Decentralized Hyper-Gradient Computation over Time-Varying Directed Networks

• URL: http://arxiv.org/abs/2210.02129v3
• Date: Tue, 13 Jun 2023 05:04:17 GMT
• Title: Decentralized Hyper-Gradient Computation over Time-Varying Directed Networks
• Authors: Naoyuki Terashita, Satoshi Hara
• Abstract summary: This paper addresses the communication issues when estimating hyper-gradients in decentralized learning (FL) We introduce an alternative optimality condition for FL using an averaging operation on model parameters and gradients. We confirm the convergence of our estimator to the true hyper-gradient both theoretically and empirically.
• Score: 13.274835852615572
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper addresses the communication issues when estimating hyper-gradients in decentralized federated learning (FL). Hyper-gradients in decentralized FL quantifies how the performance of globally shared optimal model is influenced by the perturbations in clients' hyper-parameters. In prior work, clients trace this influence through the communication of Hessian matrices over a static undirected network, resulting in (i) excessive communication costs and (ii) inability to make use of more efficient and robust networks, namely, time-varying directed networks. To solve these issues, we introduce an alternative optimality condition for FL using an averaging operation on model parameters and gradients. We then employ Push-Sum as the averaging operation, which is a consensus optimization technique for time-varying directed networks. As a result, the hyper-gradient estimator derived from our optimality condition enjoys two desirable properties; (i) it only requires Push-Sum communication of vectors and (ii) it can operate over time-varying directed networks. We confirm the convergence of our estimator to the true hyper-gradient both theoretically and empirically, and we further demonstrate that it enables two novel applications: decentralized influence estimation and personalization over time-varying networks.

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