Can you find these days any software developer who hasn’t implemented some sort of Pac-Man game and then entered the eternal loop of tweaking and improving the logic for the “pac-mouse” or “pac-monster” to find his way through the maze?


And it is fantastic! Why? Because the scenario brings us to the very core of thinking about what on earth this much-touted thing really is, in its purest essence, this thing called AI (Artificial Intelligence).

How You Got Lost in the Maze

Maybe you are one of those sad people who got stuck with all those tutorials explaining all sorts of AI concepts, got tricked by them. You gradually degraded even deeper into the rat wheel, down to the point where you found yourself browsing Wikipedia articles about established core concepts of AI, such as deep neural networks, Q-learning and reinforcement learning, Markov chains and so much more!

… And then, you stumbled with equations, got lost in the maze of your thoughts, found yourself wondering how all these things can help your Pac-Man find a way out of his maze.

Do not be pressed down by sorrow and desperation! Maybe there is light at the end of the tunnel. Let us set out together for an expedition trip into the maze of artificial intelligence!

The Core Essence of Intelligence

At the end of the day, isn’t all intelligence made out of the same matter? It’s about the will to find a better way to achieve something valuable, and it’s about the curiosity to try alternative paths to find a better way. All animals are inherently smart. They exercise this same behavior. They mostly repeat the same pattern of doing these things they need to do, to survive and reproduce.

But they are unpredictable. They do unexpected things. Sometimes their foolish play causes them trouble, but sometimes they really find something different that helps them adapt and survive. That’s why there are city foxes tattering garbage bins - hardly any ancient behavior.

The animals, they explore.

Existential Intelligence

Now, there are many levels of exploration. The most primitive level is to establish insight only through existing. The existence can be cursed or blessed, depending on where, when and how you exist. If a sunflower seed ends up on a road by the gust of whirlwind, it dies and doesn’t reproduce. But if it lands in the fertile soil, however, its offspring will be numerous.

In a way we can say that the existential intelligence has solved the question of fertile soil. From the results we can see that the highway is infertile, nothing grows on it. But look at the bloomy sunflower field beside the highway. The soil is fertile.

Neural Intelligence

We can compare plants with ideas or thoughts. If an idea is healthy and pops up at the right time in the right place, it survives and produces offspring - some fruitful action and even better ideas. Therefore we humans, considering ourselves intelligent beings, don’t actually need to physically do a stupid thing to understand its consequences. We can sit down and think whether it would be wise if “I ehm… just steal a chocolate bar from grocery to fill my stomach… Nope.”

Computer Intelligence

Similarly to humans, computers can evaluate “ideas” and pick the best ones. Back in 1997, world chess champion Garry Gasparov was beaten by IBM supercomputer Deep Blue. The chess program used a “brute-force” search algorithm to find the best moves.

Later it turned out, brute force search does not take AI really far, since the possible combinations typically grow exponentially by every step. Therefore, it became obvious that “cheaper” search algorithms were to be invented.

Sparing Search Algorithms

Better search algorithms were invented, such as Q-learning algorithm. The core idea is that instead of totally evaluating all possible combinations, each evaluation of the path usually chooses the best next step, but not always! It explores. That means, it occasionally chooses a next step that isn’t the obviously best one. This is because in a computer maze, just as in the life in general, the obviously most rewarding next step often isn’t the best path in the long term!

If you get hungry and just grab a chocolate bar from the grocery and then run, you’ll be doing fine for five to twenty minutes, but not so much anymore when the police car stops in front of you when you sit in the park with your hands and face smeared brown from the chocolate you just ate.

Back to the Maze

But now let’s get real and go back to our original problem of helping your Pac-Man mouse navigate through the maze… The point here is that if your mouse has a “GPS”, which equals a reward function to tell how far he is from the salvation measured as a linear distance from maze’s exit door, then actually a step further away from the exit door may be the right solution when consequent steps are iterated, although it does not appear to be so right away.

However, the task of going through all steps would be just too enormous for a brute-force search algorithm, but very doable for a Q-learning like approach. And not only for the mouse in the maze, also for a soccer coach when…

Building a Soccer Team

A coach wants to build up a “dream team” by starting from zero and expanding his team player by player. After adding each player, he stops to think who would be the best addition for the currently existing selection of players. Mathematically, adding those who have the best scores would create the dream team that always wins. But in reality, Theo plays miserably when Tim is in the team (maybe because Tim married his ex-girlfriend?) and Jack plays way better with his identical twin Joe on board and so on. For this reason, to find the best team you might want to occasionally try to add someone to the team who is not the best option measured by plain score. There might be hidden synergies!

Loaded Dice to the Rescue

At this point I want to introduce you to a super simple algorithm that I call now the loaded dice. The loaded dice are special dice that have been manipulated by setting internal weights and maybe fiddled a little bit at corners to produce biased outcomes.

With loaded dice, you most likely get - but not always - number six, and less likely number 5, and most unlikely number 1. Other configurations are possible when fiddled differently, for example having the results biased toward 1.

It’s great for cheating in board games, but it’s also a fundamental principle for any intelligent behavior:

Whatever you do, you’ll be most likely to get the best known results by routinely choosing the best steps you know from your experience and education to be the best ones…

But sometimes you have to try something else to find even better ways. That applies to everything, beginning from choosing the spice and ingredients for your soup to a mouse finding a path out of the maze, to everything that exists under the Sun - and maybe even beyond!

Anyway, I find this following algorithm handy yet easy-to-grasp thing to serve as a core component of an AI solution, which is about mostly selecting the nearly best option but occasionally trying out a sub-optimal solution.

Applying Onion Random to Mimic Loaded Dice

Let’s implement something now that allows us to create the “loaded dice” effect. I will call the following implementation “onion random” algorithm, because it just creates a random number within given range between 0 and initial_max_limit, and then randomly limits the number again and again. Finally we get an outcome that is a random number more likely to be closer zero than the other end of the range.

Since I like Ruby, I show my implementation in Ruby language:

def onion_random(initial_max_limit, bias_factor)
  bias_factor.times.reduce(initial_max_limit) { |new_max_limit|

What we get here is a fundamental function for artificial intelligence. It’s a programmatic implementation of biased dice. With this core AI function, my friend, you’ll get far in your life!

This function returns you a random integer number that is always smaller than the initial_max_limit that you give as a parameter. The other parameter, bias_factor is also an integer, telling how many times you randomly reduce the max number. The bigger bias_factor is, the more likely the function is to produce outcomes biased toward zero. But no matter how high the bias factor is, the chance will always exist that you still get the highest possible number, which is initial_max_limit - 1.

for example:

result = onion_random(100, 4)

You will get an outcome that is quite often zero or close to zero, but you may still occasionally get even 99.

Needless to say, you will be getting quite sexy distribution curves with this function.

Your mouse in his maze will absolutely love this.

Better Implementation With Exponential Function

To tune up the implementation even more, a smoother solution than nesting random function calls would be just taking one random number and pass it to a mathematical power function.

I’ll be back to this and even more exciting topics. Cheers!