"Learning curve" behavior comparison I am comparing two learning algorithms using the log learning rate. I plot training data size vs. Mean Absolute Error (MAE). In the figure below, you can see method 1 shown with black line and method 2 with blue line. 

One interpretation is that method 2 works better when the training data size is lower and vise versa.
I remembered something in the following line but couldn't find it looking it up online: Is it OK for the logarithmic learning curve to asymptote to an error? Or does it show a problem with the method. 
I appreciate if someone can elaborate on this or let me know if there is no such thing. Thanks!

EDITS:
This image confirms what I remembered is correct. Link: https://arxiv.org/pdf/1807.04259.pdf

 A: To me, this looks like normal behaviour. It could happen if, for example:


*

*method 1 (black line) is a more complicated model with a large number of trainable parameters

*method 2 (blue line) is a simpler model with only a few trainable parameters.


In that case, for small sample sizes:


*

*method 1 has only a few data points for a lot of parameters and overfits on the training data, leading to a high validation loss (I assume that's what you have plotted on the $y$ axis?)

*method 2 has fewer parameters, so does not overfit. The validation loss is lower than for method 1.


However, for large sample sizes:


*

*method 1, being a more complicated model, can fit the data better. Since there are more data points, there is less overfitting and the validation loss keeps decreasing.

*method 2 has only a few parameters, which do not change much upon adding more data. Since the model is simple, it cannot find a good "fit" and the validation loss bottoms out. 


There's a great paper on this exact topic: Classifier design for computer-aided diagnosis: Effects of finite sample size on the mean performance of classical and neural network classifiers by Chan and Sahiner in Medical Physics, 1999. You can find a copy here. It provides a nice explanation, including diagrams, for some toy problems where this occurs.
Here's a picture from that paper that I modified. The $A_z$ is like the accuracy, so the higher the accuracy, the lower the loss. It shows $A_z$ against inverse sample size. The L is a linear model and Q a quadratic one. For small sample sizes, the quadratic model overfits and has a lower validation accuracy. But, for high sample sizes, it can fit the data better than the linear one and has a higher accuracy.

I'd recommend reading the paper as it explains what is happening better than I can. 
