Asynchronous Distributed Bilevel Optimization

TL;DR

This paper introduces ADBO, an asynchronous distributed algorithm for bilevel optimization that addresses communication and straggler issues, with proven convergence and empirical validation on public datasets.

Contribution

It proposes the first asynchronous distributed bilevel optimization algorithm with convergence guarantees and practical efficiency improvements.

Findings

Convergence to an $ ext{epsilon}$-stationary point is theoretically guaranteed.

Iteration complexity is bounded by $ ext{O}(1/ ext{epsilon}^2)$.

Empirical results demonstrate effectiveness and efficiency on public datasets.

Abstract

Bilevel optimization plays an essential role in many machine learning tasks, ranging from hyperparameter optimization to meta-learning. Existing studies on bilevel optimization, however, focus on either centralized or synchronous distributed setting. The centralized bilevel optimization approaches require collecting massive amount of data to a single server, which inevitably incur significant communication expenses and may give rise to data privacy risks. Synchronous distributed bilevel optimization algorithms, on the other hand, often face the straggler problem and will immediately stop working if a few workers fail to respond. As a remedy, we propose Asynchronous Distributed Bilevel Optimization (ADBO) algorithm. The proposed ADBO can tackle bilevel optimization problems with both nonconvex upper-level and lower-level objective functions, and its convergence is theoretically guaranteed. Furthermore, it is revealed through theoretic analysis that the iteration complexity of ADBO to obtain the $\epsilon$-stationary point is upper bounded by $\mathcal{O}(\frac{1}{{{\epsilon ^2}}})$. Thorough empirical studies on public datasets have been conducted to elucidate the effectiveness and efficiency of the proposed ADBO.