The Benefits of Starting Anew
Whether it’s restarting your computer or doing over your golf shot, there are times when going back to square one seems like the best course of action. A new statistical analysis by Sergey Belan of the Massachusetts Institute of Technology, Cambridge, considers how hitting the reset button could help in general situations where more than one outcome is possible. The result could help in designing restart protocols for chemical synthesis applications in which a particular reaction product is preferred over other possibilities.
When considering the benefits of a restart, the prototypical situation is that of a random walker searching for a target within a time limit. One can show that the probability of success, that is, reaching the target before time runs out, can improve if the walker goes back to its starting point after, say, several minutes of searching without finding the target. Such a fixed start-over time helps avoid situations where the walker winds up in some distant region far from the target.
In his study, Belan looked at a more general set of problems in which there are multiple outcomes that end the search or process. For example, a gambler may decide to quit playing when he either doubles his money or loses it all. Belan first imagined a restart protocol where the start-over time is varied randomly after each restart. This stochastic approach offers an advantage when the average time to reach the desired result (without restart) is short compared with the average time to reach other outcomes. He then identified the general criteria for finding an optimal restart rate that maximizes the probability of ending up with the preferred outcome.
This research is published in Physical Review Letters.
Michael Schirber is a Corresponding Editor for Physics based in Lyon, France.