Khairul Eahsun Fahim MSE will converge to mean optimal values, that may not be a good fit for your use case, e.g. it will not perform well for long tail distributions, extreme values, etc.

There are two reasons why Mean Squared Error(MSE) is a bad choice for binary classification problems:

First, using MSE means that we assume that the underlying data has been generated from a normal distribution (a bell-shaped curve). In Bayesian terms this means we assume a Gaussian prior. While in reality, a dataset that can be classified into two categories (i.e binary) is not from a normal distribution but a Bernoulli distribution (Check out the answer to “Where did the Binary Cross-Entropy Loss Function come from?” for more details and also for an intro to maximum likelihood estimation).

Secondly, the MSE function is non-convex for binary classification. In simple terms, if a binary classification model is trained with MSE Cost function, it is not guaranteed to minimize the Cost function. This is because MSE function expects real-valued inputs in range(-∞, ∞), while binary classification models output probabilities in range(0,1) through the sigmoid/logistic function. Let’s visualize:

When the MSE function is passed a value that is unbounded a nice U-shaped (convex) curve is the result where there is a clear minimum point at the target value (y). On the other hand, when a bounded value from a Sigmoid function is passed to the MSE function the result is not convex; on one side the function is concave while on the other side the function convex and no clear minimum point. So, if by accident a binary classification neural network is initialized with weights which are large in magnitude such that it lands on the concave part of the MSE Cost function gradient descent will not work and consequently, weights may not update or improve very slowly(try this out in coding section). This is one of the reasons why neural networks should be carefully initialized with small values when training.

if you meed more information you can see the link

https://towardsdatascience.com/why-using-mean-squared-error-mse-cost-function-for-binary-classification-is-a-bad-idea-933089e90df7

Mean squared error (MSE) is a commonly used measure of the difference between the predicted values of a model and the actual values. MSE is often used in the context of regression analysis, where the goal is to fit a model to a set of data points and predict the value of a continuous variable. In this context, MSE can be used to evaluate the accuracy of the model by comparing the predicted values to the actual values and calculating the average squared difference between the two.

MSE can also be used in the context of cost optimization or scheduling problems, where the goal is to minimize the total cost or maximize the efficiency of a system or process. In this context, MSE can be used to evaluate the performance of different cost optimization or scheduling strategies by comparing the predicted cost or efficiency of each strategy to the actual cost or efficiency and calculating the average squared difference between the two.

To use MSE in a cost optimization or scheduling problem, you will need to follow a set of steps that involve:

It is important to note that the specific details of the optimization or scheduling problem and the methods used to solve it will depend on the specific goals of the problem and the resources available, and that it may be necessary to adjust the methods or algorithms used based on the results of the optimization or scheduling process.