Moreau Envelope

The Moreau envelope is a smoothing technique used to approximate non-smooth functions, primarily in optimization problems within machine learning. Current research focuses on applying Moreau envelopes to improve the robustness and efficiency of various algorithms, including model pruning for large language models, meta-learning, and adversarial training, often in conjunction with first-order optimization methods like gradient descent and ADMM. This approach addresses challenges like robust overfitting, computational efficiency in large-scale problems, and the need for theoretical convergence guarantees, ultimately leading to more stable and effective machine learning models. The impact spans diverse applications, from improving the efficiency of neural network training to enhancing the robustness of model interpretations.