Spend the afternoon. You can't take it with you.
   Annie Dillard

Life is full of optimal stoppings, isn't it, huh? But do you know the right time when to stop searching?

I've been reading about the Theory of Optimal Stopping. We frequently face optimal stopping problems in our daily lives, from choosing a place to live and secretaries to life partners. The fascinating question arises: do we naturally adopt the best strategies through evolution, education, or intuition? While reading about this, I found a research revealing that people often decide too soon, leaving superior options unexplored. I am guilty of this too. Sometimes I'm impatient.

This research by Amnon Rapoport and Darryl Seale demonstrates that people's success rate in finding the best candidate is reasonably close to the optimal percentage. However, most individuals follow the Look-Then-Leap Rule but leap earlier than optimal. Rapoport acknowledges the impatience in humans, which is not considered in the classical secretary problem related to the original Theory. Time is valuable, and searching incurs a time cost, explaining why people may stop searching early. Although the time cost is not accounted for in optimal stopping models, it could explain the divergence between human decision-making and these models' predictions. As Neil Bearden explains, "humans' tendency to get bored is not irrational but challenging to model rigorously" [5].

Optimal stopping problems become more significant as time turns every decision into an optimal stopping issue. This theory encapsulates the essence of the human experience, as we constantly choose when to take actions, from financial decisions to personal interactions. The secretary problem highlights the nature of time, as life, much like optimal stopping, requires us to decide based on unseen possibilities and accept high failure rates even when acting optimally.

So, what did I learn? I learned that rational decision-making is about weighing options and knowing when to stop, as hesitation and inaction are as irreversible as the action itself. Like Brian Christian and Tom Griffiths said, "No choice recurs. We may get similar choices again, but never that exact one." So, be patient. Observe. Live the present moment and don't get caught up in a constant rush of activities or decisions without considering the consequences or reflecting on their outcomes. Because I know I've made the same mistake countless times.

Well, I just wanted to learn some probability distributions and figure out how the Bayesian method and Monte Carlo simulations work to solve optimal stopping problems. And look where it got me thinking, haha! Mathematics and Computer Science teaching me a life lesson! Definitely, something to live by :)

Reading list

  1. Optimal Stopping
  2. Optimal Stopping behaviour
  3. Asymptotics of Optimal Stopping
  4. Knowing when to stop
  5. Dynamic programming and the secretary problem
  6. Algorithms to live by
  7. Bayesian Optimization Meets Bayesian Optimal Stopping

Well, now what?

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