Yu-Shiou Willy Lin | Searcharxiv

arXiv2026

Benefits and Costs of Adaptive Sampling

Multi-armed bandits are widely used for sequential experimentation in clinical trials, recommendation systems, and online platforms. While regret minimization and valid inference from adaptively collected data have each been studied extensively, a basic question remains: when does adaptivity \emph{improve estimation precision} relative to uniform designs, and how should inference be balanced against the online cost of experimentation? We first study arm-level mean estimation under mean-squared-error (MSE) objectives. We characterize when an adaptive Neyman allocation, which allocates samples according to arm variance, yields strict MSE improvements over uniform sampling. When there is variance heterogeneity across arms, these improvements arise at modest sample sizes, clarifying that adaptivity can be preferable for inference not only asymptotically, but also in many practical finite-sample settings. We then study a joint inference-regret objective that accounts for the cost of assigning units to inferior arms during experimentation. We propose the Static-Allocation Rate Policy (SARP) and Neyman-Adaptive Rate Policy (NARP), which interpolates between inference- and regret-oriented policies by adjusting exploration to the local structure of the instance. We show that SARP and NARP converge to the complete-information benchmark at the optimal rate as the sampling budget grows. Our proposed policies are practically attractive as it linearly interpolates between any standard regret-minimizing algorithm and inference-targeting adaptive policies. Yet we show it still enjoys the oracle-based asymptotic optimal rate. Simulations support the theory by demonstrating improved precision over uniform allocation while controlling performance loss across a range of instances.

stat.ME↗

arXiv2026

Model-Free Assessment of Simulator Fidelity via Quantile Curves

As generative AI models are increasingly used to simulate real-world systems, quantifying the ``sim-to-real'' gap is critical. For each input setting of interest -- which we call a \emph{scenario}, such as a survey question or operating condition -- the real and simulated systems are associated with unobserved latent population parameters, and their discrepancy varies across scenarios. A fundamental challenge is that, for any given scenario, this discrepancy cannot be observed directly, since both systems are accessible only through finite samples, often of heterogeneous sizes across scenarios. Standard predictive inference methods are therefore ill-suited, as they quantify uncertainty in observable outputs rather than latent population parameters. To address this, we construct confidence sets for these latent parameters and use them to derive a robust proxy for the sim-to-real discrepancy. We then estimate the quantile function of this proxy to obtain a distribution-level risk profile of the simulator, which supports a broad range of statistical summaries, including statistical inference for the real output distribution in a new scenario, the calculation of risk measures like Conditional Value-at-Risk (CVaR), and principled comparisons across simulators. Our method is model-agnostic and handles general output spaces, such as categorical survey responses and continuous multi-dimensional data. We demonstrate the practical utility of this method by evaluating the alignment of four major LLMs with human populations on the WorldValueBench dataset.

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