# Open DGML: Intrusion Detection Based on Open-Domain Generation Meta-Learning
## 3 System Design
### Meta-Learning Intrusion Detection  
In the dynamic field of cyber security, the introduction of meta-learning for intrusion detection represents a significant advancement, offering a robust solution to the pervasive challenge of domain shift. Open DGML leverages the innovative meta-learning domain generalization (MLDG) approach to fortify models against performance degradation when transitioning from training to novel, unseen domains. Meta-Learning Domain Generalization (MLDG)The MLDG algorithm pioneers the integration of meta-learning within domain generalization, addressing the pivotal issue of domain drift. By simulating the training/test domain shift through the synthesis of virtual test domains within each mini-batch, MLDG optimizes for performance across both training and test domains. This dual focus culminates in the development of a meta-learned model that exhibits enhanced generalization capabilities in the face of unknown domains. Assuming that \(S\) source domains and the target domain share the same task with the same label space and input features but with different statistical data, a single model parameterized by \(\theta\) is defined to solve the specified task. The algorithm flow includes meta-training and meta-testing phases. During meta-training, the model is updated across all (S\(-\)V) meta-training domains \(\overline{S}\), while in the meta-testing phase, the model undergoes virtual evaluation on \(V\) meta-training domains, simulating performance on a new domain with divergent statistical properties. For the meta-training phase, the model is updated on all \((\text{S}-\text{V})\) meta-training domains \(\overline{\mathcal{S}}\) with the loss function:  
\[\mathcal{F}(\cdot)=\frac{1}{S-V}\sum_{i=1}^{S-V}\frac{1}{N_{i}}\sum_{j=1}^{N_{i }}\ell_{\theta}\Big{(}\hat{y}_{j}^{(i)},y_{j}^{(i)}\Big{)}.\]  
where \(y_{j}^{(i)}\) denotes the \(j\)-th data point in the \(i\)-th domain. The model parameters are subsequently refined based on the gradient \(\
abla_{\theta}\) of this loss function. For the meta-testing phase, the model is evaluated on \(V\) meta-training domains with the loss function:  
\[\mathcal{G}(\cdot)=\frac{1}{V}\sum_{i=1}^{V}\frac{1}{N_{i}}\sum_{j=1}^{N_{i}} \ell_{\theta}\Big{(}\hat{y}_{j}^{(i)},y_{j}^{(i)}\Big{)}.\]  
which guides the optimization of the model for generalization across domains. The ultimate goal of the MLDG algorithm is encapsulated by the following objective:  
\[\underset{\theta}{\arg\min}\mathcal{F}(\theta)+\beta\mathcal{G}\big{(}\theta- \alpha\mathcal{F}^{\prime}(\theta)\big{)}.\]  
where \(\alpha\), \(\beta\) and \(\gamma\) are the learning rates for the respective updates. The MLDG framework has been deconstructed in various ways to accommodate different types of domain generalization problems, such as feature-wise evaluation network for heterogeneous domain generalization and regularization function in a meta-learning framework for non-uniform domain generalization settings [33; 34]. Overall, MLDG is a promising approach for domain generalization, as it can effectively improve cross-domain generalization performance by addressing the problem of domain shift [35]. Open-Domain Generalization Meta-Learning AlgorithmThe open-domain generalization meta-learning algorithm (Open DGML) is central to our intrusion detection system, designed to classify traffic into known categories within the source domains and segregate unknown categories for expert analysis. This algorithm introduces a meta-learning approach to address the domain drift phenomenon by establishing meta-learners in each source domain, capable of both domain-specific classification and generalization across all domains. The Open-DGML algorithm is shown in Algorithm 1. The algorithm begins with the random initialization of parameters \(\theta\) and iteratively performs meta-training and meta-testing phases. In the meta-training phase, small batches of data from the source domains are augmented using Mul-Mixup and utilized to train an ensemble of meta-learners.