Generalization Analysis for Controllable Learning

Yi-Fan Zhang, Xiao Zhang, Min-Ling Zhang
Proceedings of the 42nd International Conference on Machine Learning, PMLR 267:77017-77043, 2025.

Abstract

Controllability has become a critical issue in trustworthy machine learning, as a controllable learner allows for dynamic model adaptation to task requirements during testing. However, existing research lacks a comprehensive understanding of how to effectively measure and analyze the generalization performance of controllable learning methods. In an attempt to move towards this goal from a generalization perspective, we first establish a unified framework for controllable learning. Then, we develop a novel vector-contraction inequality and derive a tight generalization bound for general controllable learning classes, which is independent of the number of task targets except for logarithmic factors and represents the current best-in-class theoretical result. Furthermore, we derive generalization bounds for two typical controllable learning methods: embedding-based and hypernetwork-based methods. We also upper bound the Rademacher complexities of commonly used control and prediction functions, which serve as modular theoretical components for deriving generalization bounds for specific controllable learning methods in practical applications such as recommender systems. Our theoretical results without strong assumptions provide general theoretical guarantees for controllable learning methods and offer new insights into understanding controllability in machine learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v267-zhang25dh, title = {Generalization Analysis for Controllable Learning}, author = {Zhang, Yi-Fan and Zhang, Xiao and Zhang, Min-Ling}, booktitle = {Proceedings of the 42nd International Conference on Machine Learning}, pages = {77017--77043}, year = {2025}, editor = {Singh, Aarti and Fazel, Maryam and Hsu, Daniel and Lacoste-Julien, Simon and Berkenkamp, Felix and Maharaj, Tegan and Wagstaff, Kiri and Zhu, Jerry}, volume = {267}, series = {Proceedings of Machine Learning Research}, month = {13--19 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v267/main/assets/zhang25dh/zhang25dh.pdf}, url = {https://proceedings.mlr.press/v267/zhang25dh.html}, abstract = {Controllability has become a critical issue in trustworthy machine learning, as a controllable learner allows for dynamic model adaptation to task requirements during testing. However, existing research lacks a comprehensive understanding of how to effectively measure and analyze the generalization performance of controllable learning methods. In an attempt to move towards this goal from a generalization perspective, we first establish a unified framework for controllable learning. Then, we develop a novel vector-contraction inequality and derive a tight generalization bound for general controllable learning classes, which is independent of the number of task targets except for logarithmic factors and represents the current best-in-class theoretical result. Furthermore, we derive generalization bounds for two typical controllable learning methods: embedding-based and hypernetwork-based methods. We also upper bound the Rademacher complexities of commonly used control and prediction functions, which serve as modular theoretical components for deriving generalization bounds for specific controllable learning methods in practical applications such as recommender systems. Our theoretical results without strong assumptions provide general theoretical guarantees for controllable learning methods and offer new insights into understanding controllability in machine learning.} }
Endnote
%0 Conference Paper %T Generalization Analysis for Controllable Learning %A Yi-Fan Zhang %A Xiao Zhang %A Min-Ling Zhang %B Proceedings of the 42nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2025 %E Aarti Singh %E Maryam Fazel %E Daniel Hsu %E Simon Lacoste-Julien %E Felix Berkenkamp %E Tegan Maharaj %E Kiri Wagstaff %E Jerry Zhu %F pmlr-v267-zhang25dh %I PMLR %P 77017--77043 %U https://proceedings.mlr.press/v267/zhang25dh.html %V 267 %X Controllability has become a critical issue in trustworthy machine learning, as a controllable learner allows for dynamic model adaptation to task requirements during testing. However, existing research lacks a comprehensive understanding of how to effectively measure and analyze the generalization performance of controllable learning methods. In an attempt to move towards this goal from a generalization perspective, we first establish a unified framework for controllable learning. Then, we develop a novel vector-contraction inequality and derive a tight generalization bound for general controllable learning classes, which is independent of the number of task targets except for logarithmic factors and represents the current best-in-class theoretical result. Furthermore, we derive generalization bounds for two typical controllable learning methods: embedding-based and hypernetwork-based methods. We also upper bound the Rademacher complexities of commonly used control and prediction functions, which serve as modular theoretical components for deriving generalization bounds for specific controllable learning methods in practical applications such as recommender systems. Our theoretical results without strong assumptions provide general theoretical guarantees for controllable learning methods and offer new insights into understanding controllability in machine learning.
APA
Zhang, Y., Zhang, X. & Zhang, M.. (2025). Generalization Analysis for Controllable Learning. Proceedings of the 42nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 267:77017-77043 Available from https://proceedings.mlr.press/v267/zhang25dh.html.

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