Optimal Online Prediction in Adversarial Environments

45 Pages·2010·0.84 MB·English

Optimal Online Prediction in Adversarial
Environments
Peter Bartlett
EECS and Statistics
UC Berkeley
http://www.cs.berkeley.edu/∼bartlett
Online Prediction
(cid:73) Probabilistic Model
(cid:73) Batch: independentrandomdata.
(cid:73) Aimforsmallexpectedlosssubsequently.
(cid:73) Adversarial Model
(cid:73) Online: Sequenceofinteractionswithanadversary.
(cid:73) Aimforsmallcumulativelossthroughout.
Online Learning: Motivations
1. Adversarial model is appropriate for
(cid:73) Computer security.
(cid:73) Computational finance.

WebSpamChallenge(www.iw3c2.org)
ACM

Online Learning: Motivations
2. Understanding statistical prediction methods.
(cid:73) Many statistical methods, based on probabilistic
assumptions, can be effective in an adversarial setting.
(cid:73) Analyzing their performance in adversarial settings
provides perspective on their robustness.
(cid:73) We would like violations of the probabilistic assumptions to
have a limited impact.
Online Learning: Motivations
3. Online algorithms are also effective in probabilistic settings.
(cid:73) Easy to convert an online algorithm to a batch algorithm.
(cid:73) Easy to show that good online performance implies good
i.i.d. performance, for example.
Prediction in Probabilistic Settings
(cid:73) i.i.d. (X,Y),(X ,Y ),...,(X ,Y ) from X ×Y.
1 1 n n
(cid:73) Use data (X ,Y ),...,(X ,Y ) to choose f : X → A with
1 1 n n n
small risk,
R(f ) = E(cid:96)(Y,f (X)).
n n