Conformal prediction (CP) is a distribution-free framework for achieving probabilistic guarantees on black-box models. CP is generally applied to a model post-training. Recent research efforts, on the other hand, have focused on optimizing CP efficiency during training. We formalize this concept as the problem of conformal risk minimization (CRM). In this direction, conformal training (ConfTr) by Stutz et al.(2022) is a technique that seeks to minimize the expected prediction set size of a model by simulating CP in-between training updates. Despite its potential, we identify a strong source of sample inefficiency in ConfTr that leads to overly noisy estimated gradients, introducing training instability and limiting practical use. To address this challenge, we propose variance-reduced conformal training (VR-ConfTr), a CRM method that incorporates a variance reduction technique in the gradient estimation of the ConfTr objective function. Through extensive experiments on various benchmark datasets, we demonstrate that VR-ConfTr consistently achieves faster convergence and smaller prediction sets compared to baselines.

翻译：保形预测是一种无需分布假设的框架，可为黑盒模型提供概率性保证。保形预测通常应用于训练后的模型。然而，最近的研究工作集中于在训练过程中优化保形预测的效率。我们将这一概念形式化为保形风险最小化问题。在此方向上，Stutz等人（2022）提出的保形训练是一种通过在训练更新间模拟保形预测来最小化模型预期预测集大小的技术。尽管具有潜力，我们发现保形训练中存在严重的样本效率不足问题，导致梯度估计噪声过大，从而引发训练不稳定性并限制其实际应用。为应对这一挑战，我们提出方差缩减保形训练——一种在保形训练目标函数的梯度估计中融入方差缩减技术的保形风险最小化方法。通过在多个基准数据集上的广泛实验，我们证明方差缩减保形训练相较于基线方法能持续实现更快的收敛速度和更小的预测集。