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In this talk, we will discuss some recent advances in the applications of Bi-Level Programming Problem (BLPP). First, we study a gradient-based bi-level optimization method for learning tasks. In particular, by formulating bi-level models from the optimistic viewpoint and aggregating hierarchical objective information, we establish Bi-level Descent Aggregation (BDA), a flexible and modularized algorithmic framework for BLPP. Extensive experiments justify our theoretical results and demonstrate the superiority of the proposed BDA for different tasks, including hyper-parameter optimization and meta learning. Second, we propose a sufficient condition in the form of a partial error bound condition which guarantees the partial calmness condition. Our main result states that the partial error bound condition for the combined programs based on B and FJ conditions are generic for an important setting with applications in economics and hence the partial calmness for the combined program is not a particularly stringent assumption. Moreover we derive optimality conditions for the combined program for the generic case without any extra constraint qualifications.

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