1. A system for providing low-latency computational capacity from a virtual compute fleet, the system comprising: an electronic data store configured to store at least a program code of a user; and a virtual compute system comprising one or more hardware computing devices executing specific computer-executable instructions, said virtual compute system in communication with the electronic data store, and configured to at least: maintain a plurality of virtual machine instances on one or more physical computing devices, wherein the plurality of virtual machine instances comprise a warming pool comprising virtual machine instances having one or more software components loaded thereon and waiting to be assigned to a user, and an active pool comprising virtual machine instances currently assigned to one or more users; receive a request to execute a program code associated with a particular user on the virtual compute system, the request including information indicating the program code and the particular user associated with the program code; determine, based on the received request, a user-specified security policy specifying one or more security parameters by which the program code is to be executed; select from the warming pool or the active pool a virtual machine instance to be used to execute the program code; determine that the virtual machine instance does not contain a configured container that has the program code loaded thereon and configured according to the user-specified security policy; create a container in the selected virtual machine instance based on the user-specified security policy; and cause the program code associated with the particular user to be loaded from the electronic data store onto the container and executed in the container according to the user-specified security policy.