In this paper, we introduce a new functional point of view on bilevel optimization problems for machine learning, where the inner objective is minimized over a function space. These types of problems are most often solved by using methods developed in the parametric setting, where the inner objective is strongly convex with respect to the parameters of the prediction function. The functional point of view does not rely on this assumption and notably allows using over-parameterized neural networks as the inner prediction function. We propose scalable and efficient algorithms for the functional bilevel optimization problem and illustrate the benefits of our approach on instrumental regression and reinforcement learning tasks.

翻译：本文针对机器学习中的双层优化问题提出了一种新的函数视角，其中内层目标在函数空间上进行最小化。这类问题通常采用参数化场景下开发的方法求解，即内层目标相对于预测函数参数具有强凸性。函数视角不依赖此假设，特别允许使用过参数化神经网络作为内层预测函数。我们提出了可扩展且高效的函数双层优化算法，并通过工具变量回归与强化学习任务展示了本方法的优势。