Search Results for author: Ioannis Panageas

Found 22 papers, 2 papers with code

On Scrambling Phenomena for Randomly Initialized Recurrent Networks

1 code implementation11 Oct 2022 Vaggos Chatziafratis, Ioannis Panageas, Clayton Sanford, Stelios Andrew Stavroulakis

Recurrent Neural Networks (RNNs) frequently exhibit complicated dynamics, and their sensitivity to the initialization process often renders them notoriously hard to train.

First-order Methods Almost Always Avoid Saddle Points

no code implementations20 Oct 2017 Jason D. Lee, Ioannis Panageas, Georgios Piliouras, Max Simchowitz, Michael. I. Jordan, Benjamin Recht

We establish that first-order methods avoid saddle points for almost all initializations.

Gradient Descent Only Converges to Minimizers: Non-Isolated Critical Points and Invariant Regions

no code implementations2 May 2016 Ioannis Panageas, Georgios Piliouras

Given a non-convex twice differentiable cost function f, we prove that the set of initial conditions so that gradient descent converges to saddle points where \nabla^2 f has at least one strictly negative eigenvalue has (Lebesgue) measure zero, even for cost functions f with non-isolated critical points, answering an open question in [Lee, Simchowitz, Jordan, Recht, COLT2016].

Open-Ended Question Answering

Last-Iterate Convergence: Zero-Sum Games and Constrained Min-Max Optimization

no code implementations11 Jul 2018 Constantinos Daskalakis, Ioannis Panageas

Motivated by applications in Game Theory, Optimization, and Generative Adversarial Networks, recent work of Daskalakis et al \cite{DISZ17} and follow-up work of Liang and Stokes \cite{LiangS18} have established that a variant of the widely used Gradient Descent/Ascent procedure, called "Optimistic Gradient Descent/Ascent (OGDA)", exhibits last-iterate convergence to saddle points in {\em unconstrained} convex-concave min-max optimization problems.

Open-Ended Question Answering

The Limit Points of (Optimistic) Gradient Descent in Min-Max Optimization

no code implementations NeurIPS 2018 Constantinos Daskalakis, Ioannis Panageas

Motivated by applications in Optimization, Game Theory, and the training of Generative Adversarial Networks, the convergence properties of first order methods in min-max problems have received extensive study.

Multiplicative Weights Update with Constant Step-Size in Congestion Games: Convergence, Limit Cycles and Chaos

no code implementations NeurIPS 2017 Gerasimos Palaiopanos, Ioannis Panageas, Georgios Piliouras

Interestingly, this convergence result does not carry over to the nearly homologous MWU variant where at each step the probability assigned to action $\gamma$ is multiplied by $(1 -\epsilon)^{C(\gamma)}$ even for the simplest case of two-agent, two-strategy load balancing games, where such dynamics can provably lead to limit cycles or even chaotic behavior.

On the Analysis of EM for truncated mixtures of two Gaussians

no code implementations19 Feb 2019 Sai Ganesh Nagarajan, Ioannis Panageas

Moreover, for $d>1$ we show EM almost surely converges to the true mean for any measurable set $S$ when the map of EM has only three fixed points, namely $-\vec{\mu}, \vec{0}, \vec{\mu}$ (covariance matrix $\vec{\Sigma}$ is known), and prove local convergence if there are more than three fixed points.

Vocal Bursts Valence Prediction

Regression from Dependent Observations

no code implementations8 May 2019 Constantinos Daskalakis, Nishanth Dikkala, Ioannis Panageas

The standard linear and logistic regression models assume that the response variables are independent, but share the same linear relationship to their corresponding vectors of covariates.

regression

Depth-Width Trade-offs for ReLU Networks via Sharkovsky's Theorem

no code implementations ICLR 2020 Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

Motivated by our observation that the triangle waves used in Telgarsky's work contain points of period 3 - a period that is special in that it implies chaotic behavior based on the celebrated result by Li-Yorke - we proceed to give general lower bounds for the width needed to represent periodic functions as a function of the depth.

Open-Ended Question Answering

Last iterate convergence in no-regret learning: constrained min-max optimization for convex-concave landscapes

no code implementations17 Feb 2020 Qi Lei, Sai Ganesh Nagarajan, Ioannis Panageas, Xiao Wang

In a recent series of papers it has been established that variants of Gradient Descent/Ascent and Mirror Descent exhibit last iterate convergence in convex-concave zero-sum games.

