compensate for (something)
1. To offset (or attempt to offset) something. His sudden honesty cannot compensate for all the lies he told me over the past year.
2. To reimburse someone for something. In this usage, the recipient is named between "compensate" and "for." If you take the job, we will compensate you for all of your relocation expenses.
compensate someone for something
to pay someone [back] money for something. Don't worry. I will compensate you for your loss. Let us compensate you for your expenses.
compensate for something
to counterbalance or counteract something; to make up for something. Your present kindness will not compensate for your previous rudeness.