Application of Deep Reinforcement Learning
This honestly sounds more like a supervised learning problem.
For reinforcement learning to work, you would need a model that can constantly return values for a given input.

With social media, that would mean 


a) posting the same image with all kinds of different hashtags and expecting people to give the most appropiate hashtags likes in a short amount of time. This will not happen.
b) searching for all occurrences of an image with different hashtags. This is basically supervised learning.


I recommend finding a social media dataset first. Try to group all occurrences of an image and find the median of likes for each hashtag. Don't forget to compensate for follower count, as more popular posters will get more likes on average regardless of hashtag. Store the best hashtag as label for the given image.

You now have Y different hashtags for X different images.

From now, you can treat it as classification problem. X is your sample count, Y is the amount of possible outputs. If you don't want to write your own loss function and only want to predict the single best hashtag, use cross entropy as loss function.

Of course you still have to choose your social media dataset, appropriate images for training and NN structure, but I hope this helps as a general approach.