We show that the A-optimal design optimization problem over m design points in $${\mathbb {R}}^n$$Rn is equivalent to minimizing a quadratic function plus a group lasso sparsity inducing term over $$n\times m$$n×m real matrices. This observation allows to describe several new algorithms for A-optimal design based on splitting and block coordinate decomposition. These techniques are well known and proved powerful to treat large scale problems in machine learning and signal processing communities. The proposed algorithms come with rigorous convergence guarantees and convergence rate estimate stemming from the optimization literature. Performances are illustrated on synthetic benchmarks and compared to existing methods for solving the optimal design problem.

中文翻译：

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贝叶斯 A 最优设计与群套索之间的意外联系

我们证明了 $${\mathbb {R}}^n$$Rn 中 m 个设计点上的 A 最优设计优化问题等效于最小化二次函数加上 $$n\times m 上的组套索稀疏诱导项$$n×m 个实矩阵。这种观察允许描述基于分裂和块坐标分解的 A 最优设计的几种新算法。这些技术是众所周知的，并且被证明可以有效地处理机器学习和信号处理社区中的大规模问题。所提出的算法具有严格的收敛保证和源自优化文献的收敛率估计。性能在综合基准上进行了说明，并与解决优化设计问题的现有方法进行了比较。