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Unified Theory of Efficient Optimization and Estimation

Project description

Meta-algorithm for optimisation and estimation problems

Machine learning and other computing applications depend on optimisation and estimation problems. Consequently, researchers try to develop and understand the limitations of efficient algorithms for these problems considering the use of tailored algorithms is required to achieve the best guarantees for many of them. Previous research has demonstrated that for many optimisation problems, the conceptually simple sum-of-squares meta-algorithm can match and exceed existing efficient algorithms in terms of provable guarantees. The EU-funded UTOPEST project relies on the above-mentioned previous research aiming to increase understanding of the capabilities and limitations of the meta-algorithm. It will establish new algorithmic guarantees for basic optimisation and estimation problems, clarify the limitations of efficient algorithms for basic problems and transfer the theoretical results into practical algorithms.

Objective

The goal of this project is to make progress toward a unified theory of efficient
optimization and estimation. In many computing applications, especially machine learning,
optimization and estimation problems play an increasingly important role. For that reason, a large
research effort is devoted to developing and understanding the limitations of efficient algorithms
for these problems. For many of these problems, achieving the best known provable guarantees
required the use of algorithms that are tailored to problem specifics. In recent years, the PI’s
research with collaborators has shown that for many optimization problems, the conceptually
simple sum-of-squares meta-algorithm, despite not being tailored to problem specifics, can match
and often significantly outperform previous efficient algorithms in terms of provable guarantees.

This project aims to better understand the capabilities and limitations of this meta-algorithm,
especially for estimation problems, which have only recently begun to be studied in this light.
In this way, the project will establish new algorithmic guarantees for basic optimization and
estimation problems even in the face of non-convexity and adversarial outliers. In the same way,
the project will shed light on the limitations of efficient algorithms for basic average-case problems
like planted clique and stochastic block models.

The project also aims to transfer the obtained theoretical insights into practical algorithms
building on recent works by the PI and collaborators. Toward this goal the project will develop
new algorithms with close to linear running times that match the guarantees of the best known
polynomial-time algorithms. In order to assess their practicality, the project will perform systematic
empirical evaluations of these algorithms.

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Coordinator

EIDGENOESSISCHE TECHNISCHE HOCHSCHULE ZUERICH
Net EU contribution
€ 1 993 320,00
Address
Raemistrasse 101
8092 Zuerich
Switzerland

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Region
Schweiz/Suisse/Svizzera Zürich Zürich
Activity type
Higher or Secondary Education Establishments
Links
Other funding
€ 0,00

Beneficiaries (1)