Derivative-Free Optimization Outperforms Adam on MNIST

🔑 Enhanced Key Takeaways

• •The reported success of a derivative-free method in a 25,450-dimensional parameter space is significant, as derivative-free optimization (DFO) algorithms have historically faced challenges with high-dimensional problems, often seeing performance diminish beyond hundreds of parameters.
• •Derivative-free optimization methods are especially beneficial in scenarios where calculating gradients is impractical, unreliable, or impossible, such as with non-smooth objective functions, noisy data, or discrete search spaces.
• •Beyond the method described, other derivative-free approaches for neural network training include neuroevolution, which can optimize both network weights and architecture, and Local Search (LS) methods that have demonstrated the capacity to achieve lower loss than stochastic gradient descent (SGD), albeit sometimes with slower convergence rates.
• •Gradient-Free Method (GFM) and Stochastic GFM (SGFM) are other examples of derivative-free algorithms that have been successfully applied to training ReLU neural networks on the MNIST dataset, addressing nonsmooth nonconvex optimization problems with polynomial complexity.

🔮 Future ImplicationsAI analysis grounded in cited sources