We first prove the first inequality using Jensen's inequality, which states that for a real-valued, convex Next, we leverage the property of inequalities to prove the second inequality. However, this method has limited effectiveness in scenarios with severe domain shifts between the source and target domains. Directly taking source risk as target risk is unreliable due to domain distribution shifts between domains. This work was completed while Dapeng ( lhxxhb15@gmail.com) Subsequently, Reverse V alidation performs a reversed adaptation from the pseudo-labeled target to the source and utilizes the source risk in this reversed adaptation task for validation.

Existing approaches can be categorized into two types. The first type involves leveraging labeled source data for target-domain model selection [9,14-16]. The second type designs unsupervised metrics based on priors of the learned target-domain structure and utilizes the metrics for model selection[17,19,18,20].

Unsupervised Environment Design (UED) formalizes the problem of autocur-ricula through interactive training between a teacher agent and a student agent. The teacher generates new training environments with high learning potential, curating an adaptive curriculum that strengthens the student's ability to handle unseen scenarios. Existing UED methods mainly rely on regret, a metric that measures the difference between the agent's optimal and actual performance, to