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20162025
most citedFirst-order Methods Almost Always Avoid Saddle Points

76 citations · 264 across the 43 of their papers we have counts for

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5 papers · 1 filter

math.OC2023

Multiplicative Updates for Online Convex Optimization over Symmetric Cones

Ilayda Canyakmaz, Wayne Lin, Georgios Piliouras +1

We study online convex optimization where the possible actions are trace-one elements in a symmetric cone, generalizing the extensively-studied experts setup and its quantum counte…

math.OC2021

Constants of Motion: The Antidote to Chaos in Optimization and Game Dynamics

Georgios Piliouras, Xiao Wang

Several recent works in online optimization and game dynamics have established strong negative complexity results including the formal emergence of instability and chaos even in sm…

math.OC2021

Solving Min-Max Optimization with Hidden Structure via Gradient Descent Ascent

Lampros Flokas, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Georgios Piliouras

Many recent AI architectures are inspired by zero-sum games, however, the behavior of their dynamics is still not well understood. Inspired by this, we study standard gradient desc…

math.OC20197 cited

Efficiently avoiding saddle points with zero order methods: No gradients required

Lampros Flokas, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Georgios Piliouras

We consider the case of derivative-free algorithms for non-convex optimization, also known as zero order algorithms, that use only function evaluations rather than gradients. For a…

math.OC20195 cited

Poincaré Recurrence, Cycles and Spurious Equilibria in Gradient-Descent-Ascent for Non-Convex Non-Concave Zero-Sum Games

Lampros Flokas, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Georgios Piliouras

We study a wide class of non-convex non-concave min-max games that generalizes over standard bilinear zero-sum games. In this class, players control the inputs of a smooth function…