Stochastic Operator

Stochastic operators are mathematical tools used to model and analyze systems with inherent randomness, finding applications across diverse fields like machine learning and signal processing. Current research focuses on improving the efficiency and convergence rates of algorithms employing stochastic operators, particularly within optimization problems (e.g., using variants of Adam and Halpern iteration) and in the context of tensor completion and mixture models. These advancements aim to reduce computational costs and improve the accuracy of solutions, impacting areas such as data balancing in large language models and off-policy reinforcement learning. The development of tighter theoretical guarantees for these operators is a key area of ongoing investigation.

Papers

August 27, 2024

The Benefits of Balance: From Information Projections to Variance Reduction
Lang Liu, Ronak Mehta, Soumik Pal, Zaid Harchaoui
Contrastive Learning Complementary Benefit Variance Reduction Balancing Strategy Multidimensional Projection Representation Collapse Self Supervised Clustering Stochastic Operator

August 10, 2024

Simple and Nearly-Optimal Sampling for Rank-1 Tensor Completion via Gauss-Jordan
Alejandro Gomez-Leos, Oscar López
Practical Algorithm Sample Complexity Computational Complexity Optimal Sampling O$ Sample Low Rank Tensor Completion Stochastic Operator

December 9, 2023

Revisiting RIP guarantees for sketching operators on mixture models
Ayoub Belhadji, Rémi Gribonval
Mixture Model Feature Operator Sparse Mixture High Probability Guarantee Random Sketching Stochastic Operator

December 28, 2022

Bayesian statistical learning using density operators
Yann Berquin
Bayesian Learning Inference Problem Quantum Framework Stochastic Operator

May 20, 2022

SADAM: Stochastic Adam, A Stochastic Operator for First-Order Gradient-based Optimizer
Wei Zhang, Yu Bao
Stochastic Way First Order Adam Optimizer First Order Gradient Stochastic Operator

March 30, 2022

Marginalized Operators for Off-policy Reinforcement Learning
Yunhao Tang, Mark Rowland, Rémi Munos, Michal Valko
Reinforcement Learning Policy Evaluation Policy Reinforcement Learning Downstream Policy Learning Stochastic Operator

March 17, 2022

Stochastic Halpern Iteration with Variance Reduction for Stochastic Monotone Inclusions
Xufeng Cai, Chaobing Song, Cristóbal Guzmán, Jelena Diakonikolas
Variance Reduction Monotone Inclusion Stochastic Operator Halpern Iteration

February 4, 2022

Polynomial convergence of iterations of certain random operators in Hilbert space
Soumyadip Ghosh, Yingdong Lu, Tomasz J. Nowicki
Stochastic Gradient Descent Random Sequence Hilbert Space Iteration Head Convergence Property Stochastic Operator