As a native speaker of American English, I would only ever say "back home" and never insert a preposition between the two. I would say, "I'm going back home" when someone asks, for example, how I will spend my vacation. In this case, "home" refers to where I was raised. If I just say "I'm going home", this could just mean the place I live now OR the place I was raised.
You can use "at" with "home" as in, "I am spending the night at home" or "Cooking at home is less expensive than eating out."
If you want to use "back to" in the above context, you might tack "my house" on the end of it.
Q: Where to you want to go after dinner?
A: Let's go back to my house.
You can also use at in this context:
Q: Where did you say the blueprints were?
A: I left them back at my house OR I left them back at the house (implies
everyone knows which house is being
spoken about, but you do not
necessarily own it.
I cannot speak for how the above usage may differ in British English.
Both usages are correct, and they mean the same thing.
The only minor wrinkle is that at can be used to refer to a physical location as well as a company itself:
I work at Microsoft.
I work at the Microsoft Redmond campus.
Whereas for cannot be used this way:
I work for Microsoft.
*I work for the Microsoft Redmond campus.
The last sentence would somehow indicate that you are employed by the campus itself, which probably isn't what you mean.
Best Answer
The usage I have most often seen in quantitative technical fields is that there is an upper bound on a variable. And if you use "an upper bound of..." you are referring to that limit, rather than the variable that is being limited.
For example, "there is an upper bound of 50 miles per hour on my car's velocity."
See Mathwords.com for "upper bound of" and this article ("A Simple Upper Bound on the Redundancy of Huffman Codes") for many, many examples of "upper bound on" usage.