Compressed Decentralized Learning of Conditional Mean Embedding Operators in Reproducing Kernel Hilbert Spaces
Abstract
Conditional mean embedding (CME) operators encode conditional probability densities within Reproducing Kernel Hilbert Space (RKHS). In this paper, we present a decentralized algorithm for a collection of agents to cooperatively approximate CME over a network. Communication constraints limit the agents from sending all data to their neighbors; we only allow sparse representations of covariance operators to be exchanged among agents, compositions of which defines CME. Using a coherence-based compression scheme, we present a consensus-type algorithm that preserves the average of the approximations of the covariance operators across the network. We theoretically prove that the iterative dynamics in RKHS is stable. We then empirically study our algorithm to estimate CMEs to learn spectra of Koopman operators for Markovian dynamical systems and to execute approximate value iteration for Markov decision processes (MDPs).
Cite
Text
Hou et al. "Compressed Decentralized Learning of Conditional Mean Embedding Operators in Reproducing Kernel Hilbert Spaces." AAAI Conference on Artificial Intelligence, 2023. doi:10.1609/AAAI.V37I7.25956Markdown
[Hou et al. "Compressed Decentralized Learning of Conditional Mean Embedding Operators in Reproducing Kernel Hilbert Spaces." AAAI Conference on Artificial Intelligence, 2023.](https://mlanthology.org/aaai/2023/hou2023aaai-compressed/) doi:10.1609/AAAI.V37I7.25956BibTeX
@inproceedings{hou2023aaai-compressed,
title = {{Compressed Decentralized Learning of Conditional Mean Embedding Operators in Reproducing Kernel Hilbert Spaces}},
author = {Hou, Boya and Sanjari, Sina and Dahlin, Nathan and Bose, Subhonmesh},
booktitle = {AAAI Conference on Artificial Intelligence},
year = {2023},
pages = {7902-7909},
doi = {10.1609/AAAI.V37I7.25956},
url = {https://mlanthology.org/aaai/2023/hou2023aaai-compressed/}
}