## Random Decision Making Algorithms

Nowadays, more and more modern methods are used to analyze the world. This field brings together many highly complex algorithms that enable scientists to predict behavior. This may sound a lot like science fiction, but it is now being applied in the real world, such as in our random decision making application.

### What is an algorithm?

An algorithm is generally a set of instructions that must be executed to solve a problem. These instructions change depending on how the algorithm is used. For example, a very well-known algorithm is the YouTube algorithm, which categorizes the content of videos on the platform based on specific reference points provided for the algorithm.

Another example is the Google algorithm, which scans the content of various websites to rank them on Google. The algorithm looks for many signals, such as keywords, pictures, and much more.

Therefore, you can imagine that a large algorithm requires enormous effort. Therefore, algorithms are a very advanced method to gain insights and automate complicated processes.

### What is a randomized algorithm?

Compared to a normal algorithm, like the one from Google, a randomized algorithm brings more variables into the calculation, some of which can be random. In this way, a randomized algorithm will not always make the same decision as a simpler algorithm would.

For this reason, a randomized algorithm is suitable for research because it can represent the decisions more realistically since the same decision is not always made under the same conditions.

### What types of randomized algorithms are there?

There are different types of randomized algorithms, which have different purposes and different uses.

### The Las Vegas Algorithm

The Las Vegas algorithm is a type that uses partially random input to arrive at a correct result. This means that such an algorithm is very practical when a concrete result is needed, but the input has to be chosen variably.

In this definition of the Las Vegas algorithm, the expected complexity of the algorithms is always examined as the expected time complexity. Here it is to be expected that runs of different lengths are obtained on one input. If all runs were approximately the same length, one could simply design an equally efficient deterministic algorithm by simulating a fixed run of the randomized algorithm.

Since the random variables only affect how the algorithm proceeds, the Las Vegas algorithm always gives a correct result when it schedules. The time complexity in this case is a random variable.

### The Quicksort Algorithm

The Quicksort algorithm is a subcategory of the Las Vegas algorithm, with a slightly different mode of operation. A well-known example is the Random Quicksort algorithm, which randomly selects its random variable, but the output is always sorted. This means that best-case and worst-case examples can no longer be constructed. But the worst-case can still occur, of course.

Such an algorithm is very useful when it is necessary to simulate a problem where the worst and the best-case scenario are very relevant and need to be examined more closely.

### The Monte Carlo algorithm

The Monte Carlo algorithm follows a different approach than the other algorithms because the algorithm can also give a wrong result. A Monte Carlo algorithm is a randomized algorithm that aims to achieve a good or approximately correct result by choosing random intermediate results.

Fed with random values, the algorithm may deliver a false result with an upwardly limited probability. This is very helpful if problems are to be mapped where even a wrong result can lead to further insights.

The Monte Carlo algorithm can be used for so-called search problems and for decision problems. A search problem is a problem for which a solution must be calculated and a decision problem is a problem that must be answered with yes or no. The decision problem is especially interesting in this case.

Monte Carlo algorithms for decision problems distinguish between one-sided and two-sided errors. In the case of a two-sided error, a Monte Carlo algorithm may yield both false positives and false negatives. False positives are results where the algorithm answered “Yes” but the correct result would be “No”. False negatives are results where the algorithm answers “No” although “Yes” is the correct answer.

In case of a one-sided error, only one of the two error possibilities is allowed. A common agreement is to speak of a one-sided error and to mean False Negatives. Therefore, a one-sided error is usually understood as a false negative.

### What are Random Decision Making Algorithms used for?

Now that we have clarified what a Random Decision-Making Algorithm is, we still need to explain what such an algorithm can be used for in reality.

These algorithms help to reproduce complex processes such as weather or climate that cannot be analyzed directly. Production processes in a manufacturing company can also be simulated to uncover bottlenecks and opportunities in production. In the real estate industry, derivations can be made from previous valuations to determine the value of an object.

Algorithms are also playing an increasingly important role on the stock exchange, where both the computing capacity and the transmission speed of networks are increasing. If, for example, no analytical formula is known for the valuation of a financial product, a simulation can be used to find suitable distribution assumptions of the relevant random variables and to price complex financial contracts in a simple way.

Physicists can also use such algorithms for their research if it is necessary to map a problem that can be simulated by such an algorithm. Therefore, there are applications for Random Decision-Making algorithms in the economy, but also in science.