Summary of Projected Forward Gradient-guided Frank-wolfe Algorithm Via Variance Reduction, by M. Rostami et al.
Projected Forward Gradient-Guided Frank-Wolfe Algorithm via Variance Reduction
by M. Rostami, S. S. Kia
First submitted to arxiv on: 19 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary A recent paper proposes enhancements to the Frank-Wolfe (FW) algorithm for training deep neural networks. The FW algorithm is prone to high computational and memory costs when computing gradients for DNNs, similar to other gradient-based optimization algorithms. To address this limitation, the authors introduce the projected forward gradient (Projected-FG) method into the FW framework, offering reduced computational cost comparable to backpropagation and low memory utilization akin to forward propagation. The results show that a trivial application of Projected-FG introduces non-vanishing convergence error due to stochastic noise in the process, leading to variance in the estimated gradient. To mitigate this issue, the authors propose a variance reduction approach by aggregating historical Projected-FG directions. They demonstrate rigorously that this approach ensures convergence to the optimal solution for convex functions and to a stationary point for non-convex functions. The effectiveness and efficiency of this approach are validated through a numerical example. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper improves the Frank-Wolfe algorithm, which trains deep neural networks but has high costs. It combines the algorithm with another method called Projected-FG, making it faster and using less memory like forward propagation. However, this combination introduces some noise that affects how well the model works. To fix this, the authors suggest averaging previous directions to reduce this noise. They show that this approach makes sure the model gets better results for both simple and complex problems. |
Keywords
* Artificial intelligence * Backpropagation * Optimization
