# EigenGame Unloaded: When playing games is better than optimizing

arXiv: https://arxiv.org/abs/2102.04152 · HTML: https://mlsanity.com/paper/2102.04152/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 46 references that are in the map.
- First posted on arXiv 8 Feb 2021.

## Builds on (most cited first, 16 of 16)

- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Towards a Human-like Open-Domain Chatbot](https://mlsanity.com/paper/2001.09977/) (2020)
- [Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clustering](https://mlsanity.com/paper/1807.04518/) (2018)
- [Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decomposition](https://mlsanity.com/paper/1504.05477/) (2015)
- [GEMSEC: Graph Embedding with Self Clustering](https://mlsanity.com/paper/1802.03997/) (2018)
- [Input Sparsity Time Low-Rank Approximation via Ridge Leverage Score Sampling](https://mlsanity.com/paper/1511.07263/) (2015)
- [Frequent Directions : Simple and Deterministic Matrix Sketching](https://mlsanity.com/paper/1501.01711/) (2015)
- [EigenGame: PCA as a Nash Equilibrium](https://mlsanity.com/paper/2010.00554/) (2020)
- [First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Rate](https://mlsanity.com/paper/1607.07837/) (2016)
- [A Stochastic PCA and SVD Algorithm with an Exponential Convergence Rate](https://mlsanity.com/paper/1409.2848/) (2014)
- [Improved Distributed Principal Component Analysis](https://mlsanity.com/paper/1408.5823/) (2014)
- [Exponentially convergent stochastic k-PCA without variance reduction](https://mlsanity.com/paper/1904.01750/) (2019)
- [Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysis](https://mlsanity.com/paper/1702.08169/) (2017)
- [Stochastic Approximation on Riemannian manifolds](https://mlsanity.com/paper/1711.10754/) (2017)
- [Convergence Analysis of Riemannian Stochastic Approximation Schemes](https://mlsanity.com/paper/2005.13284/) (2020)
- [Scalable Adaptive Stochastic Optimization Using Random Projections](https://mlsanity.com/paper/1611.06652/) (2016)

## Built on by (most cited first, 13 of 13)

- [Operator SVD with Neural Networks via Nested Low-Rank Approximation](https://mlsanity.com/paper/2402.03655/) (2024)
- [A Novel Stochastic Gradient Descent Algorithm for Learning Principal Subspaces](https://mlsanity.com/paper/2212.04025/) (2022)
- [One Rank at a Time: Cascading Error Dynamics in Sequential Learning](https://mlsanity.com/paper/2505.22602/) (2025)
- [Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environments](https://mlsanity.com/paper/2209.10958/) (2022)
- [A Non-Negative Matrix Factorization Game](https://mlsanity.com/paper/2104.05069/) (2021)
- [Speeding up PCA with priming](https://mlsanity.com/paper/2109.03709/) (2021)
- [The Symmetric Generalized Eigenvalue Problem as a Nash Equilibrium](https://mlsanity.com/paper/2206.04993/) (2022)
- [Stochastic Parallelizable Eigengap Dilation for Large Graph Clustering](https://mlsanity.com/paper/2207.14589/) (2022)
- [A Generalized EigenGame with Extensions to Multiview Representation Learning](https://mlsanity.com/paper/2211.11323/) (2022)
- [Nash Equilibria via Stochastic Eigendecomposition](https://mlsanity.com/paper/2411.02308/) (2024)
- [Revisiting Orbital Minimization Method for Neural Operator Decomposition](https://mlsanity.com/paper/2510.21952/) (2025)
- [Eigenfunction Extraction for Ordered Representation Learning](https://mlsanity.com/paper/2510.24672/) (2025)
- [AdaPaD: Adaptive Parallel Deflation for PEFT with Self-Correcting Rank Discovery](https://mlsanity.com/paper/2605.10741/) (2026)

## Abstract (arXiv)

We build on the recently proposed EigenGame that views eigendecomposition as a competitive game. EigenGame's updates are biased if computed using minibatches of data, which hinders convergence and more sophisticated parallelism in the stochastic setting. In this work, we propose an unbiased stochastic update that is asymptotically equivalent to EigenGame, enjoys greater parallelism allowing computation on datasets of larger sample sizes, and outperforms EigenGame in experiments. We present applications to finding the principal components of massive datasets and performing spectral clustering of graphs. We analyze and discuss our proposed update in the context of EigenGame and the shift in perspective from optimization to games.