### Summary

Anytime algorithms are flexible computation methods that provide better solutions the more computation time they have. Essentially, these algorithms can yield a valid solution at any point in time, with the quality of answers generally improving as time goes on.

### ELI5

Imagine you’re searching for lost treasure in a field. You could go over the field inch by inch, making sure you don’t miss anything, but that would take a lot of time. Instead, you decide to start by quickly looking over the whole field, then go back and search more carefully where you think the treasure might be. You can stop at any moment you want, but the longer you search, the more likely it is that you’ll find the treasure. That’s how an anytime algorithm works!

### In-depth explanation

Anytime algorithms are computation strategies that solve optimization problems and can provide a solution at any point in the computation. They work in a continuous manner, and their name comes from their property to deliver progressively refined solutions as they are allowed to run for longer timespans.

These algorithms are typically used in situations where solution quality is variable, resources are unpredictable, or time constraints exist. They are particularly effective in decision-making environments, robotics and real-time systems where time for computation can be limited.

The main design goal of anytime algorithms is to return the best possible solution given the allotted computation time. It means an anytime algorithm will perform a trade-off between the quality of the solution and the computation time. If an anytime algorithm is forced to stop prematurely, it will aim to have the best possible partial answer ready.

Although the quality of the solution generally improves with time, it’s not always a linear development. For example, an algorithm might find a fairly good solution quite early on, then spend a long time exploring less fruitful avenues before eventually finding a better solution.

Several types of anytime algorithms exist, including contract, interruptible, and real-time algorithms. Contract algorithms require a specified amount of computation time beforehand and offer no benefit if terminated early. Interruptible algorithms can be stopped and resumed but also don’t provide partial results. Real-time anytime algorithms offer the best of both worlds, allowing frequent, provisional results that get better over time.

As a key element of real-world AI systems, anytime algorithms are fundamental to achieving effective and flexible decision-making, especially in dynamic, unpredictable environments.

Bounded Rationality, Computational Intelligence, Decision-Making System, Heuristic Search, Optimization Algorithm, Real-Time Systems, Stochastic Algorithm.