For instance, researchers are examining the gene network derived from the gene expression data of patients to investigate a rare disease.

Identifying helpful clients, however, presents challenging and often introduces significant overhead.

However, if error is heavy-tailed, some policies obtain arbitrarily high reward despite achieving no more utility than the base model-a phenomenon we call catastrophic Goodhart. We adapt a discrete optimization method to measure the tails of reward models, finding that they are consistent with light-tailed error.

To fill this gap, we propose a general and rigorous method, namely boundary decomposition for nadir objective vector estimation (BDNE).

It is crucial to ensure reliable and robust performance in various applications. Current optimizers often struggle with zero-shot optimization and require intricate hyperparameter tuning to adapt to new tasks.

Bilevel optimization methods solve problems with hierarchical structures, optimizing two interdependent objectives: an inner-level objective and an outer-level one. Initially used in machine learning for model selection [Bennett et al., 2006] and sparse feature learning [Mairal et al., 2012], these methods gained popularity as efficient alternatives to grid search for hyper-parameter tuning [Feurer and Hutter,