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On the number of trials needed to distinguish similar alternatives

Author

Listed:
  • Flavio Chierichetti

    (a Dipartimento di Informatica, Sapienza University of Rome, Rome, Italy 00185; and;)

  • Ravi Kumar

    (b Google, Mountain View, CA 94043)

  • Andrew Tomkins

    (b Google, Mountain View, CA 94043)

Abstract

Consider the process of testing two vintages of wine, two TV manufacturing processes, or two recommendation algorithms to determine whether one is preferred. Under the standard model of discrete choice, we study a wide range of A/B testing approaches to determine how many samples are required to pick a winner. We observe that, as quality (and level of investment) increases, the distinctions between alternatives become increasingly fine grained. We analyze the setting where the degree of difference between alternatives shrinks toward zero, and compute closed-form expressions for the asymptotically exact sample complexity of each test type. From this characterization, we are able to make specific recommendations for testing methodology at all target levels of error.

Suggested Citation

  • Flavio Chierichetti & Ravi Kumar & Andrew Tomkins, 2022. "On the number of trials needed to distinguish similar alternatives," Proceedings of the National Academy of Sciences, Proceedings of the National Academy of Sciences, vol. 119(31), pages 2202116119-, August.
    • Handle: RePEc:nas:journl:v:119:y:2022:p:e2202116119
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