# Fast hill climbing algorithm that can stabilize when near optimal

I have a floating point number x from [1, 500] that generates a binary y of 1 at some probability p. And I'm trying to find the x that has highest p. I'm assuming there's only one maximum.

I know we can do this with simulated annealing but I don't think I should hard code temperature because I need to use the same algorithm when x could be from [1, 3000] or the p distribution is little bit different.

Is there an algorithm that can converge fast to the x with highest p while making sure it doesn't jump around too much after it's achieved for e.x. within 0.1% of the optimal x? Specifically, it would be great if it stabilizes when near < 0.1% of optimal x.

• You're assuming only one global maximum, or only one local maximum? – Omar Dec 8 '17 at 5:42
• Yup, global maximum – Jae Dec 8 '17 at 19:00