The phrase "without supervision" could be replaced with any number of synonyms depending on the context in which it is used. Some possible alternatives include unsupervised, unmonitored, uncontrolled, unchecked, free-range, self-directed, self-regulated, independent, self-governed, autonomous, self-managed, self-organized, self-reliant, self-sufficient, free-willed, unattended and unguided. Each of these words have a slightly different connotation and might be more appropriate in certain situations. For instance, "unmonitored" might be used to describe a situation where someone is not being watched closely, while "autonomous" implies a higher degree of independence or self-determination.