learning and doubly robust regression. This calibration significantly improves the quality of the imputed covariates, leading to much better regret guarantees. Our analysis highlights the practical value of having an accurate pre-trained model in sequential decision-making tasks and suggests that model elasticity may serve as a fundamental metric for understanding and improving the integration of pre-trained models in a wide range of data-driven decision-making problems.

Constrained Online Decision-Making: A Unified Framework

Contextual online decision-making problems with constraints appear in various real-world applications, such as personalized recommendation with resource limits and dynamic pricing with fairness constraints. In this paper, we investigate a general formulation of sequential decision-making with stage-wise feasibility constraints, where at each round, the learner must select an action based on observed context while ensuring a problem-specific feasibility criterion. We propose a unified algorithmic framework that captures many existing constrained learning problems, including constrained bandits, stream active learning, online hypothesis testing, and model calibration. Central to our approach is the concept of upper counterfactual confidence bound, which enables the design of practically efficient online algorithms using any offline conditional density estimation oracle. Technically, to handle feasibility constraints, we introduce a generalized notion of the eluder dimension, extending it from the classical setting based on square loss to a broader class of metric-like probability divergences, which could capture the complexity of various density function classes and characterize the loss incurred due to feasibility constraint uncertainty. Our result offers a principled foundation for constrained sequential decision-making in both theory and practice.

Constrained Online Decision-Making with Density Estimation Oracles

Contextual online decision-making problems with constraints appear in a wide range of real-world applications, such as personalized recommendation with resource limits, adaptive experimental design, and decision-making under safety or fairness requirements. In this paper, we investigate a general formulation of sequential decision-making with stage-wise feasibility constraints, where at each round, the learner must select an action based on observed context while ensuring that a problem-specific feasibility criterion is satisfied. We propose a unified algorithmic framework that captures many existing constrained learning problems, including constrained bandits, active learning with label budgets, online hypothesis testing with Type I error control, and model calibration. Central to our approach is the concept of upper counterfactual confidence bounds, which enables the design of practically efficient online algorithms with strong theoretical guarantee using any offline conditional density estimation oracle. Technically, to handle feasibility constraints in complex environments, we introduce a generalized notion of the eluder dimension - extending it from the classical setting based on square loss to a broader class of metric-like probability divergences. This allows us to capture the complexity of various density function classes and characterize the utility regret incurred due to feasibility constraint uncertainty. Our result offers a principled foundation for constrained sequential decision-making in both theory and practice.