This assumes you can only hold beliefs that are adjacent to your current beliefs (i.e. the graph of your beliefs over time must be continuous). I disagree with

This assumes you can only hold beliefs that are adjacent to your current beliefs (i.e. the graph of your beliefs over time must be continuous). I disagree with that assumption. You can explore ideas that you don't hold, and these can be quite varied from your current beliefs. Once you find an idea that you put more confidence into that your current beliefs, then that idea becomes your belief. The local optimum from high-climbing doesn't constrain you in a world where your beliefs can teleport from one hill to another.