arXiv subjects

Chengchang Liu

Publications and source records attributed to Chengchang Liu.

22 records · Page 2Linked to original sources

arXiv2024

A Communication and Computation Efficient Fully First-order Method for Decentralized Bilevel Optimization

Bilevel optimization, crucial for hyperparameter tuning, meta-learning and reinforcement learning, remains less explored in the decentralized learning paradigm, such as decentralized federated learning (DFL). Typically, decentralized bilevel methods rely on both gradients and Hessian matrices to approximate hypergradients of upper-level models. However, acquiring and sharing the second-order oracle is compute and communication intensive. % and sharing this information incurs heavy communication overhead. To overcome these challenges, this paper introduces a fully first-order decentralized method for decentralized Bilevel optimization, $\text{C}^2$DFB which is both compute- and communicate-efficient. In $\text{C}^2$DFB, each learning node optimizes a min-min-max problem to approximate hypergradient by exclusively using gradients information. To reduce the traffic load at the inner-loop of solving the lower-level problem, $\text{C}^2$DFB incorporates a lightweight communication protocol for efficiently transmitting compressed residuals of local parameters. % during the inner loops. Rigorous theoretical analysis ensures its convergence % of the algorithm, indicating a first-order oracle calls of $\tilde{\mathcal{O}}(ε^{-4})$. Experiments on hyperparameter tuning and hyper-representation tasks validate the superiority of $\text{C}^2$DFB across various typologies and heterogeneous data distributions.

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arXiv2024

Incremental Gauss--Newton Methods with Superlinear Convergence Rates

This paper addresses the challenge of solving large-scale nonlinear equations with Hölder continuous Jacobians. We introduce a novel Incremental Gauss--Newton (IGN) method within explicit superlinear convergence rate, which outperforms existing methods that only achieve linear convergence rate. In particular, we formulate our problem by the nonlinear least squares with finite-sum structure, and our method incrementally iterates with the information of one component in each round. We also provide a mini-batch extension to our IGN method that obtains an even faster superlinear convergence rate. Furthermore, we conduct numerical experiments to show the advantages of the proposed methods.

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arXiv2023

Communication Efficient Distributed Newton Method with Fast Convergence Rates

We propose a communication and computation efficient second-order method for distributed optimization. For each iteration, our method only requires $\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension. We also provide theoretical analysis to show the proposed method has the similar convergence rate as the classical second-order optimization algorithms. Concretely, our method can find~$\big(ε, \sqrt{dLε}\,\big)$-second-order stationary points for nonconvex problem by $\mathcal{O}\big(\sqrt{dL}\,ε^{-3/2}\big)$ iterations, where $L$ is the Lipschitz constant of Hessian. Moreover, it enjoys a local superlinear convergence under the strongly-convex assumption. Experiments on both convex and nonconvex problems show that our proposed method performs significantly better than baselines.

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arXiv2022

Quasi-Newton Methods for Saddle Point Problems and Beyond

This paper studies quasi-Newton methods for solving strongly-convex-strongly-concave saddle point problems (SPP). We propose greedy and random Broyden family updates for SPP, which have explicit local superlinear convergence rate of ${\mathcal O}\big(\big(1-\frac{1}{nκ^2}\big)^{k(k-1)/2}\big)$, where $n$ is dimensions of the problem, $κ$ is the condition number and $k$ is the number of iterations. The design and analysis of proposed algorithm are based on estimating the square of indefinite Hessian matrix, which is different from classical quasi-Newton methods in convex optimization. We also present two specific Broyden family algorithms with BFGS-type and SR1-type updates, which enjoy the faster local convergence rate of $\mathcal O\big(\big(1-\frac{1}{n}\big)^{k(k-1)/2}\big)$. Additionally, we extend our algorithms to solve general nonlinear equations and prove it enjoys the similar convergence rate.

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