  We consider a general class of non-linear Bellman equations. These open up a
design space of algorithms that have interesting properties, which has two
potential advantages. First, we can perhaps better model natural phenomena. For
instance, hyperbolic discounting has been proposed as a mathematical model that
matches human and animal data well, and can therefore be used to explain
preference orderings. We present a different mathematical model that matches
the same data, but that makes very different predictions under other
circumstances. Second, the larger design space can perhaps lead to algorithms
that perform better, similar to how discount factors are often used in practice
even when the true objective is undiscounted. We show that many of the
resulting Bellman operators still converge to a fixed point, and therefore that
the resulting algorithms are reasonable and inherit many beneficial properties
of their linear counterparts.
