Uses a randomness temperature, which starts high for exploration and slowly decreases by one of the Simulated Annealing Schedules. Whenever you are about to take a step, each step must be “accepted” with probability given by the Metropolis Criteria. Intuition: “sometimes, you try something that’s bad, to jump out of local optima.” Metropolis Criteria \begin{align} P(\text{accept}) = \begin{cases} 1, \text{if}\ \Delta y \leq 0\ \min \left(e^{-\frac{\Delta y}{t}}, 1\right), \text{otherwise} \end{cases} \end{align} where t is the temperature; meaning—-even if the next point \Delta y > 0 (meaning its bad, because it increases loss), we sometimes take that ponit still. Simulated Annealing Schedule we need to decrease t by a schedule over time Log \begin{equation} t = t \frac{\ln (2)}{\ln (k+1)} \end{equation} Exponential best one

Fast \begin{equation} t = \frac{t}{k} \end{equation}