"Deep Learning" by Goodfellow > The function we want to minimize or maximize is called the objective function, or criterion. When we are minimizing it, we may also call it the cost function, loss function, or error function. In this book, we use these terms interchangeably, though some machine learning publications assign special meaning to some of these terms.
Andrew NG >"Finally, the loss function was defined with respect to a single training example. It measures how well you're doing on a single training example. I'm now going to define something called the cost function, which measures how well you're doing an entire training set. So the cost function J which is applied to your parameters W and B is going to be the average with one of the m of the sum of the loss function applied to each of the training examples and turn."
Objective function: is our target, whether minimize or maximize; e.g. MLE maximum likelihood estimation Cost function: is sum of loss function with additional regularization term. (on a trianing set scale); e.g. MSE mean squared error Loss function: is a function defined on data point, prediction and label, which measures penalty. (on a single sample). e.g. Square loss, hinge loss