{"ID":2848252,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.26983","arxiv_id":"2510.26983","title":"Limited-Memory LRSGA: An Iterative Method for Computing Nash Equilibria in Competitive Optimization Problems","abstract":"We introduce LMLRSGA, a limited memory variant of Low Rank Symplectic Gradient Adjustment (LRSGA) for differentiable games. It is an iterative scheme for approximating Nash equilibria with first order like cost while retaining the stabilizing effect of symplectic second order corrections via low rank information. By storing only a limited history of curvature pairs, LMLRSGA is well suited to high parameter competitive models such as GANs. In particular, we provide a per iteration spectral stability condition for LRSGA near Nash equilibria, a limited memory implementation (LMLRSGA) based on adapted two loop recursions together with a local convergence analysis for fixed history length, and an empirical evaluation on GAN training on MNIST and FashionMNIST, including spectral diagnostics of the training dynamics.","short_abstract":"We introduce LMLRSGA, a limited memory variant of Low Rank Symplectic Gradient Adjustment (LRSGA) for differentiable games. It is an iterative scheme for approximating Nash equilibria with first order like cost while retaining the stabilizing effect of symplectic second order corrections via low rank information. By st...","url_abs":"https://arxiv.org/abs/2510.26983","url_pdf":"https://arxiv.org/pdf/2510.26983v2","authors":"[\"Katherine Rossella Foglia\",\"Francesco Sergio Pisani\",\"Vittorio Colao\"]","published":"2025-10-30T20:19:04Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[\"Generative Adversarial Network\"]","has_code":false}