Researchers decipher Feynman’s notes on solution to ‘optimal stopping problem’

Researchers have deciphered theoretical physicist Richard Feynman’s handwritten notes on a solution to the ‘optimal stopping problem’-such as when to stop ordering dishes at a new restaurant and settle for the familiar, most loved one, or while searching for a partner.
Findings are published in the journal Proceedings of the National Academy of Sciences.
Researchers, including those from the UK’s Oxford University, said optimal stopping problems arise in one’s everyday life, not only while trying to decide what to eat, but also while finding a home, deciding who to marry, selecting a parking spot, and knowing when to quit a job.
“The essence of the problem is that the value of exploring, of looking around and trying something new, decreases the opportunities you’re going to have to make use of that information,” co-author Tom Griffiths, professor at Princeton University, US told The Guardian.
The team also tested out Feynman’s solution- they found that people use a decision threshold that decreases linearly in proportion to the number of trials remaining, achieving a performance remarkably close to the optimal solution found by Feynman.
The story begins in the 1970s, when on a certain day, Feynman went to a Thai restaurant in Glendale, California with a friend Ralph Leighton for lunch.
Leighton was caught in a dilemma of whether to order his favourite dish, the ginger chicken, or try a new one with a chance of being better.
The theoretical physicist Richard Feynman converted the dilemma into a mathematical problem- and solved it, but did not publish the results.
However, the handwritten notes and their meaning have remained a mystery for decades.
“Here we present the fully deciphered problem and solution, prove its optimality, generalise it to related problems, and compare the results to human behaviour,” the authors wrote.
Feyman’s optimal policy specifies decreasing thresholds for switching from exploring new dishes to exploiting the best, with thresholds varying based on the distribution of the quality of dishes, they said.
The team connected the result to existing psyhocology literature on “optimal stopping problems” and used a generalised version of the solution to explore how the underlying distribution of the quality of the options influences people’s choices.
The researchers asked 2,520 participants to imagine living in a city for varied periods of time. Restaurants available and their quality were indicated.
The team found that the threshold for exploration fell in a linear manner in proportion to the number of nights of stay remaining in the city, rather than the threshold decreasing more and more rapidly.
“We show that people tend to explore more than predicted by linear thresholds, and that different distributions of quality result in thresholds with the same slope but different intercepts,” the authors wrote.
“These results indicate that people adapt linear thresholds used in optimal stopping tasks in a way that is sensitive to the underlying distribution- a simple strategy that we show is nearly as effective as Feynman’s solution,” they said. (PTI)