I have seen people talk about +R and use prong collars or E collars. I'd like an explanation on that as well. It just doesn't seem like +R. I'm not saying I don't agree with some of the training tools but I don't see how they can be claimed as +R.
Are they referring to prong collars and e-collars as "reinforcement?" Because that could be accurate. You can use those tools to reinforce behaviors by taking away negative stimulus. In operant conditioning terms that would be called negative reinforcement. You could also use the e-collar the same way as a clicker on vibrate, which is what some people do with deaf dogs.
Side note: I had a discussion with a positive trainer once about the appropriate use of aversives to prevent dangerous or psychologically damaging situations from occurring (i.e. better to suppress bad behavior than have it cause a dog fight). They ended up agreeing with me that it was appropriate but disagreed that it constituted training. For them, it constituted management and they didn't believe the dog would learn anything from the situation. So yeah, even a positive trainer might resort to aversives in a pinch, they will just deny that they are training and say that it was an emergency management technique. You can see this in Sophia Yin's videos where she is jerking a dog around on a head halter. So that's how some people get around it, philosophically.
There are some extreme people out there that even believe that a "no reward" marker is damaging to a dog. I don't really get it. I understand that if you use NRMs incorrectly, you will kill the desire to learn quickly, but I don't see how their use itself is a bad thing. That is one side of positive only training. But I think that's very extreme and most people would agree even if they use +R that bad behavior still has to have consequences, it just doesn't merit physical punishment.
I have had the same issues vis a vis distraction proofing that you are describing. I think +R is most effective when you can control the environment, because then you can always set the dog up for success and control the level of distraction. If you can't control the environment, it will still work but it will take a lot longer. For your example of being distracted by other dogs or people, you have to find the "thinking and learning zone," the distance at which your dog is still deciding whether or not to pay attention to you, and reward them consistently when they do pay attention (sometimes with prompting). Then you can gradually decrease the distance. Yes, it is possible to teach reliable behaviors this way. For example, in an environment I *can* control (the kitchen) I can work with my dog with tasty food all over the floor and she won't touch it, because we started with her leaving food alone in my hand, then leaving food alone in my open hand, then leaving food alone on the floor. She learned that making the choice to leave it alone would more consistently result in a reward in the long run than trying to get the food. In fact, leaving the food alone results in a reward 100% of the time, lunging for the food results in a reward 0% of the time. You can apply this principle to anything, but
only if you can control the environment.
BTW this did not take long to teach because it was easy to set the dog up for success. Much harder to do this when you can't control the movement of other people or dogs. So in your case, paying attention to you instead of the other people/dogs needs to result in a reward 100% of the time, and losing focus needs to result in some kind of negative punishment. It should never result in the dog gaining attention from the people or other dogs (good luck with that! This is why +R in a skinner box works much better than +R in real life). Usually withdrawing from the distraction is negative punishment, but I haven't had much luck with that because I don't have the same problem. For my dog, retreating is actually a functional reward because she is uncomfortable.
Anyway that was just a really long-winded way of explaining how you can handle distraction-proofing. It's just showing the dog that certain behaviors are more rewarding than others. Will it work off-lead with squirrels and cats? I doubt it. I used a prong collar for cat-proofing and I'm really glad I did.