arXiv subjects

Lesi Chen

Publications and source records attributed to Lesi Chen.

21 records · Page 2Linked to original sources

arXiv2024

An Efficient Stochastic Algorithm for Decentralized Nonconvex-Strongly-Concave Minimax Optimization

This paper studies the stochastic nonconvex-strongly-concave minimax optimization over a multi-agent network. We propose an efficient algorithm, called Decentralized Recursive gradient descEnt Ascent Method (DREAM), which achieves the best-known theoretical guarantee for finding the $ε$-stationary points. Concretely, it requires $\mathcal{O}(\min (κ^3ε^{-3},κ^2 \sqrt{N} ε^{-2} ))$ stochastic first-order oracle (SFO) calls and $\tilde{\mathcal{O}}(κ^2 ε^{-2})$ communication rounds, where $κ$ is the condition number and $N$ is the total number of individual functions. Our numerical experiments also validate the superiority of DREAM over previous methods.

cs.LG↗

arXiv2024

Faster Gradient-Free Algorithms for Nonsmooth Nonconvex Stochastic Optimization

We consider the optimization problem of the form $\min_{x \in \mathbb{R}^d} f(x) \triangleq \mathbb{E}_ξ [F(x; ξ)]$, where the component $F(x;ξ)$ is $L$-mean-squared Lipschitz but possibly nonconvex and nonsmooth. The recently proposed gradient-free method requires at most $\mathcal{O}( L^4 d^{3/2} ε^{-4} + ΔL^3 d^{3/2} δ^{-1} ε^{-4})$ stochastic zeroth-order oracle complexity to find a $(δ,ε)$-Goldstein stationary point of objective function, where $Δ= f(x_0) - \inf_{x \in \mathbb{R}^d} f(x)$ and $x_0$ is the initial point of the algorithm. This paper proposes a more efficient algorithm using stochastic recursive gradient estimators, which improves the complexity to $\mathcal{O}(L^3 d^{3/2} ε^{-3}+ ΔL^2 d^{3/2} δ^{-1} ε^{-3})$.

math.OC↗

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.

math.OC↗