Fundamental Tradeoffs in Learning with Prior Information

Anirudha Majumdar
Proceedings of the 40th International Conference on Machine Learning, PMLR 202:23558-23573, 2023.

Abstract

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner’s prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano’s inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

Cite this Paper

BibTeX
@InProceedings{pmlr-v202-majumdar23a, title = {Fundamental Tradeoffs in Learning with Prior Information}, author = {Majumdar, Anirudha}, booktitle = {Proceedings of the 40th International Conference on Machine Learning}, pages = {23558--23573}, year = {2023}, editor = {Krause, Andreas and Brunskill, Emma and Cho, Kyunghyun and Engelhardt, Barbara and Sabato, Sivan and Scarlett, Jonathan}, volume = {202}, series = {Proceedings of Machine Learning Research}, month = {23--29 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v202/majumdar23a/majumdar23a.pdf}, url = {https://proceedings.mlr.press/v202/majumdar23a.html}, abstract = {We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner’s prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano’s inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.} }
Endnote
%0 Conference Paper %T Fundamental Tradeoffs in Learning with Prior Information %A Anirudha Majumdar %B Proceedings of the 40th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2023 %E Andreas Krause %E Emma Brunskill %E Kyunghyun Cho %E Barbara Engelhardt %E Sivan Sabato %E Jonathan Scarlett %F pmlr-v202-majumdar23a %I PMLR %P 23558--23573 %U https://proceedings.mlr.press/v202/majumdar23a.html %V 202 %X We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner’s prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano’s inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.
APA
Majumdar, A.. (2023). Fundamental Tradeoffs in Learning with Prior Information. Proceedings of the 40th International Conference on Machine Learning, in Proceedings of Machine Learning Research 202:23558-23573 Available from https://proceedings.mlr.press/v202/majumdar23a.html.

Related Material