What is Local Optimality in Nonconvex-Nonconcave Minimax Optimization?

By Chi Jin, Praneeth Netrapalli, Michael I. Jordan. 2019

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Citations in the corpus

GenDICE: Generalized Offline Estimation of Stationary Values (2020, background): “For the general neural network for (τ, f), although there are several progress recently (Lin et al., 2018; Jin et al., 2019; Lin et al., 2019) about the convergence to a stationary point or local minimum, it remains a largely open problem to quantify the optimization error, which is out of the…”
Tilted Empirical Risk Minimization (2020, background): “While minimizing the k-loss is more desirable than ERM in many applications, the k-loss is non-smooth (and generally non-convex), and is challenging to solve for large-scale problems (Jin et al., 2020; Nouiehed et al., 2019b).”
Global Convergence and Variance-Reduced Optimization for a Class of Nonconvex-Nonconcave Minimax Problems (2020, background): “Indeed, it is common to use diﬀerent learning rates for x and y in GDA algorithms for nonconvex minimax problems; see e.g., Jin et al. [2019] and Lin et al. [2019].”
Rényi Fair Inference (2019, methodology): “Several algorithms have been recently proposed for solving such non-convex min-max optimization problems Sanjabi et al. (2018); Nouiehed et al. (2019); Jin et al. (2019).”
The complexity of constrained min-max optimization (2020, background): “Several kinds of those have been proposed in the literature [14, 24, 30].”
Minimax Theorem for Latent Games or: How I Learned to Stop Worrying about Mixed-Nash and Love Neural Nets (2020, background): “This result contrasts with the negative result of Jin et al. (2019) who construct a nonconvex-nonconcave game where pure global minimax does not exist.”
On Solving Minimax Optimization Locally: A Follow-the-Ridge Approach (2019, methodology): “First, it has undesirable convergence properties: it fails to converge to some local minimax and can converge to ﬁxed points that are not local minimax (Jin et al., 2019; Daskalakis and Panageas, 2018).”