Optimal Polynomial-Time Estimators: A Bayesian Notion of Approximation Algorithm
Abstract
We introduce a new concept of approximation applicable to decision problems and functions, inspired by Bayesian probability. From the perspective of a Bayesian reasoner with limited computational resources, the answer to a problem that cannot be solved exactly is uncertain and therefore should be described by a random variable. It thus should make sense to talk about the expected value of this random variable, an idea we formalize in the language of average-case complexity theory by introducing the concept of "optimal polynomial-time estimators." We prove some existence theorems and completeness results, and show that optimal polynomial-time estimators exhibit many parallels with "classical" probability theory.
- Publication:
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arXiv e-prints
- Pub Date:
- August 2016
- DOI:
- 10.48550/arXiv.1608.04112
- arXiv:
- arXiv:1608.04112
- Bibcode:
- 2016arXiv160804112K
- Keywords:
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- Computer Science - Computational Complexity
- E-Print:
- 86 pages