Convergence to Second-Order Stationarity for Non-negative Matrix Factorization: Provably and Concurrently

no code implementations26 Feb 2020 Ioannis Panageas, Stratis Skoulakis, Antonios Varvitsiotis, Xiao Wang

Non-negative matrix factorization (NMF) is a fundamental non-convex optimization problem with numerous applications in Machine Learning (music analysis, document clustering, speech-source separation etc).

Clustering

Better Depth-Width Trade-offs for Neural Networks through the lens of Dynamical Systems

no code implementations ICML 2020 Vaggos Chatziafratis, Sai Ganesh Nagarajan, Ioannis Panageas

The expressivity of neural networks as a function of their depth, width and type of activation units has been an important question in deep learning theory.

Learning Theory

Logistic-Regression with peer-group effects via inference in higher order Ising models

no code implementations18 Mar 2020 Constantinos Daskalakis, Nishanth Dikkala, Ioannis Panageas

In this work we study extensions of these to models with higher-order sufficient statistics, modeling behavior on a social network with peer-group effects.

regression

Efficient Statistics for Sparse Graphical Models from Truncated Samples

no code implementations17 Jun 2020 Arnab Bhattacharyya, Rathin Desai, Sai Ganesh Nagarajan, Ioannis Panageas

We show that ${\mu}$ and ${\Sigma}$ can be estimated with error $\epsilon$ in the Frobenius norm, using $\tilde{O}\left(\frac{\textrm{nz}({\Sigma}^{-1})}{\epsilon^2}\right)$ samples from a truncated $\mathcal{N}({\mu},{\Sigma})$ and having access to a membership oracle for $S$.

Global Convergence of Multi-Agent Policy Gradient in Markov Potential Games

1 code implementation NeurIPS 2021 Stefanos Leonardos, Will Overman, Ioannis Panageas, Georgios Piliouras

Counter-intuitively, insights from normal-form potential games do not carry over as MPGs can consist of settings where state-games can be zero-sum games.

Teamwork makes von Neumann work:Min-Max Optimization in Two-Team Zero-Sum Games

no code implementations29 Sep 2021 Fivos Kalogiannis, Ioannis Panageas, Emmanouil-Vasileios Vlatakis-Gkaragkounis

Motivated by recent advances in both theoretical and applied aspects of multiplayer games, spanning from e-sports to multi-agent generative adversarial networks, we focus on min-max optimization in team zero-sum games.

Independent Natural Policy Gradient Always Converges in Markov Potential Games

no code implementations20 Oct 2021 Roy Fox, Stephen Mcaleer, Will Overman, Ioannis Panageas

Recent results have shown that independent policy gradient converges in MPGs but it was not known whether Independent Natural Policy Gradient converges in MPGs as well.

Multi-agent Reinforcement Learning

Towards convergence to Nash equilibria in two-team zero-sum games

no code implementations7 Nov 2021 Fivos Kalogiannis, Ioannis Panageas, Emmanouil-Vasileios Vlatakis-Gkaragkounis

On a brighter note, we propose a first-order method that leverages control theory techniques and under some conditions enjoys last-iterate local convergence to a Nash equilibrium.

Vocal Bursts Valence Prediction

Accelerated Multiplicative Weights Update Avoids Saddle Points almost always

no code implementations25 Apr 2022 Yi Feng, Ioannis Panageas, Xiao Wang

We consider non-convex optimization problems with constraint that is a product of simplices.

Efficiently Computing Nash Equilibria in Adversarial Team Markov Games

no code implementations3 Aug 2022 Fivos Kalogiannis, Ioannis Anagnostides, Ioannis Panageas, Emmanouil-Vasileios Vlatakis-Gkaragkounis, Vaggos Chatziafratis, Stelios Stavroulakis

In this work, we depart from those prior results by investigating infinite-horizon \emph{adversarial team Markov games}, a natural and well-motivated class of games in which a team of identically-interested players -- in the absence of any explicit coordination or communication -- is competing against an adversarial player.

Multi-agent Reinforcement Learning

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