Whether it's coming to grips with a new video game, or honing a new skill, there is an ideal sweet spot for learning, somewhere between too easy and too hard. A new study, using machine learning algorithms, is suggesting that the optimal learning zone involves failing around 15 percent of the time.

In pedagogical circles there has long been an awareness of a kind of "Goldilocks zone" for the most efficient learning. If something is way too difficult we will quickly give up, and if something is too simple it gets boring and our attention drifts away.

"These ideas that were out there in the education field – that there is this 'zone of proximal difficulty,' in which you ought to be maximizing your learning – we've put that on a mathematical footing," explains lead author on the new study, Robert Wilson.

The new research set out to quantify this learning sweet spot by training a set of machine learning algorithms on some simple binary classification tasks. By adjusting the error rate of the model the researchers could exactly home in on the optimal difficulty level that achieves the fastest pace of learning. That optimal error rate turned out to be 15.87 percent.

"If you have an error rate of 15 percent or accuracy of 85 percent, you are always maximizing your rate of learning in these two-choice tasks," says Wilson.

In terms of translating these results to human learning, Wilson notes the so-called "85 percent rule" only explicitly applies to binary classification tasks with explicit right and wrong answers. One example he gives is that of a radiologist identifying tumors in patient scans.

"You get better at figuring out there's a tumor in an image over time, and you need experience and you need examples to get better," Wilson explains. "I can imagine giving easy examples and giving difficult examples and giving intermediate examples. If I give really easy examples, you get 100 percent right all the time and there's nothing left to learn. If I give really hard examples, you'll be 50 percent correct and still not learning anything new, whereas if I give you something in between, you can be at this sweet spot where you are getting the most information from each particular example."

So, as Wilson affirms, this does not mean the best student at school is actually the one averaging B or B+ grades, but the research does suggest a highly specific level of difficulty does result in optimal learning. The most explicit immediate takeaway from the research is for those scientists developing machine learning algorithms, including multilayered feedforward and recurrent neural networks. The conclusion suggests machine learning can be optimized by adjusting accuracy rates to hit 85 percent.

For more complex forms of human learning, the 85 percent rule is not immediately transferable. Wilson and his collaborators hope to explore broader forms of human learning, but generally he believes the results of this study should push educators to be more encouraging when students make mistakes. The implication is quite clearly that the best learning involves a small volume of mistakes.

"If you are taking classes that are too easy and acing them all the time, then you probably aren't getting as much out of a class as someone who's struggling but managing to keep up," Wilson notes. "The hope is we can expand this work and start to talk about more complicated forms of learning."

The research was published in the journal Nature Communications.

Source: University of Arizona