# Adaptive Sampling for Convex Regression

@article{Simchowitz2018AdaptiveSF, title={Adaptive Sampling for Convex Regression}, author={Max Simchowitz and Kevin G. Jamieson and Jordan W. Suchow and Thomas L. Griffiths}, journal={ArXiv}, year={2018}, volume={abs/1808.04523} }

In this paper, we introduce the first principled adaptive-sampling procedure for learning a convex function in the $L_\infty$ norm, a problem that arises often in the behavioral and social sciences. We present a function-specific measure of complexity and use it to prove that, for each convex function $f_{\star}$, our algorithm nearly attains the information-theoretically optimal, function-specific error rate. We also corroborate our theoretical contributions with numerical experiments, finding…

## 3 Citations

Efficient Minimax Optimal Estimators For Multivariate Convex Regression

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This work is the first to show the existence of efﬁcient minimax optimal estimators for non-Donsker classes that their corresponding Least Squares Estimators are provably minimax sub-optimal ; a result of independent interest.

Problem Dependent View on Structured Thresholding Bandit Problems

- Computer ScienceICML
- 2021

This work investigates the problem dependent regime in the stochastic Thresholding Bandit problem under several shape constraints and provides upper and lower bounds for the probability of error in both the concave and monotone settings, as well as associated algorithms.

The Influence of Shape Constraints on the Thresholding Bandit Problem

- Computer ScienceCOLT
- 2020

These rates demonstrate that the dependence on $K$ of the minimax regret varies significantly depending on the shape constraint, which highlights the fact that the shape constraints modify fundamentally the nature of the TBP.

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