# On the dynamics of boosting

Conference Paper

In order to understand AdaBoost's dynamics, especially its ability to maximize margins, we derive an associated simplified nonlinear iterated map and analyze its behavior in low-dimensional cases. We find stable cycles for these cases, which can explicitly be used to solve for Ada- Boost's output. By considering AdaBoost as a dynamical system, we are able to prove R̈atsch and Warmuth's conjecture that AdaBoost may fail to converge to a maximal-margin combined classifier when given a 'nonoptimal' weak learning algorithm. AdaBoost is known to be a coordinate descent method, but other known algorithms that explicitly aim to maximize the margin (such as AdaBoost and arc-gv) are not. We consider a differentiable function for which coordinate ascent will yield a maximum margin solution. We then make a simple approximation to derive a new boosting algorithm whose updates are slightly more aggressive than those of arcgv.

### Duke Authors

### Cited Authors

- Rudin, C; Daubechies, I; Schapire, RE

### Published Date

- January 1, 2004

### Published In

### International Standard Serial Number (ISSN)

- 1049-5258

### International Standard Book Number 10 (ISBN-10)

- 0262201526

### International Standard Book Number 13 (ISBN-13)

- 9780262201520

### Citation Source

- Scopus