Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach

Zeyuan Allen-Zhu; Yuanzhi Li; Aarti Singh; Yining Wang

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arXiv · 1711.05174

Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach

Zeyuan Allen-Zhu·Yuanzhi Li·Aarti Singh·Yining Wang

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Abstract

The experimental design problem concerns the selection of k points from a potentially large design pool of p-dimensional vectors, so as to maximize the statistical efficiency regressed on the selected k design points. Statistical efficiency is measured by optimality criteria, including A(verage), D(eterminant), T(race), E(igen), V(ariance) and G-optimality. Except for the T-optimality, exact optimization is NP-hard. We propose a polynomial-time regret minimization framework to achieve a $(1+\varepsilon)$ approximation with only $O(p/\varepsilon^2)$ design points, for all the optimality criteria above. In contrast, to the best of our knowledge, before our work, no polynomial-time algorithm achieves $(1+\varepsilon)$ approximations for D/E/G-optimality, and the best poly-time algorithm achieving $(1+\varepsilon)$-approximation for A/V-optimality requires $k = \Omega(p^2/\varepsilon)$ design points.

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BibTeX RIS

Zeyuan Allen-Zhu, Yuanzhi Li, Aarti Singh, Yining Wang. 2017-11-14. Near-Optimal Discrete Optimization for Experimental Design: A Regret Minimization Approach. https://arxiv.org/abs/1711.05174

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