The learning rate looks a bit high. The curve decreases too fast for my taste and flattens out very soon. I would try 0.0005 or 0.0001 as a base learning rate if I wanted to get additional performance. You can quit after several epochs anyways if you see that this does not work.
The question you have to ask yourself though is how much performance do you need and how close you are to accomplishing the performance required. I mean that you are probably training a neural network for a specific purpose. Often times you can get more performance out of the network by increasing its capacity, instead of fine tuning the learning rate which is pretty good if not perfect anyways.