We examine the connections between deterministic, complete, and general global optimisation of continuous functions and a general concept of regression from the perspective of constructive type theory via the concept of 'searchability'. We see how the property of convergence of global optimisation is a straightforward consequence of searchability. The abstract setting allows us to generalise searchability and continuity to higher-order functions, so that we can formulate novel convergence criteria for regression, derived from the convergence of global optimisation. All the theory and the motivating examples are fully formalised in the proof assistant Agda.

中文翻译：

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通过全局优化进行回归的建设性类型理论方法

我们通过“可搜索性”的概念，从构造类型理论的角度检查连续函数的确定性、完全性和一般全局优化与回归的一般概念之间的联系。我们看到全局优化收敛的属性如何是可搜索性的直接结果。抽象设置允许我们将可搜索性和连续性推广到高阶函数，以便我们可以制定新的回归收敛标准，从全局优化的收敛导出。所有理论和激励示例都在证明助手 Agda 中完全形式化。