Decentralized Bilevel Optimization

Chen, Xuxing; Huang, Minhui; Ma, Shihua

doi:10.48550/arxiv.2206.05670

Cited by 3 publications

(7 citation statements)

References 16 publications

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“…Algorithm Communication Gc(f, ǫ) Gc(g, ǫ) JV (g, ǫ) HV (g, ǫ) Non-Fed StocBiO [20] O(κ 5 ǫ −2 ) O(κ 9 ǫ −2 ) O(κ 5 ǫ −2 ) O(κ 6 ǫ −2 ) Non-Fed MRBO [50] O(p(κ)ǫ −1. 5 ) O(p(κ)ǫ −1. 5 ) O(p(κ)ǫ −1.…”

Section: Typementioning

confidence: 99%

“…5 ) O(κ 13 ǫ −2. 5 ) O(κ 8 ǫ −2. 5 ) O(κ 9 ǫ −2.5 ) (5) FedBiOAcc O(M −1/3 κ 62/9 ǫ −1 ) O(M −1 κ 8 ǫ −1.…”

Section: Typementioning

confidence: 99%

“…5 ) O(κ 9 ǫ −2.5 ) (5) FedBiOAcc O(M −1/3 κ 62/9 ǫ −1 ) O(M −1 κ 8 ǫ −1. 5 ) O(κ 8 ǫ −1.5 ) Oκ 8 ǫ −1. 5 ) O(κ 8 ǫ −1.…”

Section: Typeunclassified

“…However, most of these algorithms focus on standard single level optimization problems. In this Table 1: Comparisons of the Federated/Non-distributed bilevel optimization algorithms for finding an ǫ-stationary point of (1) or (5) (Defined by Type, which could be (1), (5) or Non-Fed). Gc(f, ǫ) and Gc(g, ǫ) denote the number of gradient evaluations w.r.t.…”

Section: Introductionmentioning

confidence: 99%

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Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Li¹,

Huang²,

Huang³

2023

Preprint

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Bilevel Optimization has witnessed notable progress recently with new emerging efficient algorithms, yet it is underexplored in the Federated Learning setting. It is unclear how the challenges of Federated Learning affect the convergence of bilevel algorithms. In this work, we study Federated Bilevel Optimization problems. We first propose the FedBiO algorithm that solves the hyper-gradient estimation problem efficiently, then we propose FedBiOAcc to accelerate FedBiO. FedBiO has communication complexity O(ǫ −1.5 ) with linear speed up, while FedBiOAcc achieves communication complexity O(ǫ −1 ), sample complexity O(ǫ −1.5 ) and also the linear speed up. We also study Federated Bilevel Optimization problems with local lower level problems, and prove that FedBiO and FedBiOAcc converges at the same rate with some modification. The Federated Bilevel Optimization problem with local lower level problem is included in the preliminary version [28].

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Section: Typementioning

confidence: 99%

“…5 ) O(κ 13 ǫ −2. 5 ) O(κ 8 ǫ −2. 5 ) O(κ 9 ǫ −2.5 ) (5) FedBiOAcc O(M −1/3 κ 62/9 ǫ −1 ) O(M −1 κ 8 ǫ −1.…”

Section: Typementioning

confidence: 99%

“…5 ) O(κ 9 ǫ −2.5 ) (5) FedBiOAcc O(M −1/3 κ 62/9 ǫ −1 ) O(M −1 κ 8 ǫ −1. 5 ) O(κ 8 ǫ −1.5 ) Oκ 8 ǫ −1. 5 ) O(κ 8 ǫ −1.…”

Section: Typeunclassified

Section: Introductionmentioning

confidence: 99%

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Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Li¹,

Huang²,

Huang³

2023

Preprint

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“…In addition, these approaches cannot be directly applied here due to the computation of either the Hessian inverse or a product of Hessians of the NUM objective, which requires each node to know the infeasible global network information, which is not practical. Although several decentralized bilevel optimization methods have been proposed by [40,41,42,43,44], they consider general bilevel objective functions without taking the channel capacity, the transmission links and the structured NUM objectives into account, and hence cannot be directly applied to the NUM problems. Then, the main contributions of this paper are summarized below:…”

Section: Introductionmentioning

confidence: 99%

Network Utility Maximization with Unknown Utility Functions: A Distributed, Data-Driven Bilevel Optimization Approach

Ji¹,

Lü²

2023

Preprint

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Fair resource allocation is one of the most important topics in communication networks. Existing solutions almost exclusively assume each user utility function is known and concave. This paper seeks to answer the following question: how to allocate resources when utility functions are unknown, even to the users? This answer has become increasingly important in the next-generation AI-aware communication networks where the user utilities are complex and their closed-forms are hard to obtain. In this paper, we provide a new solution using a distributed and data-driven bilevel optimization approach, where the lower level is a distributed network utility maximization (NUM) algorithm with concave surrogate utility functions, and the upper level is a data-driven learning algorithm to find the best surrogate utility functions that maximize the sum of true network utility. The proposed algorithm learns from data samples (utility values or gradient values) to autotune the surrogate utility functions to maximize the true network utility, so works for unknown utility functions. For the general network, we establish the nonasymptotic convergence rate of the proposed algorithm with nonconcave utility functions. The simulations validate our theoretical results and demonstrate the great effectiveness of the proposed method in a real-world network.

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Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiation

Xiao¹,

Ji²

2023

Preprint

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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 (i.e., 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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Decentralized Bilevel Optimization

Cited by 3 publications

References 16 publications

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Communication-Efficient Federated Bilevel Optimization with Local and Global Lower Level Problems

Network Utility Maximization with Unknown Utility Functions: A Distributed, Data-Driven Bilevel Optimization Approach

Communication-Efficient Federated Hypergradient Computation via Aggregated Iterative Differentiation

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