Have you ever been able to solve a problem at work that nobody else could, or solve it faster, or cleaner, or more robustly, by virtue of having learned previously about some random topic which you had no idea would one day be applicable to your work? I think most programmers have, and I'd hope that a good boss at a good organization would understand that - as long as you're accomplishing everything that's required of the job - independent learning is a great use of (a reasonable fraction of your) time that will benefit both you and the business.