What is an acceptable value of square loss in machine learning (using mxnet gluon's square loss function)? I have checked the gluon's square loss function implementation in mxnet, where it is calculated as follows:
$$L=\frac{1}{2}\sum_i\left|label_i−pred_i\right|^2$$
https://mxnet.apache.org/versions/1.8.0/api/python/docs/api/gluon/loss/index.html#mxnet.gluon.loss.L2Loss
The key here is that the loss is squared and then multiplied by $\frac{1}{2}$.
Now, let's suppose I want to predict a label ∈ {0,1} where P(1)=P(0)=0.5
And instead of doing any calculation I simply always predict that my value is equal to 0.5
If the label is 1, I get a loss $L=\frac{1}{2}\sum_i\left|1−0.5\right|^2$=0.125
And if my label is 0, I also get $L=\frac{1}{2}\sum_i\left|0−0.5\right|^2$=0.125
Does this mean I should aim for my loss to be less than 0.125 for my predictions to be of any use?
Or in this case ( if labels are ∈ {0,1} ), would it be more sensible to switch to softmax model?

Your constant prediction of $0.5$ is a great benchmark. Meteorological forecasters would call it a "climatological forecast", i.e., one that only relies on the overall and unconditional distribution of your target variable.
Any other model should improve on this benchmark. If it doesn't, you are better off with the simple benchmark.
"Of any use" implies, well, putting predictions to use. In some applications, even tiny improvements over trivial benchmarks can be valuable (e.g., in stock price predictions). In other applications, the improvement would need to be larger for us to use the model over the benchmark.
Whether you should switch to a softmax depends on the quality of your final output. If a model with softmax yields better predictions, then by all means, use it.
