mlsanityData to 14 Oct 2026

EigenGame Unloaded: When playing games is better than optimizing

arXiv 2102.04152 ↗First posted 8 Feb 2021stat.ML cs.AI cs.LGcited by 13

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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.

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

16 of 46 references.

References · 16

  1. 2018Spectral Normalization for Generative Adversarial Networkscited by 1,636
  2. 2020Towards a Human-like Open-Domain Chatbotcited by 470
  3. 2018Turning Big data into tiny data: Constant-size coresets for k-means, PCA and projective clusteringcited by 94
  4. 2015Randomized Block Krylov Methods for Stronger and Faster Approximate Singular Value Decompositioncited by 64
  5. 2018GEMSEC: Graph Embedding with Self Clusteringcited by 61
  6. 2015Input Sparsity Time Low-Rank Approximation via Ridge Leverage Score Samplingcited by 46
  7. 2015Frequent Directions : Simple and Deterministic Matrix Sketchingcited by 39
  8. 2020EigenGame: PCA as a Nash Equilibriumcited by 39
  9. 2016First Efficient Convergence for Streaming k-PCA: a Global, Gap-Free, and Near-Optimal Ratecited by 32
  10. 2014A Stochastic PCA and SVD Algorithm with an Exponential Convergence Ratecited by 18
  11. 2014Improved Distributed Principal Component Analysiscited by 14
  12. 2019Exponentially convergent stochastic k-PCA without variance reductioncited by 12
4 more
  1. 2017Communication-efficient Algorithms for Distributed Stochastic Principal Component Analysiscited by 10
  2. 2017Stochastic Approximation on Riemannian manifoldscited by 7
  3. 2020Convergence Analysis of Riemannian Stochastic Approximation Schemescited by 5
  4. 2016Scalable Adaptive Stochastic Optimization Using Random Projectionscited by 3

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 5; 2023: 0; 2024: 2; 2025: 3; 2026: 1.

13 papers.

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  1. 2024Operator SVD with Neural Networks via Nested Low-Rank Approximationcited by 13
  2. 2022A Novel Stochastic Gradient Descent Algorithm for Learning Principal Subspacescited by 7
  3. 2025One Rank at a Time: Cascading Error Dynamics in Sequential Learningcited by 3
  4. 2022Developing, Evaluating and Scaling Learning Agents in Multi-Agent Environmentscited by 2
  5. 2021A Non-Negative Matrix Factorization Gamecited by 0
  6. 2021Speeding up PCA with primingcited by 0
  7. 2022The Symmetric Generalized Eigenvalue Problem as a Nash Equilibriumcited by 0
  8. 2022Stochastic Parallelizable Eigengap Dilation for Large Graph Clusteringcited by 0
  9. 2022A Generalized EigenGame with Extensions to Multiview Representation Learningcited by 0
  10. 2024Nash Equilibria via Stochastic Eigendecompositioncited by 0
  11. 2025Revisiting Orbital Minimization Method for Neural Operator Decompositioncited by 0
  12. 2025Eigenfunction Extraction for Ordered Representation Learningcited by 0
1 more
  1. 2026AdaPaD: Adaptive Parallel Deflation for PEFT with Self-Correcting Rank Discoverycited by 0