(Book Excerpt) A Metaphor for AI Learning Through Optimization
[In my upcoming book—AI Wisdom: Meta-Principles of Thinking and Learning (March 2025)— I describe the durable AI concepts that can be taught in any subject. Prior to this excerpt from Chapter 6 (“Learning”), I describe optimization, one of two key ways that AI learns, as a process for getting to the best of many possibilities for unchanging, unopposed challenges. Many AI models learn through optimization, but we also encounter optimization problems routinely in life and work.]
Opti-Bot
Imagine you are exploring another earth-size planet, but you’re in orbit and a robot I’ll call Opti-Bot is at the surface. You get to control the robot’s position.
Opti-Bot has some peculiar features. For one, it can’t move across the ground, but in this Star Trek fantasy world that doesn’t stop it from being able to teleport precisely to any location on the planet. Each time you tell Opti-Bot where to go, it gives you the altitude of ground level at that location. Oh, and Opti-Bot is blind. It has no camera.
Your task is to reliably find the highest point on the planet in a reasonable amount of time using only Opti-Bot.
There are constraints. The robot can power a limited number of teleportations, and each altitude measurement takes some time.
Yeah, there are many holes in this make believe. What, NASA can’t spend a few bucks on a camera? The people who built the orbiter hadn’t heard of RADAR? Then there’s the paradox that Opti-Bot can’t know what spot to teleport to unless it knows the ground level. It’ll teleport into solid rock or gassy nothingness.
Hey … whatever. It’s an analogy. You get to hop around, you get the altitude everywhere you hop, you can’t sense anything else, and you have to find the highest peak.
How would you go about this task?
You might teleport to every degree of latitude and longitude—360 × 360 = 129,600 locations (assuming an Earth-sized planet). At the equator, that's roughly 69 miles between each point.
But we know some mountains can be very steep, and it is unclear what terrain this new planet has. A gap of 69 miles is too big; we’d risk skipping over the tallest peak. If we go to a tenth of a degree of latitude and longitude, then that’s about 13 billion locations! If it takes a minute to get the altitude at each location and decide where to go next, then it would take almost 300 years to complete.
This kind of strategy, called exhaustive search, quickly becomes untenable. There are just too many possibilities.
Let’s try another approach. What if you compare the altitudes of two or more nearby locations, and take short hops to continue in the direction of higher altitude? If that’s done until no other direction is uphill, then it’s a peak.
That might get you to a pretty high altitude if you are lucky enough to start somewhere in a major mountain range, but this “hill climbing” strategy gets you to a peak. It doesn’t get you to the highest peak. Maybe it only gets you to the top of the mulch pile in our alien counterpart’s back yard.
A better approach might sample the altitudes at some random locations and then hill climb from the ones that are already at significant altitudes. That doesn’t guarantee the highest peak either, but at least you’d be likely to end up in the Himalayas somewhere, even if not Mt. Everest.
The reality is there is no perfect way to do this. The optimal strategy is too dependent on the nature of the underlying terrain. A planet as smooth as a cue ball might have a top altitude of a few meters, reachable by hill climbing from any location on the planet. Or it could have Grand Canyons and Mt. Everest’s all over the place.
Beyond highlighting optimization challenges, the Opti-Bot metaphor previews key ideas about how AI learns and improves. The same fundamental trade-offs between thorough search, quick improvement, and exploring multiple starting points shape how AI—or any other higher intelligence—must figure out what’s best when presented with lots of options.
[Next section: Understanding Optimization]
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