# Are there some needs to prove that object function can be reduced to cost function? [duplicate]

I'm a student studying ML.

After I searched the differences between the loss function, cost function, and object function, I had some questions.

Objective function, cost function, loss function: are they the same thing?

As the above answer, object function is a more generic function than cost function. And object function can have a different formula like the maximum likelihood function, which is neither loss function nor cost function.

But as I understood about ML (especially gradient-based learning), we can train our ML models by optimizing our cost function to converge to maxima/minima point, and at that time, we calculate gradient per each weight parameter to converge optima points.

In short, when we train our models, we use the cost function to compute gradients.

If cost function and object function are the same, that isn't a huge problem, but otherwise, then we need to prove our object function can be optimized through optimizing our cost function? In other words, do we need to explicitly prove that our object function could be reduced to our cost function??

If not, why we don't need to prove it?

• What is written in the linked answer is "A loss function is a part of a cost function which is a type of an objective function". So all cost functions are objective functions in that context.
– Ale
Dec 10, 2020 at 9:14
• Does this answer your question? Objective function, cost function, loss function: are they the same thing?
– Ale
Dec 10, 2020 at 9:14
• @Ale oh I missed it. Maybe, you are right. Then, we don't need to prove the relationship btw cost function and object function, because the cost function is an object function itself. Thx. Dec 10, 2020 at 14:30
• You call "objective function" what you want to optimize, here your objective function is the cost function.
– Ale
Dec 10, 2020 at 15:14