Algorithms to Live By

The third chapter of Algorithms to Live By is about sorting. Some examples of sorting you might encounter: Ordering books on a shelf (if you still have physical ones) Participating in a tournament orders individuals/teams by skill (with varying degrees of reliability) Sorting food in your fridge so you know where to look for things With more digitization these days, computers will handle most of the mundane sorting like ordering documents, but it’s interesting to realize how we naturally follow some of these algorithms. Let’s take an example of ordering your todo list by priority: ...

The explore exploit chapter in the book “Algorithms to Live By” looks into the problem called the “Multi-armed Bandit”. The “Multi-armed Bandit” is when you have multiple independent choices with different reward probabilities, and you can only try one at a time (like a slot machine). One algorithm that the book describes to tackle this problem is the Gittins Index. The Gittins Index is a fairly complicated calculation, but the idea for the slot machines example is that it favors exploration of new machines when there is less data gathered about the odds. The amount that the index favors exploration is calculated from the “discount” factor, the higher the discount factor, the more exploration. For example, if you only have a few minutes to test the machines, then you might choose a lower discount factor, because you don’t have time to test any one thoroughly, so stick with a decent one if you find it. With a high 90% factor, shown in the graph below, even a machine with a 9 to 5 win ratio would have a lower Gittins Index than an untested machine, guiding the player to move on. ...

I’ve been reading through the book Algorithms to Live By, and I thought it would be interesting to summarize or think of an application for each chapter since the book is about how algorithms influence or can be used in everyday decisions. The first chapter is about the Optimal Stopping problem, which deals with deciding when to, well stop, given a decision that costs something over time. One example in the book is about hiring a secretary, or some other job candidate. According to the math, if you want to find the top candidate, you should reject the first 37% applicants in order to establish a baseline for the candidate quality, then accept the first candidate that outperforms the baseline. ...