Robust Decision Trees Against Adversarial Examples

We developed a novel algorithm to train robust decision tree based models (notably, Gradient Boosted Decision Tree). This repo contains our implementation under theXGBoost framework. We plan to merge robust training as a feature to XGBoost upstream in near future.

Please refer to our paper for more details on the proposed algorithm:

Hongge Chen, Huan Zhang, Duane Boning, and Cho-Jui Hsieh"Robust Decision Trees Against Adversarial Examples",ICML 2019[video of the talk][slides][poster]

We also provide our implementation of an attack proposed inKantchelian et al. ICML 2016to test the robustness of a GBDT model. This method uses Mixed Integer Linear Programming (MILP) to find theexact minimumadversarial example.

Sep 4, 2019: Checkout our new tree ensemble verification method in NeurIPS 2019! It is much faster and very tight compared to MILP.[GitHub][paper]

Installation

Clone this repo and compile it:

git clone --recursive https://github /chenhongge/RobustTrees.git
cd RobustTrees
./build.sh

For detailed compilation options please refer toXGBoost Documentation. For building Python package interface, seethese instructions.

Run

Since our code is based on XGBoost with the addition of robust training, the interface is exactly the same as XGBoost. We use the same configuration file format as in XGBoost. To run a configuration file to train your model, simply run

./xgboost <configuration file>

Indata/folder we provide some example configuration files to start with. See sectiondownload the datasetto download the required datasets. For example, to train a 200-tree MNIST model with depth 8 and epsilon 0.3, just run

./xgboost data/ori_mnist.conf

Configuration files with.unrobuse natural training and those without .unrobuse our proposed robust training. In natural training, the tree_methodparameter is set asexact.

Configuration Parameters

We added two additional parameters to XGBoost:

(1)tree_methodcontrols which training method to use. We add a new optionrobust_exactfor this parameter. Settingtree_method = robust_exactwill use our proposed robust training. For other training methods, please refer toXGBoost documentation.

(2)robust_epsis the L inifity perturbation norm (epsilon) used in training. Since the sameepsilonvalue will be applied for all features, it is recommended tonormalize your data(e.g., make sure all features are in range 0 - 1). Normalization will not change tree performance

Please refer toXGBoost Documentationfor all other parameters used in XGBoost.

Known Issues

XGBoost treats all missing feature values in LIBSVM input file as actually "missing" and deals with them specially to improve accuracy. But in our robust training setting, we assume no missing values, since a perturbation from "missing" to a certainepsilonvalue is not clearly defined. To workaround this issue, it is suggested to manually add 0 back for all missing values in LIBSVM input so that XGBoost treats them as 0 values rather than missing values. Otherwise, when evaluating robustness, if a model is trained on datasets with missing values and tested on a point with missing feature values, that missing feature should not be perturbed in an attack.

Note that in the original LIBSVM format,missing features values are defined as 0.Applying the workaround above will need to explicitly write 0 features in LIBSVM input. We will add an option to provide a cleaner fix to this issue in a future release.

Reproducing Results on Our Paper

Download the datasets

First download the datasets. We normalized all feature values to [0,1] already.

cddata
./download_data.sh

You may also run each line ofdownload_data.shto download each individual dataset. The datasets are in LIBSVM format.

Now just run each configuration file to train models, for example:

#train a robust MNIST model, epsilon is set to 0.3 in conf file
./xgboost data/ori_mnist.conf
#train a natural MNIST model
./xgboost data/ori_mnist.unrob.conf

Testing Robustness

Here we provide our implementation of an attack proposed inKantchelian et al. ICML 2016to test the robustness of a GBDT model. This method uses Mixed Integer Linear Programming (MILP) to find the exact minimumadversarial example. The formulation in the original paper can only handle binary classification models. We generalized this formulation to multi-class models by targeting all classes other than the predicted one.

This code uses Gurobi to solve the MILP problem and is tested in Python 3.6.8. We suggest to use Conda to manage your Python environments. The following packages need to be installed:

#just install the original XGBoost
conda install -c conda-forge xgboost
conda install -c gurobi gurobi
conda install -c anaconda scipy
conda install -c anaconda scikit-learn
conda install -c anaconda numpy

After training, you will get a.modelfile. We provide robust and natural 200-tree MNIST models inmnist_models/.To run the attack, simply do

Python xgbKantchelianAttack.py -d=<path to data> -m=<path to the model> -c=<number of classes>

Some datasets' LIBSVM may index the features starting from 0, such as HIGGS and cod-rna. If that is the case, add a parameter--feature_start=0.

You can also use-o=<which point to start>,-n=<how many point to be attacked>to choose the points you want to attack.

In Kantchelian et al.'s algorithm, a guard value is used, which can be specified with--guard_val=<guard value>.You may also round the threshold values in the model to certain number of digits by setting --round_digits=<number of digits>.

For example, to run attack on trained MNIST models in the previous step, download MNIST data and run:

#attack robust MNIST model
Python xgbKantchelianAttack.py -d=data/ori_mnist.test0 -m=mnist_models/robust_mnist_0200.model -c=10
#attack natural MNIST model
Python xgbKantchelianAttack.py -d=data/ori_mnist.test0 -m=mnist_models/natural_mnist_0200.model -c=10

The output of the script will give us average Linf distortion and running time over all examples.

Known Issues

This implemetation of Kantchelian's attack is based on the.jsonmodel file dumped by XGBoost. XGBoost can only offer precision up to 8 digits, but the minimum difference between two nodes' thresholds in the json file can be smaller than 1e-8 (due to floating-point error in dump). Here rounding may be an option, but it may be tricky to choose guard value after rounding. For example, if we round thresholds to 1e-6, then guard value should be at least less than 5e-7 to avoid mistake. If we do not round thresholds, XGBoost's predict()may give wrong results on some adversarial examples. Those adversarial examples are perturbed across the thresholds, but since the perturbation is so small, in XGBoost'spredict(),the perturbation fails to misclassify. Therefore, we add a manual predict function to give output based on the.jsontree file produced by XGBoost. This manual prediction should always work.