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I'm training a deep convolutional graph neural network. I noticed that for a particular learning rate (0.001, represented by the red/orange/blue solid lines), the training and test RMSE keep decreasing even after 500 epochs. Is there a way to speed this up? I tried using a higher learning rate (0.01, shown in gray), but that lead to a higher test RMSE.

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If you reduce the learning rate, you slow down how fast the gradient descent algorithm traverses the loss function. You can think of this as meaning smaller, more localised 'steps'. A higher learning rate means larger steps, and hence faster traversal. A downside is that by taking larger steps, you can potentially 'overshoot' the optimal solution - this likely explains the higher RMSE.

You could consider changing your batch size, using a different optimiser and changing your neural network structure (layering and size of your convolutions). You have a lot of different levers to pull.

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