Blackwell Approachability and Low-Regret Learning are Equivalent
Machine Learning
2010-11-10 v1 Computer Science and Game Theory
Abstract
We consider the celebrated Blackwell Approachability Theorem for two-player games with vector payoffs. We show that Blackwell's result is equivalent, via efficient reductions, to the existence of "no-regret" algorithms for Online Linear Optimization. Indeed, we show that any algorithm for one such problem can be efficiently converted into an algorithm for the other. We provide a useful application of this reduction: the first efficient algorithm for calibrated forecasting.
Keywords
Cite
@article{arxiv.1011.1936,
title = {Blackwell Approachability and Low-Regret Learning are Equivalent},
author = {Jacob Abernethy and Peter L. Bartlett and Elad Hazan},
journal= {arXiv preprint arXiv:1011.1936},
year = {2010}
}