Beware the trap of the local optimum

Lots of problems look a little like this:

1-11. Local and global optima.

The Y-axis measures success at whatever problem you’re trying to solve.

You start at the farthest left point on the curve and you can move left or right a little bit every time you work on the problem.

After you make it to the top of the first hill, the only way to make it to the top of the second hill is by going down first.

In jujitsu, if I’m lucky enough to get to mount, my instinct is to camp out there. Maybe I can submit the other guy by sweating on him. I’m in a relatively safe position now, so I don’t want to take risks. In other words, I’m at the local optimum.

If I go for a submission like an arm bar, given my current skill level, my opponent will probably escape the mount, and I’ll be in a worse position afterward.

So in a self-defense situation, it might be smart to camp. The failure penalty is high!

But in class, because the cost of failure is so low (really, I just don’t get to feel like a badass when I tap out) I am wasting an opportunity to learn (and move to the right along the curve)!