We study smooth strongly convex--strongly concave minimax optimization with general nonlinear coupling in the deterministic unconstrained setting. We propose a pure single-loop damped extragradient method with fixed parameters and two new full-gradient evaluations per iteration after one initialization query. The method uses an auxiliary feedback recursion and requires no inner solves, accuracy schedules, or staged restarts. We establish last-iterate linear convergence and show that reducing the squared Euclidean distance to the saddle point to an $\varepsilon$ fraction of its initial value requires $O(\sqrt{\kappa_x\kappa_y}\log(2\kappa_x\kappa_y/\varepsilon))$ full-gradient queries, where $\kappa_x=L/\mu_x$ and $\kappa_y=L/\mu_y$. This bound attains the optimal condition-number order up to logarithmic factors through fixed explicit updates. Numerical experiments demonstrate the effectiveness of the method.
This work proposes a novel single-loop algorithm based on a constrained reformulation in which lower-level stationarity is imposed as a constraint, and constructs a regularized Lagrangian by introducing a quadratic regularizer and restricting the dual variable to a bounded domain.
We develop single-loop stochastic projected damped extragradient methods for stochastic nonconvex--(strongly) concave minimax optimization, with complexity guarantees for both game stationarity (GS) and optimization stationarity (OS). Our approach combines a stochastic projected damped extragradient (SPDE) method with...
Hui-Ling Zhang, Min-hao Zhang, Zi Xu· 2 citations· ⚡1
This work proposes a nonlinear-residual linearized augmented Lagrangian method (NR-LALM) that replaces this subproblem by a regularized Gauss-Newton-type step while retaining the classical multiplier update based on the nonlinear constraint residual.
Ben-Qi Liu, Kangkang Deng, Zichen Wang et al.· 0 citations
A new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization and a lower bound of $\Omega(L^2D_Y\Delta_\phi\varepsilon^{-3})$ for optimization stationarity over projected zero-respecting first-order methods is established.
This work proposes a smooth approximation of PBO through reformulation, penalization and regularization, and establishes convergence guarantees in terms of both minimizers and stationarity, and develops two single-loop algorithms for deterministic and stochastic PBOs, respectively.
Qi Cao, Bo Zeng, Shang-Zhi Zeng et al.· 0 citations
We study nonsmooth convex-concave saddle-point problems over compact convex sets, assuming access to stochastic subgradients of the payoff function. We develop single-loop projection-free algorithms that use linear minimization oracles over the primal and dual domains. Unlike prior projection-free approaches that rely...
Learn how Google DeepMind and GovTech Singapore uses lightweight on-device Gemma models to intercept conversational scams in private chats with zero cloud data egress.
