Approximate Function Evaluation via Multi-Armed Bandits

Tavor Z. Baharav, Gary Cheng, Mert Pilanci, David Tse
Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, PMLR 151:108-135, 2022.

Abstract

We study the problem of estimating the value of a known smooth function f at an unknown point $\mu \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of $\mu$ corresponding to directions of the function with larger directional derivatives is more sample-efficient. However, as $\mu$ is unknown, the optimal sampling frequencies are also unknown. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-\delta$ returns an $\epsilon$ accurate estimate of $f(\mu)$. We generalize our algorithm to adapt to heteroskedastic noise, and prove asymptotic optimality when f is linear. We corroborate our theoretical results with numerical experiments, showing the dramatic gains afforded by adaptivity.

Cite this Paper

BibTeX
@InProceedings{pmlr-v151-baharav22a, title = { Approximate Function Evaluation via Multi-Armed Bandits }, author = {Baharav, Tavor Z. and Cheng, Gary and Pilanci, Mert and Tse, David}, booktitle = {Proceedings of The 25th International Conference on Artificial Intelligence and Statistics}, pages = {108--135}, year = {2022}, editor = {Camps-Valls, Gustau and Ruiz, Francisco J. R. and Valera, Isabel}, volume = {151}, series = {Proceedings of Machine Learning Research}, month = {28--30 Mar}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v151/baharav22a/baharav22a.pdf}, url = {https://proceedings.mlr.press/v151/baharav22a.html}, abstract = { We study the problem of estimating the value of a known smooth function f at an unknown point $\mu \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of $\mu$ corresponding to directions of the function with larger directional derivatives is more sample-efficient. However, as $\mu$ is unknown, the optimal sampling frequencies are also unknown. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-\delta$ returns an $\epsilon$ accurate estimate of $f(\mu)$. We generalize our algorithm to adapt to heteroskedastic noise, and prove asymptotic optimality when f is linear. We corroborate our theoretical results with numerical experiments, showing the dramatic gains afforded by adaptivity. } }
Endnote
%0 Conference Paper %T Approximate Function Evaluation via Multi-Armed Bandits %A Tavor Z. Baharav %A Gary Cheng %A Mert Pilanci %A David Tse %B Proceedings of The 25th International Conference on Artificial Intelligence and Statistics %C Proceedings of Machine Learning Research %D 2022 %E Gustau Camps-Valls %E Francisco J. R. Ruiz %E Isabel Valera %F pmlr-v151-baharav22a %I PMLR %P 108--135 %U https://proceedings.mlr.press/v151/baharav22a.html %V 151 %X We study the problem of estimating the value of a known smooth function f at an unknown point $\mu \in \mathbb{R}^n$, where each component $\mu_i$ can be sampled via a noisy oracle. Sampling more frequently components of $\mu$ corresponding to directions of the function with larger directional derivatives is more sample-efficient. However, as $\mu$ is unknown, the optimal sampling frequencies are also unknown. We design an instance-adaptive algorithm that learns to sample according to the importance of each coordinate, and with probability at least $1-\delta$ returns an $\epsilon$ accurate estimate of $f(\mu)$. We generalize our algorithm to adapt to heteroskedastic noise, and prove asymptotic optimality when f is linear. We corroborate our theoretical results with numerical experiments, showing the dramatic gains afforded by adaptivity.
APA
Baharav, T.Z., Cheng, G., Pilanci, M. & Tse, D.. (2022). Approximate Function Evaluation via Multi-Armed Bandits . Proceedings of The 25th International Conference on Artificial Intelligence and Statistics, in Proceedings of Machine Learning Research 151:108-135 Available from https://proceedings.mlr.press/v151/baharav22a.html.

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