Decentralized Stochastic Bilevel Optimization with Improved per-Iteration Complexity
This work addresses a bottleneck in decentralized bilevel optimization for machine learning applications like meta-learning and hyperparameter optimization, offering an incremental improvement in efficiency.
The paper tackles the challenge of designing a decentralized stochastic bilevel optimization algorithm with sample complexity and convergence rate comparable to SGD, without requiring exact Hessian or Jacobian computations. The proposed algorithm achieves this by using only first-order stochastic oracles and Hessian-vector and Jacobian-vector products, matching the best known sample complexity while improving per-iteration complexity.
Bilevel optimization recently has received tremendous attention due to its great success in solving important machine learning problems like meta learning, reinforcement learning, and hyperparameter optimization. Extending single-agent training on bilevel problems to the decentralized setting is a natural generalization, and there has been a flurry of work studying decentralized bilevel optimization algorithms. However, it remains unknown how to design the distributed algorithm with sample complexity and convergence rate comparable to SGD for stochastic optimization, and at the same time without directly computing the exact Hessian or Jacobian matrices. In this paper we propose such an algorithm. More specifically, we propose a novel decentralized stochastic bilevel optimization (DSBO) algorithm that only requires first order stochastic oracle, Hessian-vector product and Jacobian-vector product oracle. The sample complexity of our algorithm matches the currently best known results for DSBO, and the advantage of our algorithm is that it does not require estimating the full Hessian and Jacobian matrices, thereby having improved per-iteration complexity.