Efficient Gradient Approximation Method for Constrained Bilevel Optimization

Abstract

Bilevel optimization has been developed for many machine learning tasks with large-scale and high-dimensional data. This paper considers a constrained bilevel optimization problem, where the lower-level optimization problem is convex with equality and inequality constraints and the upper-level optimization problem is non-convex. The overall objective function is non-convex and non-differentiable. To solve the problem, we develop a gradient-based approach, called gradient approximation method, which determines the descent direction by computing several representative gradients of the objective function inside a neighborhood of the current estimate. We show that the algorithm asymptotically converges to the set of Clarke stationary points, and demonstrate the efficacy of the algorithm by the experiments on hyperparameter optimization and meta-learning.

References in corpus (9)

• TADAM: Task dependent adaptive metric for improved few-shot learning
• Bilevel Programming for Hyperparameter Optimization and Meta-Learning
• On Nonconvex Optimization for Machine Learning: Gradients, Stochasticity, and Saddle Points
• Bilevel Optimization: Convergence Analysis and Enhanced Design
• Convergence of Meta-Learning with Task-Specific Adaptation over Partial Parameters
• On the Iteration Complexity of Hypergradient Computation
• Truncated Back-propagation for Bilevel Optimization
• CRPO: A New Approach for Safe Reinforcement Learning with Convergence Guarantee
• Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond