When finding the maximum margin separator in the primal form we have the quadratic program:

$$min\frac{1}{2}||\theta||^2$$ $$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq 1, \ t=1,...,n$$

Saying basically to find the maximum margin separator. The margin size will be:

$$\frac{1}{||\theta||}$$

does the size of the margin change whether we change the constant of the constraints?

i.e. if we have:

$$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq k, \ t=1,...,n$$

instead of 1?

If it does not matter, why doesn't this matter? How is it an equivalent formulation regardless of the exact constant for the constraint?

When finding the maximum margin separator in the primal form we have the quadratic program

$$min\frac{1}{2}||\theta||^2$$ $$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq 1, \ t=1,...,n,$$

saying basically to find the maximum margin separator. The margin size will be:

$$\frac{1}{||\theta||}.$$

Does the size of the margin change if we change the constants of the constraint?

That is, if we have

$$\text{ subject to: } y^{(t)}(\theta \cdot x^{(t)} + \theta_0) \geq k, \ t=1,...,n,$$

instead of 1?

If it does not matter, why doesn't this matter? How is it an equivalent formulation regardless of the exact constants for the constraint?