The paper "Length Optimization in Conformal Prediction" by Shayan Kiyani, George Pappas, and Hamed Hassani addresses the challenges of conditional validity and length efficiency in conformal prediction (CP). The authors propose a novel framework called Conformal Prediction with Length-Optimization (CPL), which constructs prediction sets that are both conditionally valid and have optimal length. The framework operates by optimizing a minimax problem where the minimization part ensures conditional validity and the maximization part optimizes the length of the prediction sets. In the infinite sample regime, strong duality results show that CPL achieves optimal length and conditional validity. For finite samples, the authors provide guarantees that ensure conditionally valid prediction sets. Extensive empirical evaluations on various datasets in classification, regression, and text-related settings demonstrate that CPL outperforms state-of-the-art methods in terms of prediction set size while maintaining conditional validity. The paper also discusses the role of covariates in length optimization and provides theoretical guarantees for the finite-sample regime.The paper "Length Optimization in Conformal Prediction" by Shayan Kiyani, George Pappas, and Hamed Hassani addresses the challenges of conditional validity and length efficiency in conformal prediction (CP). The authors propose a novel framework called Conformal Prediction with Length-Optimization (CPL), which constructs prediction sets that are both conditionally valid and have optimal length. The framework operates by optimizing a minimax problem where the minimization part ensures conditional validity and the maximization part optimizes the length of the prediction sets. In the infinite sample regime, strong duality results show that CPL achieves optimal length and conditional validity. For finite samples, the authors provide guarantees that ensure conditionally valid prediction sets. Extensive empirical evaluations on various datasets in classification, regression, and text-related settings demonstrate that CPL outperforms state-of-the-art methods in terms of prediction set size while maintaining conditional validity. The paper also discusses the role of covariates in length optimization and provides theoretical guarantees for the finite-sample regime.