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Article overview
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Continuous Prediction with Experts' Advice | | Victor Sanches Portella
; Christopher Liaw
; Nicholas J. A. Harvey
; | | Date: |
1 Jun 2022 | | Abstract: | Prediction with experts’ advice is one of the most fundamental problems in
online learning and captures many of its technical challenges. A recent line of
work has looked at online learning through the lens of differential equations
and continuous-time analysis. This viewpoint has yielded optimal results for
several problems in online learning.
In this paper, we employ continuous-time stochastic calculus in order to
study the discrete-time experts’ problem. We use these tools to design a
continuous-time, parameter-free algorithm with improved guarantees for the
quantile regret. We then develop an analogous discrete-time algorithm with a
very similar analysis and identical quantile regret bounds. Finally, we design
an anytime continuous-time algorithm with regret matching the optimal
fixed-time rate when the gains are independent Brownian Motions; in many
settings, this is the most difficult case. This gives some evidence that, even
with adversarial gains, the optimal anytime and fixed-time regrets may
coincide. | | Source: | arXiv, 2206.00236 | | Services: | Forum | Review | PDF | Favorites | |
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