Research map / Optimization / Nonconvex and smooth optimization
Poincaré Recurrence, Cycles and Spurious Equilibria in Gradient-Descent-Ascent for Non-Convex Non-Concave Zero-Sum Games
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Apply continuous GDA from a safe initialization in a two-strategy hidden bilinear game | Hidden bilinear games · Hidden bilinear games, two strategies | trajectory behavior | Mixed |
| Apply continuous GDA from a safe initialization in a higher-dimensional hidden bilinear game | Hidden bilinear games · Hidden bilinear games, more than two strategies | trajectory behavior | Mixed |
| Allow local optima in the hidden functions that violate the safety conditions | Continuous GDA · Hidden bilinear games | convergence to spurious equilibria | Hurt |
| Time-average the strategies and utilities along safe continuous-GDA trajectories | Continuous GDA · Hidden bilinear games, safe initializations | time-averaged strategies and utilities | Helped |
| Discretize GDA for sigmoid hidden functions from a safe initialization | Hidden bilinear games · Hidden bilinear games with sigmoid functions, safe initializations | energy invariant H | Hurt |
| Allow a suitable learning rate and functions with local optima in discrete GDA | Discrete GDA · Hidden bilinear games | convergence to spurious equilibria | Hurt |
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