reviews: 
Comments: This paper proposes a novel framework, termed Balanced Online Knowledge Distillation, for addressing the challenge of domain generalization. The paper initially underscores the critical role of domain-specific knowledge within the domain generalization task. Subsequently, it advocates for the integration of both domain-invariant and domain-specific knowledge through an online distillation strategy. Additionally, the paper endeavors to undertake a theoretical analysis to substantiate the efficacy of domain-specific knowledge in scenarios where the target domain exhibits resemblances to the source domain, while also elucidating the advantages of the online distillation strategy in enhancing generalization performance.
Strengths: 1.The paper proposes the Balanced Online Knowledge Distillation framework, which combines domain-invariant and domain-specific knowledge and employs the strategy of online knowledge distillation, which is a novel attempt. 
2.The paper attempts to provide a theoretical analysis of the effectiveness of domain-specific knowledge in cases where the target domain has similar properties to the source domain, and how online knowledge distillation strategies can reduce the domain generalization error boundaries.
3.The English writing and essay organizations are good.
Weaknesses: 1.I would like to get more explanatory notes about the domain loss . From my perspective, the idea involves leveraging the text embedding of domain i as the positive sample of the Specific Embedding of domain i, while employing the text embedding of the domain other than i as the negative sample of the Specific Embedding of domain i. Given this interpretation, it may be more coherent to redefine the loss function.
2.When computing the Kullback-Leibler (KL) divergence loss, it is imperative to establish a clear delineation regarding which distribution is employed to guide the other. In this context, Equation (4) suggests that  signifies the utilization of the domain expert adapter to guide the student model. However, in Equation (6), the intended implication is for the student model to guide the domain expert adapter, a distinction not currently reflected in the discourse. Furthermore, the corresponding definition of  in Equation (5) remains unspecified.
3.Within the part labeled "Effectiveness of Domain-Specific Knowledge for Domain Generalization" in the Theoretical Discussion section, the current exposition primarily underscores the significance of shared attributes between the source and target domains. This emphasis appears somewhat detached from the core concept of "domain-specific knowledge."
4.Equation (7) does not seem to lead to the derivation of equation (11) within the specified conditions delineated in equation (10).
5.Does the student model learning from both Invariant Embedding and Specific Embedding create a conflict of knowledge?
6.While the results are advanced on multiple datasets, the performance on the Terra Incognita and Digits datasets is too poor.
7.Domain expert adapters should be a key module, but the corresponding details are missing from both the figure and the text.
Recommendation: 5
Reviewer confidence: 4
Soundness/correctness: 3
Clarity: 3