{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/gradient-descent-ascent-provably-converges-to","title":"Gradient Descent-Ascent Provably Converges to Strict Local Minmax Equilibria with a Finite Timescale Separation","arxiv_id":"2009.14820","date":"2020-09-30","proceeding":"ICLR 2021 1","authors":["Tanner Fiez","Lillian Ratliff"],"abstract":"We study the role that a finite timescale separation parameter $\\tau$ has on gradient descent-ascent in two-player non-convex, non-concave zero-sum games where the learning rate of player 1 is denoted by $\\gamma_1$ and the learning rate of player 2 is defined to be $\\gamma_2=\\tau\\gamma_1$. Existing work analyzing the role of timescale separation in gradient descent-ascent has primarily focused on the edge cases of players sharing a learning rate ($\\tau =1$) and the maximizing player approximately converging between each update of the minimizing player ($\\tau \\rightarrow \\infty$). For the parameter choice of $\\tau=1$, it is known that the learning dynamics are not guaranteed to converge to a game-theoretically meaningful equilibria in general. In contrast, Jin et al. (2020) showed that the stable critical points of gradient descent-ascent coincide with the set of strict local minmax equilibria as $\\tau\\rightarrow\\infty$. In this work, we bridge the gap between past work by showing there exists a finite timescale separation parameter $\\tau^{\\ast}$ such that $x^{\\ast}$ is a stable critical point of gradient descent-ascent for all $\\tau \\in (\\tau^{\\ast}, \\infty)$ if and only if it is a strict local minmax equilibrium. Moreover, we provide an explicit construction for computing $\\tau^{\\ast}$ along with corresponding convergence rates and results under deterministic and stochastic gradient feedback. The convergence results we present are complemented by a non-convergence result: given a critical point $x^{\\ast}$ that is not a strict local minmax equilibrium, then there exists a finite timescale separation $\\tau_0$ such that $x^{\\ast}$ is unstable for all $\\tau\\in (\\tau_0, \\infty)$. Finally, we empirically demonstrate on the CIFAR-10 and CelebA datasets the significant impact timescale separation has on training performance.","url_abs":"https://arxiv.org/abs/2009.14820v1","url_pdf":"https://arxiv.org/pdf/2009.14820v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"gradient-descent-ascent-provably-converges-to","repo_url":"https://github.com/fiezt/Finite-Learning-Ratio","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":null}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":null,"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}