Statistical Inference for Misspecified Contextual Bandits

2025-09-07

AI Summary

Contextual bandits (e.g., LinUCB) often fail to converge—and thus invalidate statistical inference—under reward model misspecification, a pervasive issue in real-world adaptive experiments (e.g., approximating complex dynamical systems with linear models). To address this, we propose a novel adaptive algorithmic framework with provable convergence guarantees under general misspecification, overcoming the non-convergence limitation of existing methods. Building upon this, we construct an inverse probability weighting–based Z-estimator (IPW-Z) and develop its asymptotic theory alongside a robust variance estimator, enabling the first asymptotically normal inference under arbitrary model misspecification. Simulation studies demonstrate that our method yields robust, data-efficient confidence intervals in both online and offline settings, substantially outperforming prior approaches restricted to specific misspecification structures.

Technology Category

• Machine Learning: Online Learning & Bandits
• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• User Modeling, Personalization and Recommendation: User modeling for targeted and personalized online advertising
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Contextual bandit algorithms have transformed modern experimentation by enabling real-time adaptation for personalized treatment and efficient use of data. Yet these advantages create challenges for statistical inference due to adaptivity. A fundamental property that supports valid inference is policy convergence, meaning that action-selection probabilities converge in probability given the context. Convergence ensures replicability of adaptive experiments and stability of online algorithms. In this paper, we highlight a previously overlooked issue: widely used algorithms such as LinUCB may fail to converge when the reward model is misspecified, and such non-convergence creates fundamental obstacles for statistical inference. This issue is practically important, as misspecified models -- such as linear approximations of complex dynamic system -- are often employed in real-world adaptive experiments to balance bias and variance. Motivated by this insight, we propose and analyze a broad class of algorithms that are guaranteed to converge even under model misspecification. Building on this guarantee, we develop a general inference framework based on an inverse-probability-weighted Z-estimator (IPW-Z) and establish its asymptotic normality with a consistent variance estimator. Simulation studies confirm that the proposed method provides robust and data-efficient confidence intervals, and can outperform existing approaches that exist only in the special case of offline policy evaluation. Taken together, our results underscore the importance of designing adaptive algorithms with built-in convergence guarantees to enable stable experimentation and valid statistical inference in practice.

Problem

• Addressing non-convergence in contextual bandits under model misspecification
• Ensuring valid statistical inference despite adaptive data collection
• Providing robust confidence intervals for misspecified reward models

Innovation

• Convergent algorithms under model misspecification
• Inverse-probability-weighted Z-estimator framework
• Asymptotic normality with consistent variance estimation