Why is image classification tasks are dominated by minimizing cost function instead of maximizing ones?

I was watching a video of policy gradient by Andrej Karpathy at 10:00 there shows an equation for supervised learning for image classification.

$$max\sum _{i}log \:p(y_i|x_i)$$

I have worked with image classification models before but I always used a minimizing cost function aka loss function. I also never seen some one using maximizing cost function for image classification in the wild.

• Why image classification tasks are dominated by loss functions?
• What is the advantages of a minimizing loss function over a maximizing loss function in image classification?
• Other than RL where else maximizing cost functions are used?

There is really no difference between minimizing a cost function and maximizing a value function. One can be the reciprocal of the other, or the negative of the other, for example.

• It is worth noting that the function that the OP gives is in fact the negative of the usual multi-class loss function. I would hazard a guess that Andrej used it to make a more direct comparison with RL. – Neil Slater Oct 14 '19 at 6:56