Gradient Descent Optimization for ImageNet Training: Which is Faster?

(i) It is possible for Stochastic Gradient Descent to converge faster than Batch Gradient Descent.

Explanation: Stochastic Gradient Descent (SGD) updates the weights after each individual training example, which can lead to faster convergence compared to Batch Gradient Descent (BGD), which updates the weights after processing the entire training set. SGD's frequent updates can help it escape from local minima faster and find a better solution. However, SGD may also have more oscillations and noise in the learning process compared to BGD.

(ii) It is possible for Mini Batch Gradient Descent to converge faster than Stochastic Gradient Descent.

Explanation: Mini Batch Gradient Descent (MBGD) updates the weights after processing a small batch of training examples, typically between 10 and 1000. MBGD combines the advantages of SGD and BGD by providing a compromise between frequent updates and more stable convergence. It can converge faster than SGD as it benefits from some level of noise reduction from the averaging of gradients in each batch.

(iii) It is possible for Mini Batch Gradient Descent to converge faster than Batch Gradient Descent.

Explanation: Mini Batch Gradient Descent (MBGD) can converge faster than Batch Gradient Descent (BGD) because it updates the weights more frequently than BGD, but still benefits from some level of noise reduction due to the averaging of gradients in each mini-batch. MBGD strikes a balance between frequent updates and computational efficiency.

(iv) It is possible for Batch Gradient Descent to converge faster than Stochastic Gradient Descent.

Explanation: It is less likely for Batch Gradient Descent (BGD) to converge faster than Stochastic Gradient Descent (SGD) because BGD updates the weights only after processing the entire training set, which can be computationally expensive. SGD, on the other hand, updates the weights after each individual training example, allowing it to converge faster in many cases. However, in certain scenarios where the dataset is small and noise-free, BGD may converge faster than SGD.