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Federated bilevel learning has received increasing attention in various emerging machine learning and communication applications. Recently, several Hessian-vector-based algorithms have been proposed to solve the federated bilevel optimization problem. However, several important properties in federated learning such as the partial client participation and the linear speedup for convergence (i.e., the convergence rate and complexity are improved linearly with respect to the number of sampled clients) in the presence of non-i.i.d.~datasets, still remain open. In this paper, we fill these gaps by proposing a new federated bilevel algorithm named FedMBO with a novel client sampling scheme in the federated hypergradient estimation. We show that FedMBO achieves a convergence rate of $$\mathcal{O}\big(\frac{1}{\sqrt{nK}}+\frac{1}{K}+\frac{\sqrt{n}}{K^{3/2}}\big)$$ on non-i.i.d.~datasets, where $$n$$ is the number of participating clients in each round, and $$K$$ is the total number of iteration. This is the first theoretical linear speedup result for non-i.i.d.~federated bilevel optimization. Extensive experiments validate our theoretical results and demonstrate the effectiveness of our proposed method.
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Communication-efficient federated hypergradient computation via aggregated iterative differentiation
Federated bilevel optimization has attracted increasing attention due to emerging machine learning and communication applications. The biggest challenge lies in computing the gradient of the upper-level objective function (ie, hypergradient) in the federated setting due to the nonlinear and distributed construction of a series of global Hessian matrices. In this paper, we propose a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation (AggITD). AggITD is simple to implement and significantly reduces the communication cost by conducting the federated hypergradient estimation and the lower-level optimization simultaneously. We show that the proposed AggITD-based algorithm achieves the same sample complexity as existing approximate implicit differentiation (AID)-based approaches with much fewer communication rounds in the presence of data heterogeneity. Our results also shed light on the great advantage of ITD over AID in the federated/distributed hypergradient estimation. This differs from the comparison in the non-distributed bilevel optimization, where ITD is less efficient than AID. Our extensive experiments demonstrate the great effectiveness and communication efficiency of the proposed method.
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- Award ID(s):
- 2326592
- PAR ID:
- 10505578
- Publisher / Repository:
- International Conference on Machine Learning
- Date Published:
- Format(s):
- Medium: X
- Location:
- International Conference on Machine Learning
- Sponsoring Org:
- National Science Foundation
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