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I usually use "at the cost of", but my editor made it "at the expense of". For example, the following sentence:

The counts in Table 2 are all based on implementations that are optimized for computational cost, which comes at the cost of significantly increased storage costs in ...

was replaced by

The counts in Table 2 are all based on implementations that are optimized for computational cost, which comes at the expense of significantly increased storage costs in ...

Can anyone help explain the difference?

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    Your editor didn't like seeing "computational cost ... at the cost of ... increased storage costs ..." (and probably other costs as well). It's repetitive. At the cost of, at the expense of, at the sacrifice of, and to the detriment of are near synonyms. Had you instead written "... optimized for computational expense, which comes at the expense of significantly increased storage expenses in ..." he might well have changed "at the expense of" to "at the cost of" to avoid an overly-repetitive sentence.
    – David Hammen
    Commented Jan 4, 2015 at 21:23
  • @DavidHammen When you say someone does something at the expense of something else, it means that what they do harms that "something else". So, when you say "He works so hard at the expense of his health", his working so hard harms his health. Inceased storage costs are the result of something else and not what is damaged! What do you think?
    – Englishfreak
    Commented Jan 4, 2015 at 22:01
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    @Cheiloproclitic - "At the expense of" can mean "to the detriment of someone or something", but can also mean "costing more (elsewhere)", "paid for elsewhere", or "paid for by some other entity". In this case, the decrease computational costs in this case means paying more money for computer storage. "At the expense of" certainly fits here.
    – David Hammen
    Commented Jan 4, 2015 at 22:07
  • @DavidHammen So we can use it to refer to the result of what you do, right? So you can say "He always says what he thinks, at the expense of annoying others", and it means annoying others is the possible result of his saying what he thinks?
    – Englishfreak
    Commented Jan 4, 2015 at 22:19

4 Answers 4

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"Cost" is naturally an attribute of the relevant object (eg "what was its cost?"), while "Expense" relates rather to the relevant person (eg "at his expense"). After all, to cost and to spend are different, though related, concepts.

In your example, it may be (as suggested in the comment above) that your editor simply preferred to avoid repetition of the word "cost". Alternatively, your editor's correction could be said to have personalised the "significantly increased storage costs", depicting the storage costs as having "to pay the cost of" the computational costs.

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At the expense of can be understood to be something doing damage, if you will, to the storage costs, whereas at the cost of seems to imply more of direct damage to you.

IMO you are correct.

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    Increased storage costs is detrimental.
    – David Hammen
    Commented Jan 4, 2015 at 21:20
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To buy something at the cost/expense/price of something = to get something that you want but only by losing something else.

At the expense of = at the cost of.

Definition of at the cost of:

by giving up or hurting (something else).

Example:

She completed the project on time but at the cost of her health.

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I am not 100% sure, but I don't agree with the editor. To me, 'at the cost of X' means that you get X by doing something. By contrast, 'at the expense of X' means that you lose X by doing something. So it is completely opposite. For example,

I smoke at the cost of death.

and

I smoke at the expense of life.

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