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Epsilon-Minimax Solutions of Statistical Decision Problems

Author

Listed:
  • Andr'es Aradillas Fern'andez
  • Jos'e Blanchet
  • Jos'e Luis Montiel Olea
  • Chen Qiu
  • Jorg Stoye
  • Lezhi Tan

Abstract

A decision rule is epsilon-minimax if it is minimax up to an additive factor epsilon. We present an algorithm for provably obtaining epsilon-minimax solutions for a class of statistical decision problems. In particular, we are interested in problems where the statistician chooses randomly among I decision rules. The minimax solution of these problems admits a convex programming representation over the (I-1)-simplex. Our suggested algorithm is a well-known mirror subgradient descent routine, designed to approximately solve the convex optimization problem that defines the minimax decision rule. This iterative routine is known in the computer science literature as the hedge algorithm and is used in algorithmic game theory as a practical tool to find approximate solutions of two-person zero-sum games. We apply the suggested algorithm to different minimax problems in the econometrics literature. An empirical application to the problem of optimally selecting sites to maximize the external validity of an experimental policy evaluation illustrates the usefulness of the suggested procedure.

Suggested Citation

  • Andr'es Aradillas Fern'andez & Jos'e Blanchet & Jos'e Luis Montiel Olea & Chen Qiu & Jorg Stoye & Lezhi Tan, 2025. "Epsilon-Minimax Solutions of Statistical Decision Problems," Papers 2509.08107, arXiv.org, revised Jan 2026.
    • Handle: RePEc:arx:papers:2509.08107
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    References listed on IDEAS

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    1. Tetsuya Kaji & Elena Manresa & Guillaume Pouliot, 2023. "An Adversarial Approach to Structural Estimation," Econometrica, Econometric Society, vol. 91(6), pages 2041-2063, November.
    2. Anne G. Balter & Johannes M. Schumacher & Nikolaus Schweizer, 2024. "Solving Maxmin Optimization Problems via Population Games," Journal of Optimization Theory and Applications, Springer, vol. 201(2), pages 760-789, May.
    3. Jean N. Lee & Jonathan Morduch & Saravana Ravindran & Abu Shonchoy & Hassan Zaman, 2021. "Poverty and Migration in the Digital Age: Experimental Evidence on Mobile Banking in Bangladesh," American Economic Journal: Applied Economics, American Economic Association, vol. 13(1), pages 38-71, January.
    4. Timothy B. Armstrong & Patrick Kline & Liyang Sun, 2025. "Adapting to Misspecification," Econometrica, Econometric Society, vol. 93(6), pages 1981-2005, November.
    5. Freund, Yoav & Schapire, Robert E., 1999. "Adaptive Game Playing Using Multiplicative Weights," Games and Economic Behavior, Elsevier, vol. 29(1-2), pages 79-103, October.
    6. Stoye, Jörg, 2012. "Minimax regret treatment choice with covariates or with limited validity of experiments," Journal of Econometrics, Elsevier, vol. 166(1), pages 138-156.
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