This is a section that is still in it’s beginning stage. Please contribute if you can put into words your vision on the issue.
To open the subject, one can maybe say there are two aspects to discuss, which of course can be worked out much more:
1. Audience Rules
This can be the relatively ‘technical’ issue of how performance- and audience space are defined, and in which way performers are allowed to interact with the audience (and vice versa).
See also Context (&basic agreements).
For example: Are you performing only on stage or also in between the audience? Is the audience allowed to change position or even come on stage? Or is it a ‘4th wall’ performance (where spaces are clearly seperated and performers never acknowledge the presence of the audience at all)?
Also consider that if there are any rules that the audience should know about, how is that communicated to them, prior to (or during) the performance?
2. Relationship and Attitude towards your audience
What is the way you see your relationship with the audience as a performer: Do you perform for them or for something else? Do you acknowledge their presence or ignore them? These are all issues related to States of Being (& roles to take)
More questions to consider these attitudes/roles: Is the audience for you simply an uninvolved witness, are they accomplices in your deed or are they paying customers (or maybe a combination of the three)? Do you want them to know that you are improvising or decidedly not?
One thing worthwhile discussing in this context is the issue of ‘hosting’:
In how far do you feel responsible for being a ‘good host’ for your audience? In the end, they are your ‘guests’, having come to your performance, or not? Or maybe you reject seeing your relationship with your audience in this way… Sometimes, the role of the ‘host’ is played by someone else (not the improvisation performers), but always we do have to relate to the fact that there are people who have come to see us. So how do we see our role in this, how de we see our relationship to them?
Please add your vision on the subject and/or more related questions.
Interdisciplinary Instant Composition 
One of our teachers, I think it was Andrew Morrish, says if you are not having a good time on stage, the audience is not having a good time either. I would postulate that the structure of an improvisational piece is predicated as much on the audience as it is on the performers, the place, the accessories, the weather and the time. While we can perform for ourselves, we are here on this earth for the relationships, and the audience/performer relationship is a formal context of considerable importance.
Very true. Thanks for adding this, createursdelinstant. I totally agree with Andrew and also your postulation 😉 . Our relationship with the audience is in my opinion one of the most important things to look at when we work on live performance. It is also one of the most confused/confusing issues in contemporary art, as some artists defend their attitude of not being bothered with audience at all with the argument that it is not their job to ‘entertain’ their audience. But ‘taking care of the relationship’ doesn’t need to mean at all that you have to entertain. It is simply about giving value and consideration to the fact that someone else is giving you attention and therefore you also give attention to that shared moment (which includes the other). It is very straightforward in fact, but then again, which relationships are ever (only) straightforward ? 🙂