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New Method Boosts Best-Arm Identification with Cheap Proxy Scores

Tianyi Ma, Hanzhang Qin, Ruihao Zhu, Jierui Zuo· July 9, 2026 View original

Key takeaways

  • Leveraging cheap proxy scores can drastically reduce the cost of best-arm identification in decision-making.
  • The PROBE algorithm provides a statistically robust way to integrate proxies, even when their correlation with true rewards is unknown.
  • Sample complexity improvements are directly proportional to the strength of the reward-proxy correlation.
  • This method is applicable to various data-driven decision-making problems across industries.

Who benefits

E-commerceMarketingFinanceHealthcareProduct Development

Summary

This research introduces PROBE, a phase-elimination algorithm for fixed-confidence best-arm identification that leverages cheap, correlated proxy scores from ML/LLMs to reduce the need for costly reward observations. It effectively transforms the problem into a heteroscedastic identification task, improving sample efficiency by accounting for the proxy's correlation with the true reward.

Traditional best-arm identification, a core model for data-driven decision-making, often faces high costs for each reward observation. This new study addresses this by integrating readily available, inexpensive proxy scores, such as those generated by machine learning or large language models, into the identification process. The challenge lies in learning the unknown correlation between these cheap proxies and the actual costly rewards online, without compromising the correctness of the identification. The proposed algorithm, PROBE (PRoxy OLS for Best-arm Exploration), tackles this by using a control-variate adjustment. This technique converts the problem into a heteroscedastic identification scenario, where the sample complexity is significantly improved by a factor related to the residual variance (1 minus the squared correlation). Empirical tests on synthetic data and an auto-loan pricing simulation, utilizing both LLM and tabular proxies, confirm that PROBE delivers substantial sample savings. These savings directly correlate with the strength of the reward-proxy relationship, validating the theoretical predictions and demonstrating the method's practical efficiency.

Why it matters

Professionals in fields requiring efficient decision-making under uncertainty can significantly reduce data collection costs and accelerate experimentation by leveraging cheap proxy models. This method offers a statistically sound way to incorporate readily available, low-cost predictions into critical identification tasks.

How to implement this in your domain

  1. 1Identify decision-making scenarios where collecting true reward data is expensive but cheap proxy predictions (e.g., from LLMs or simpler ML models) are available.
  2. 2Integrate the PROBE algorithm into existing experimental design or A/B testing frameworks to guide resource allocation.
  3. 3Train proxy models to generate scores correlated with the desired outcomes, ensuring they are cost-effective to produce.
  4. 4Monitor the correlation between proxy scores and actual rewards online to continuously refine the identification process.
  5. 5Apply the method in areas like product feature testing, marketing campaign optimization, or financial model selection to reduce observation costs.

Original post by Tianyi Ma, Hanzhang Qin, Ruihao Zhu, Jierui Zuo

"arXiv:2607.06879v1 Announce Type: new Abstract: Best-arm identification is a canonical model for data-driven decision-making, but in many applications each reward observation is costly. Motivated by the growing availability of cheap predictions from machine learning and large lan…"

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Originally posted by Tianyi Ma, Hanzhang Qin, Ruihao Zhu, Jierui Zuo on X · view source

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