If the garbage is located where the person left it for the regular trash collector to come and get it, then yes, the police can collect the garbage without a warrant.  For example, if you leave your trash on the drive-way for the collector and that is where the collector has always picked up discarded trash-- then it would be considered abandoned property at the point the bag or container was placed in that spot which you have made open to the public, even though the garbage is technically on private property.By contrast, however, if the garbage is not in it's usual spot--- for example by the front door waiting to taken to it's usual spot, then that may not be considered discarded property.  It seems like a fine line, but the distiction is important to discern what is abandoned or discarded property and what is not.