  Boosting is a popular ensemble algorithm that generates more powerful
learners by linearly combining base models from a simpler hypothesis class. In
this work, we investigate the problem of adapting batch gradient boosting for
minimizing convex loss functions to online setting where the loss at each
iteration is i.i.d sampled from an unknown distribution. To generalize from
batch to online, we first introduce the definition of online weak learning edge
with which for strongly convex and smooth loss functions, we present an
algorithm, Streaming Gradient Boosting (SGB) with exponential shrinkage
guarantees in the number of weak learners. We further present an adaptation of
SGB to optimize non-smooth loss functions, for which we derive a O(ln N/N)
convergence rate. We also show that our analysis can extend to adversarial
online learning setting under a stronger assumption that the online weak
learning edge will hold in adversarial setting. We finally demonstrate
experimental results showing that in practice our algorithms can achieve
competitive results as classic gradient boosting while using less computation.
