Here is a mosaic from Pompeii showing a Roman dog in a leash:

(Image from Wikipedia.)
Other similar pictures of mosaics are easy to find online, so I am confident that dog leashes were a well known thing in Roman culture. But I have yet to see a similar picture with the other end of the leash in a human hand.
Did the Romans walk their dogs in leashes the way we modern people often do? Or were leashes just used to tether the dog to a building or other structure to prevent them from leaving their guard post or otherwise escaping? I am interested in any kind of evidence, but we should probably try to focus on written evidence as this is a language site. Are there passages in Roman literature that describe what dogs in leashes do?
Any written descriptions of dogs in leashes would help here. If, for example, all or most written mentions of a dog in a leash have nothing to do with walking a dog, I will happily accept that the Romans did not probably walk their dogs. If they had no concept for walking a dog, I would not assume anyone to have explicitly mention their not doing so. But given the archaeological evidence, I would be very surprised not to have several written accounts of dogs in leashes.
This is connected to whether dogs were kept indoors or outdoors. If some were kept indoors, then they had to be left out to do their business — any such accounts would be great to see. If only outdoors, then walking a dog might be less useful.