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A.2 MainProofsketch In this section we will give a theoretical guarantee for the performance of our algorithm. Essentially, it measures the largest total difference of value estimation among all the functions in f Ft for the fixed inputsxt,i wherei [M]. Lemma 2. If (βt 0 | t N) is a nondecreasing sequence and Ft:=n Themainstructure ofthisproof issimilar toproposition 3,section CinEluder dimension's paper, and we will only point out the subtle details that makes the difference. Apart from the notations section 3, we add more symbols for the regret analysis. Next, we will show thatf h is a feasible solution for the optimization ofFt.

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

This bound guides the design of an optimal exploration policy attaining minimal sample complexity. However, this lower bound involves solving a hard non-convex optimization problem.

Y et, to our knowledge, every metric for alignment is a posteriori, i.e., a system is deemed aligned as