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.

The current methods for estimating the nadir objective vector perform effectivelyonly onspecific MOPs.

The average prediction accuracy, measured by the MSE, can be found in Tab.

Deep state-space models (DSSMs) enable temporal predictions by learning the underlying dynamics ofobservedsequence data.

We exemplify our result in two tasks of interest in statistical learning: a) classification for a mixture with sparse means, wherewestudytheefficiencyof `1penaltywithrespectto `2;b)max-marginmulticlass classification, where we characterise the phase transition on the existence ofthemulti-class logistic maximum likelihood estimator forK >2.

Thisworkdiscusses howtoachieveworst-case Out-Of-Distribution(OOD) generalization for avariety of distributions based on arelatively small labeling cost.