Boosting as Frank-Wolfe
This work addresses a computational bottleneck in boosting algorithms for machine learning practitioners, offering an incremental improvement by unifying existing methods into a more efficient framework.
The paper tackles the issue of boosting algorithms for soft margin optimization, where LPBoost is fast but has worst-case inefficiency, while ERLPBoost and C-ERLPBoost have better guarantees but high per-iteration cost. The result is a generic boosting scheme combining Frank-Wolfe with any secondary algorithm, achieving the same convergence guarantee as ERLPBoost and performing comparably to LPBoost in experiments.
Some boosting algorithms, such as LPBoost, ERLPBoost, and C-ERLPBoost, aim to solve the soft margin optimization problem with the $\ell_1$-norm regularization. LPBoost rapidly converges to an $ε$-approximate solution in practice, but it is known to take $Ω(m)$ iterations in the worst case, where $m$ is the sample size. On the other hand, ERLPBoost and C-ERLPBoost are guaranteed to converge to an $ε$-approximate solution in $O(\frac{1}{ε^2} \ln \frac{m}ν)$ iterations. However, the computation per iteration is very high compared to LPBoost. To address this issue, we propose a generic boosting scheme that combines the Frank-Wolfe algorithm and any secondary algorithm and switches one to the other iteratively. We show that the scheme retains the same convergence guarantee as ERLPBoost and C-ERLPBoost. One can incorporate any secondary algorithm to improve in practice. This scheme comes from a unified view of boosting algorithms for soft margin optimization. More specifically, we show that LPBoost, ERLPBoost, and C-ERLPBoost are instances of the Frank-Wolfe algorithm. In experiments on real datasets, one of the instances of our scheme exploits the better updates of the secondary algorithm and performs comparably with LPBoost.