How to optimize for time correlated hidden function - the magical candy machine

Question

Let's assume that we have this magical candy machine which takes candies as input and delivers again candies as output.

1. For any given time t, it picks a random function which is strictly increasing up to a point such as f(2) = 6 here, and then it strictly decreases. It likes to be challenging but if you become greedy it punishes you like most of the stuff in life.

   f(1) = 5

   f(2) = 6

   f(3) = 4

   f(4) = 2

   f(100) = 0

2. The tricky point is that this function is changing all the time, but still highly correlated with time. So f() will be similar between t(1) and t(2), but very different between t(1) and t(100).

I want to write a program to maximize my candies using this magical candy machine. I know the fundamentals of ML but I'm not sure which approach would fit best here. Any ideas?

Note: You can only play only once every minute.