## 1 Introduction  
Leaf area index (LAI), which characterizes the structure and functioning of vegetation, is usually defined as half of the total green leaf area per unit horizontal ground surface area [1; 2]. LAI is one of the most important vegetation biophysical parameters, and a key variable for climate modeling, evapotranspiration modeling and crop modeling, and it is recognized as an Essential Climate Variable (ECV) by the Global Climate Observing System [3; 4; 5; 6; 7; 8]. LAI has a wide range of applications regarding agricultural fields, and it has been demonstrated to be an essential indicator for crop growth monitoring and key variables for crop yield forecasting [9; 10; 11]. Therefore, it is of special relevance to retrieve LAI in a timely and accurate manner. Remote sensing techniques provide promising alternatives to obtaining crop biophysical parameters by high temporally and spatially continuous means over large areas. To date, there are mainly three categories of methods developed to retrieve LAI based on optical remote sensing data, which are statistical methods, physically based methods, and hybrid methods [12; 13; 14]. Statistical methods can be further divided into parametric and non-parametric regression methods. Parametric regression methods usually consist of an explicit relationship between biophysical parameters and vegetation indices, while non-parametric regression methods define regression models learnt from the training dataset [15]. Non-parametric algorithms can be split into linear and non-linear regression methods; the latter is also commonly referred to as machine learning regression algorithms (MLRAs). While physically-based methods are applications of physical laws establishing cause-effect relationships, a hybrid method combines elements of non-parametric statistics and physically-based methods [13], whereas these two methods are both sophisticated models that demand a large number of parameters, which are usually difficult to obtain in practice. Empirical parametric models typically make use of a limited number of spectral bands [13; 16]. However, nonparametric models can make full use of spectral information, and directly learn the input-output relationships from a given training dataset, which makes these models attractive alternatives for crop LAI retrieval. With the development of remote sensing, more and more optical remote sensing satellites have been launched (e.g., Landsat 8, Sentinel-2, and Chinese GF-1, GF-2 and newly launched GF-6), which ensures the availability of high spatial, high temporal resolution satellite remote sensing data, and correspondingly, high dimensional (spatial, temporal and spectral) of remote sensing data amounts to large data volume, which also poses great challenges for more efficient, robust and accurate algorithms in a wide variety of applications with remote sensing. Recently, machine learning (ML), a broad subfield of artificial intelligence, has attracted considerable attention in remote sensing applications for classification and regression problems, and encouraging results have been obtained [17; 18; 19; 20; 21; 22; 23]. With advances in computer technology and associated techniques, ML has drawn tremendous interest in a variety of fields to address complex problems. ML can be broadly defined as computational methods using experience to improve performance or to make accurate predictions [24]. ML has been extensively applied to biophysical parameter retrievals due to the ability to accurately approximate robust relationships between input-output data, which provides tremendous opportunities for remote sensing-based applications. Considering ML regression algorithms, a more efficient, robust, and accurate model for crop LAI retrieval should be established. Despite the considerable advances in ML for remote sensing applications, challenging problems remain in the selection of MLRAs for crop LAI retrieval among the variety of ML algorithms available, as well as the optimal number of training sample size and spectral bands to different MLRAs.