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, which admit natural functional bilevel structures.

翻译：本文提出了一种面向机器学习中双层优化问题的新函数视角，其中内层目标在函数空间中被最小化。这类问题通常采用参数化方法求解，此时内层目标需关于预测函数的参数呈强凸性。而函数型视角无需依赖该假设，尤其允许使用过参数化神经网络作为内层预测函数。我们针对函数型双层优化问题设计了可扩展的高效算法，并通过工具变量回归与强化学习任务验证了方法的优势——这些任务天然具有函数型双层结构。