A constrained risk inequality for general losses

John Duchi; Feng Ruan

A constrained risk inequality for general losses

Statistics and Data Science

Research output: Contribution to journal › Conference article › peer-review

Abstract

We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions P₀ and P₁, we find a lower bound for the risk of estimating a parameter θ(P₁) under P₁ given an upper bound on the risk of estimating the parameter θ(P₀) under P₀. The inequality is a useful tool, as its proof relies only on the Cauchy-Schwartz inequality, it applies to general losses, including optimality gaps in stochastic convex optimization, and it transparently gives risk lower bounds on super-efficient and adaptive estimators.

Original language	English (US)
Pages (from-to)	802-810
Number of pages	9
Journal	Proceedings of Machine Learning Research
Volume	130
State	Published - 2021
Event	24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021 - Virtual, Online, United States Duration: Apr 13 2021 → Apr 15 2021

ASJC Scopus subject areas

Artificial Intelligence
Software
Control and Systems Engineering
Statistics and Probability

Cite this

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title = "A constrained risk inequality for general losses",

abstract = "We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions P0 and P1, we find a lower bound for the risk of estimating a parameter θ(P1) under P1 given an upper bound on the risk of estimating the parameter θ(P0) under P0. The inequality is a useful tool, as its proof relies only on the Cauchy-Schwartz inequality, it applies to general losses, including optimality gaps in stochastic convex optimization, and it transparently gives risk lower bounds on super-efficient and adaptive estimators.",

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AB - We provide a general constrained risk inequality that applies to arbitrary non-decreasing losses, extending a result of Brown and Low [Ann. Stat. 1996]. Given two distributions P0 and P1, we find a lower bound for the risk of estimating a parameter θ(P1) under P1 given an upper bound on the risk of estimating the parameter θ(P0) under P0. The inequality is a useful tool, as its proof relies only on the Cauchy-Schwartz inequality, it applies to general losses, including optimality gaps in stochastic convex optimization, and it transparently gives risk lower bounds on super-efficient and adaptive estimators.

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JF - Proceedings of Machine Learning Research

T2 - 24th International Conference on Artificial Intelligence and Statistics, AISTATS 2021

Y2 - 13 April 2021 through 15 April 2021

ER -

A constrained risk inequality for general losses

Abstract

ASJC Scopus subject areas

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