# On the power of random information

## TL;DR

This paper investigates how random information compares to optimal information in approximation and integration problems, showing that randomness can be nearly optimal in some cases and significantly worse in others.

## Contribution

It provides new theoretical results and a survey on the effectiveness of random versus optimal information in computational problems.

## Key findings

- Random information is nearly optimal for some problems.
- In other problems, random information performs much worse than optimal.
- The paper offers a comprehensive overview of known and new results.

## Abstract

We study approximation and integration problems and compare the quality of optimal information with the quality of random information. For some problems random information is almost optimal and for some other problems random information is much worse than optimal information. We prove new results and give a short survey of known results.