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From ancient chemistry experiments to artificial intelligence: How is random search changing the world of optimization?
With the advancement of science and technology, various numerical optimization methods emerge in endlessly. Among them, Random Search (RS), as a numerical optimization technique that does not require gradient calculation, has begun to attract the attention of many scientists and engineers. This method works with continuous or non-differentiable functions, making it an important tool for solving complex problems.
Random search is not just a mathematical method, but a strategy that changes our understanding and application of optimization.
With Anderson's review of this method in 1953, the concept of random search gradually took shape. Anderson mentioned using a series of hypotheses with a specific arrangement to find the best solution. These searches can be performed as grid or sequence searches in the parameter space, and iterate continuously on the basis of the best guess.
Random search is named after Rastrigin, who proposed this method in the early days and performed basic mathematical analysis. RS searches for better positions by iteratively moving through the search space. The candidate solutions of each round depend on the search results of the previous round, which allows this method to quickly converge to a good solution in some cases.
If the effective search area only occupies 5% of the entire search space, the probability of successfully finding at least one good configuration after 60 attempts will be more than 95%.
Random search has been widely used in hyperparameter optimization of artificial neural networks. As data volumes grow and problems become more complex, effective search methods become increasingly important. Random search can not only adapt to complex data structures, but also quickly screen out the best solutions in a large number of configurations.
Random search algorithm
The basic random search algorithm is as follows:
- Initialize a random position x in the search space.
- Until the termination condition is met (for example, a certain number of iterations or appropriate fitness is reached), repeat the following steps:
- Randomly sample a position y from the hypersphere at the current position x.
- If f(y) < f(x), move to the new position by setting x = y.
The power of random search lies in its ability to circumvent the limitations of traditional methods and still find effective solutions in complex environments.
Random search variations
Although the random search process can run randomly, there are also a variety of structured random search variations designed to increase search efficiency. For example, the Friedman-Savage procedure is a strategy that searches sequentially on each parameter and takes a set of guesses with spatial patterns.
On the other hand, Fixed Step Size Random Search (FSSRS) and Optimized Step Size Random Search (OSSRS) are other variants based on random search. FSSRS searches by sampling from a fixed-radius hypersphere, while OSSRS focuses on how to adjust the radius of the hypersphere to accelerate convergence.
The structured variant of random search shows its potential to improve search efficiency and accuracy.
Related research and applications
Stochastic optimization is a field closely related to stochastic search. These methods often derive key information from observational data. For example, the Luus–Jaakola method uses uniformly distributed sampling for simple stepwise optimization. In addition, pattern search methods focus on searching along the coordinate axes of the search space and use an exponentially decreasing step size strategy.
Like any technology, random search also faces challenges, especially performance issues in large data sets and high-dimensional spaces. However, the flexibility and versatility of random search make it still a very popular choice even in current artificial intelligence applications.
Random search is slowly becoming a trend-setting force, not only changing traditional optimization thinking, but also promoting innovation in the entire technological world. What new technologies and methods will be born in the future to further expand the application fields of random search?
