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Towards Minimax Online Learning with Unknown Time Horizon
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BibTeX
@MISC{Luo_towardsminimax,
author = {Haipeng Luo and Robert E. Schapire},
title = {Towards Minimax Online Learning with Unknown Time Horizon},
year = {}
}
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Abstract
We consider online learning when the time hori-zon is unknown. We apply a minimax analysis, beginning with the fixed horizon case, and then moving on to two unknown-horizon settings, one that assumes the horizon is chosen randomly ac-cording to some distribution, and the other which allows the adversary full control over the hori-zon. For the random horizon setting with re-stricted losses, we derive a fully optimal mini-max algorithm. And for the adversarial horizon setting, we prove a nontrivial lower bound which shows that the adversary obtains strictly more power than when the horizon is fixed and known. Based on the minimax solution of the random horizon setting, we then propose a new adap-tive algorithm which “pretends ” that the hori-zon is drawn from a distribution from a special family, but no matter how the actual horizon is chosen, the worst-case regret is of the optimal rate. Furthermore, our algorithm can be com-bined and applied in many ways, for instance, to online convex optimization, follow the per-turbed leader, exponential weights algorithm and first order bounds. Experiments show that our algorithm outperforms many other existing algo-rithms in an online linear optimization setting. 1.
Keyphrases
towards minimax online learning unknown time horizon minimax analysis optimal mini-max algorithm random horizon fixed horizon case unknown-horizon setting special family worst-case regret actual horizon minimax solution adversary full control per-turbed leader random horizon setting time hori-zon algorithm outperforms many way optimal rate online learning convex optimization online linear optimization first order bound new adap-tive algorithm adversarial horizon setting exponential weight algorithm adversary obtains re-stricted loss
