Learning to optimize:A tutorial for continuous and mixed-integer optimization

Learning to optimize(L2O)stands at the intersection of traditional optimization and machine learning,utilizing the capabilities of machine learning to enhance conventional optimization techniques.As real-world optimization problems frequently share common structures,L2O provides a tool to exploit these structures for better or faster solutions.This tutorial dives deep into L2O techniques,introducing how to accelerate optimization algorithms,promptly estimate the solutions,or even reshape the optimization problem itself,making it more adaptive to real-world applications.By considering the prerequisites for successful applications of L2O and the structure of the optimization problems at hand,this tutorial provides a comprehensive guide for practitioners and researchers alike.

Gradient-based algorithms for multi-objective bi-level optimization

Multi-objective bi-level optimization(MOBLO)addresses nested multi-objective optimization problems common in a range of applications.However,its multi-objective and hierarchical bi-level nature makes it notably complex.Gradient-based MOBLO algorithms have recently grown in popularity,as they effectively solve crucial machine learning problems like meta-learning,neural architecture search,and reinforcement learning.Unfortunately,these algorithms depend on solving a sequence of approximation subproblems with high accuracy,resulting in adverse time and memory complexity that lowers their numerical efficiency.To address this issue,we propose a gradient-based algorithm for MOBLO,called gMOBA,which has fewer hyperparameters to tune,making it both simple and efficient.Additionally,we demonstrate the theoretical validity by accomplishing the desirable Pareto stationarity.Numerical experiments confirm the practical efficiency of the proposed method and verify the theoretical results.To accelerate the convergence of gMOBA,we introduce a beneficial L2O(learning to optimize)neural network(called L2O-gMOBA)implemented as the initialization phase of our gMOBA algorithm.Comparative results of numerical experiments are presented to illustrate the performance of L2O-gMOBA.