  Tuning of model-based boosting algorithms relies mainly on the number of
iterations, while the step-length is fixed at a predefined value. For complex
models with several predictors such as Generalized Additive Models for
Location, Scale and Shape (GAMLSS), imbalanced updates of predictors, where
some distribution parameters are updated more frequently than others, can be a
problem that prevents some submodels to be appropriately fitted within a
limited number of boosting iterations. We propose an approach using adaptive
step-length (ASL) determination within a non-cyclical boosting algorithm for
GAMLSS to prevent such imbalance. Moreover, for the important special case of
the Gaussian distribution, we discuss properties of the ASL and derive a
semi-analytical form of the ASL that avoids manual selection of the search
interval and numerical optimization to find the optimal step-length, and
consequently improves computational efficiency. We show competitive behavior of
the proposed approaches compared to penalized maximum likelihood and boosting
with a fixed step-length for GAMLSS models in two simulations and two
applications, in particular for cases of large variance and/or more variables
than observations. In addition, the idea of the ASL is also applicable to other
models with more than one predictor like zero-inflated count model, and brings
up insights into the choice of the reasonable defaults for the step-length in
simpler special case of (Gaussian) additive models.
