Solving Weakly-Convex-Weakly-Concave Saddle-Point Problems as Weakly-Monotone Variational Inequality

By Qihang Lin, Mingrui Liu, Hassan Rafique, Tianbao Yang. 2018

51 citations recorded by the source corpus.

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1. Sergey Levine
2. Bo Dai
3. Michael I. Jordan
4. Ofir Nachum
5. Chi Jin
6. Jason D. Lee
7. Lihong Li
8. Yoshua Bengio

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…”
• On Gradient Descent Ascent for Nonconvex-Concave Minimax Problems (2019, background): “…of goodness or the development of new procedures for reducing oscillations [Daskalakis and Panageas, 2018b, Adolphs et al., 2018, Mazumdar et al., 2019] and speeding up the convergence of gradient dynamics [Heusel et al., 2017, Balduzzi et al., 2018, Mertikopoulos et al., 2019, Lin et al., 2018].”
• Multi-Agent Reinforcement Learning: A Selective Overview of Theories and Algorithms (2019, background): “Such an exploration may also benefit from the recent advances of nonconvex-(non)concave optimization (Lin et al., 2018; Jin et al., 2019; Nouiehed et al., 2019).”
• Minmax Optimization: Stable Limit Points of Gradient Descent Ascent are Locally Optimal (2019, background): “Lin et al. [2018] consider a special case of the nonconvex-nonconcave minmax problem, where the function f ( · , · ) satisfies a variational inequality.”
• Optimistic Dual Extrapolation for Coherent Non-monotone Variational Inequalities (2021, background): “Assumption 3 assumes the existence of weak solutions, which is also adopted in [25].”
• Solving a Class of Non-Convex Min-Max Games Using Iterative First Order Methods (2019, methodology): “In an effort to solve the more general non-convex non-concave setting, [34] developed a framework that converges to ε-first order stationarity/Nash equilibrium under the assumption that there exists a solution to the Minty variational inequality at each iteration.”