I don't think "satisficer" is a good name for the concept you're describing here. For one thing, I think it's weird to see a satisficer with just a function (I presume that's what u is?) as its input--where's the threshold of acceptability?
I think a well-specified satisficer as traditionally conceived looks like this:
Thus we can consider some problem (basically, the set X that describes all possible solutions), and throw a satisficer S(u,u_0,(x_t)) at it, and know exactly which solution x will be picked by S. (I think my notation for the proposal sequence is awkward; if there's a finite set of solutions, we can describe it as a permutation of that set, but that implies some restrictions I don't like. I'm using the parentheses so I can differentiate (x_t), the set of all of them, and x_t, the t-th one.)
Some obvious generalizations suggest themselves: the desirability threshold, rather than just looking at u(x_t), could look at some function of u(x_i) and x_i where i ranges from 0 to t. x_t+1 could depend on u(x_i) rather than just t. x_t+1 could have a source of randomness (in which case we now have a distribution over solutions, rather than a single known solution).
We can then talk about other properties. Perhaps we want to describe satisficers that consider the entire solution space X as "complete," or the ones that only consider each solution at most once "nonrepeating." Most importantly for you, though, a "well-behaved" satisficer has that the property that the proposal sequence x_t is arranged in ascending order by some measure n(x_t) of effort and negative externalities. Maintaining the correct level of illumination in a room by adjusting the curtains comes very early in the ordering; launching a satellite to block the sun comes much, much later; launching a mission to destroy the sun comes so late in the ordering it is almost certain it will not be reached.
This property suggests that a well-behaved satisficer is basically solving two optimization problems simultaneously, on u and n. (The way you'd actually write it is min n(x) s.t. u(x)>u_0, x\in X.)
To maintain the computational simplicity that satsificers are useful for, though, we wouldn't want to write it as a minimization problem. This requires us to use a less restrictive version of 'well-behaved,' where the proposal function is 'generally' increasing in effort rather than strictly nondecreasing in effort.
Thanks for your suggestion.
A putative new idea for AI control; index here.
EDIT: The definition of satisficer I'm using here is the informal one of "it tries to achieve a goal, without making huge changes on the universe" rather than "it's an agent that has utility u and threshold t". If you prefer the standard notation, think of this as a satisficer where t is not fixed, but dependent on some facts in the world (such as the ease of increasing u). I'm trying to automate the process of designing and running a satisficer: people generally chose t given facts about the world (how easy it is to achieve, for instance), and I want the whole process to be of low impact.
I've argued that the definition of a satisficer is underdefined, because there are many pathological behaviours all compatible with satsificer designs. This contradict the intuitive picture that many people have of a satisficer, which is an agent that does the minimum of effort to reach its goal, and doesn't mess up the outside world more than it has to. And if it can't accomplish the goals without messing up the outside world, it would be content not to.
In the spirit of "if you want something, you have to define it, then code it, rather than assuming you can get if for free through some other approach", can we spell out what features we would want from such a satisficer? Preferably in a simpler format that our intuitions.
It seems to me that if you had a proper u-satisficer S(u), then for many (real or hypothetical) v-maximiser M(v) out there, M(v) would find that:
Further, S(u):
A subsequent post will present an example of a satisficer using some of these ideas.
A few other much less-developed thoughts about satisficers: