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arXiv · 2405.04636

Data-driven Error Estimation: Excess Risk Bounds without Class Complexity as Input

Sanath Kumar Krishnamurthy·Anna Lyubarskaja·Emma Brunskill·Susan Athey
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Abstract

Constructing confidence intervals that are simultaneously valid across a class of estimates is central to tasks such as multiple mean estimation, generalization guarantees, and adaptive experimental design. We frame this as an ``error estimation problem," where the goal is to determine a high-probability upper bound on the maximum error for a class of estimates. We propose an entirely data-driven approach that derives such bounds for both finite and infinite class settings, naturally adapting to a potentially unknown correlation structure of random errors. Notably, our method does not require class complexity as an input, overcoming a major limitation of existing approaches. We present our simple yet general solution and demonstrate applications to simultaneous confidence intervals, excess-risk control and optimizing exploration in contextual bandit algorithms.

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Sanath Kumar Krishnamurthy, Anna Lyubarskaja, Emma Brunskill, Susan Athey. 2024-05-07. Data-driven Error Estimation: Excess Risk Bounds without Class Complexity as Input. https://arxiv.org/abs/2405.04636

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