Motivated by the advances in conformal prediction (CP), we propose conformal predictive programming (CPP), an approach to solve chance constrained optimization (CCO) problems, i.e., optimization problems with nonlinear constraint functions affected by arbitrary random parameters. CPP utilizes samples from these random parameters along with the quantile lemma -- which is central to CP -- to transform the CCO problem into a deterministic optimization problem. We then present two tractable reformulations of CPP by: (1) writing the quantile as a linear program along with its KKT conditions (CPP-KKT), and (2) using mixed integer programming (CPP-MIP). CPP comes with marginal probabilistic feasibility guarantees for the CCO problem that are conceptually different from existing approaches, e.g., the sample approximation and the scenario approach. While we explore algorithmic similarities with the sample approximation approach, we emphasize that the strength of CPP is that it can easily be extended to incorporate different variants of CP. To illustrate this, we present robust conformal predictive programming to deal with distribution shifts in the uncertain parameters of the CCO problem.

翻译：受共形预测（CP）进展的启发，我们提出共形预测规划（CPP），这是一种解决机会约束优化（CCO）问题的方法，即处理受任意随机参数影响的非线性约束函数的优化问题。CPP利用这些随机参数的样本以及分位数引理（这是CP的核心），将CCO问题转化为确定性优化问题。随后，我们通过两种方式提出CPP的易处理重述：（1）将分位数表示为线性规划及其KKT条件（CPP-KKT），以及（2）使用混合整数规划（CPP-MIP）。CPP为CCO问题提供了边际概率可行性保证，这从概念上不同于现有方法，例如样本近似和场景方法。虽然我们探讨了与样本近似方法的算法相似性，但我们强调CPP的优势在于可以轻松扩展以融入CP的不同变体。为了说明这一点，我们提出了鲁棒共形预测规划，以处理CCO问题中不确定参数的分布偏移。