Exponential Weights Algorithms for Selective Learning

06/29/2021
by   Mingda Qiao, et al.
0

We study the selective learning problem introduced by Qiao and Valiant (2019), in which the learner observes n labeled data points one at a time. At a time of its choosing, the learner selects a window length w and a model ℓ̂ from the model class ℒ, and then labels the next w data points using ℓ̂. The excess risk incurred by the learner is defined as the difference between the average loss of ℓ̂ over those w data points and the smallest possible average loss among all models in ℒ over those w data points. We give an improved algorithm, termed the hybrid exponential weights algorithm, that achieves an expected excess risk of O((loglog|ℒ| + loglog n)/log n). This result gives a doubly exponential improvement in the dependence on |ℒ| over the best known bound of O(√(|ℒ|/log n)). We complement the positive result with an almost matching lower bound, which suggests the worst-case optimality of the algorithm. We also study a more restrictive family of learning algorithms that are bounded-recall in the sense that when a prediction window of length w is chosen, the learner's decision only depends on the most recent w data points. We analyze an exponential weights variant of the ERM algorithm in Qiao and Valiant (2019). This new algorithm achieves an expected excess risk of O(√(log |ℒ|/log n)), which is shown to be nearly optimal among all bounded-recall learners. Our analysis builds on a generalized version of the selective mean prediction problem in Drucker (2013); Qiao and Valiant (2019), which may be of independent interest.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
02/12/2019

A Theory of Selective Prediction

We consider a model of selective prediction, where the prediction algori...
research
03/14/2016

Online Isotonic Regression

We consider the online version of the isotonic regression problem. Given...
research
06/30/2021

Nearly-Tight and Oblivious Algorithms for Explainable Clustering

We study the problem of explainable clustering in the setting first form...
research
04/13/2023

Active Cost-aware Labeling of Streaming Data

We study actively labeling streaming data, where an active learner is fa...
research
08/06/2023

Self-Directed Linear Classification

In online classification, a learner is presented with a sequence of exam...
research
02/08/2019

Bandit Principal Component Analysis

We consider a partial-feedback variant of the well-studied online PCA pr...
research
05/09/2012

Virtual Vector Machine for Bayesian Online Classification

In a typical online learning scenario, a learner is required to process ...

Please sign up or login with your details

Forgot password? Click here to reset