Kernel conditional mean embeddings (CMEs) offer a powerful framework for representing conditional distribution, but they often face scalability and expressiveness challenges. In this work, we propose a new method that effectively combines the strengths of deep learning with CMEs in order to address these challenges. Specifically, our approach leverages the end-to-end neural network (NN) optimization framework using a kernel-based objective. This design circumvents the computationally expensive Gram matrix inversion required by current CME methods. To further enhance performance, we provide efficient strategies to optimize the remaining kernel hyperparameters. In conditional density estimation tasks, our NN-CME hybrid achieves competitive performance and often surpasses existing deep learning-based methods. Lastly, we showcase its remarkable versatility by seamlessly integrating it into reinforcement learning (RL) contexts. Building on Q-learning, our approach naturally leads to a new variant of distributional RL methods, which demonstrates consistent effectiveness across different environments.

本论文介绍了一种将深度学习与核条件均值嵌入相结合的新方法，解决了核条件均值嵌入在可扩展性和表达能力方面的挑战，并在条件密度估计和强化学习中达到了竞争性能。

神经核条件均值嵌入