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.

基于对可信度预测 (CP) 的进展，我们提出了一种名为可信度预测编程 (CPP) 的方法，用于解决具有非线性约束函数和任意随机参数影响的机会约束优化问题 (CCO)。CPP 利用这些随机参数的样本和量化引理 (对于 CP 来说至关重要)，将 CCO 问题转化为确定性优化问题。我们还通过两个容易处理的重构 CPP：(1) 将量化引理写成一个线性规划问题及其 KKT 条件 (CPP-KKT)，(2) 使用混合整数规划 (CPP-MIP)。CPP 对 CCO 问题具有边际概率可行性保证，这与现有方法 (如样本近似和方案方法) 在概念上不同。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 的优势在于它可以轻松扩展以包含不同的 CP 变体。为了说明这一点，我们提出了鲁棒可信度预测编程，以处理 CCO 问题中不确定参数的分布变化。