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.

我们介绍了一种新的功能性观点，用于机器学习领域的双层优化问题，其中内部目标函数在函数空间上最小化。我们提出了可扩展和高效的算法来解决这个功能性双层优化问题，并且通过在仪器回归和强化学习任务上展示了我们方法的优点。

机器学习的功能双层优化

Functional Bilevel Optimization for Machine Learning

Deep reinforcement learning algorithms that estimate state and state-action
value functions have been shown to be effective in a variety of challenging
domains, including learning control strategies from raw image pixels. However,
algorithms that estimate state and state-action value functions typically
assume a fully observed state and must compensate for partial observations by
using finite length observation histories or recurrent networks. In this work,
we propose a new deep reinforcement learning algorithm based on counterfactual
regret minimization that iteratively updates an approximation to an
advantage-like function and is robust to partially observed state. We
demonstrate that this new algorithm can substantially outperform strong
baseline methods on several partially observed reinforcement learning tasks:
learning first-person 3D navigation in Doom and Minecraft, and acting in the
presence of partially observed objects in Doom and Pong.

本研究提出了一种新的基于反事实遗憾最小化的深度强化学习算法，能够有效处理部分观测状态，并在 Doom 和 Minecraft 中的学习第一人称的 3D 导航以及在 Doom 和 Pong 中进行部分观测对象的动作等强化学习任务中显著优于现有基线算法。