TITLE: Unknown Knowns and Explanation-Based Learning
AUTHOR: Eugene Wallingford
DATE: August 30, 2019 4:26 PM
DESC:
-----
BODY:
Like me, you probably see references to this classic quote
from Donald Rumsfeld all the time:
There are known knowns; there are things we know we know.
We also know there are known unknowns; that is to say, we
know there are some things we do not know. But there are
also unknown unknowns -- the ones we don't know we don't
know.
I recently ran across it again in
an old Epsilon Theory post
that uses it to frame the difference between decision making
under risk (the known unknowns) and decision-making under
uncertainty (the unknown unknowns). It's a good read.
Seeing the passage again for the umpteenth time, it occurred
to me that no one ever seems to talk about the fourth quadrant
in that grid: the unknown knowns. A quick web search turns up
a few articles
such as this one,
which consider unknown knowns from the perspective of others
in a community: maybe there are other people who know
something that you do not. But my curiosity was focused on
the first-person perspective that Rumsfeld was implying. As a
knower, what does it mean for something to be an unknown known?
My first thought was that this combination might not be all
that useful in the real world, such as the investing context
that
Ben Hunt
writes about in Epsilon Theory. Perhaps it doesn't make any
sense to think about things you don't know that you know.
As a student of AI, though, I suddenly made an odd connection
... to explanation-based learning. As I described in
a blog post twelve years ago:
Back when I taught Artificial Intelligence every year, I
used to relate a story from
Russell and Norvig
when talking about the role knowledge plays in how an agent
can learn. Here is the quote that was my inspiration, from
Pages 687-688 of their 2nd edition:
Sometimes one leaps to general conclusions after only one
observation. Gary Larson once drew a cartoon in which a
bespectacled caveman, Zog, is roasting his lizard on the
end of a pointed stick. He is watched by an amazed crowd
of his less intellectual contemporaries, who have been
using their bare hands to hold their victuals over the
fire. This enlightening experience is enough to convince
the watchers of a general principle of painless cooking.
I continued to use this story long after I had moved on from
this textbook, because it is a wonderful example of
explanation-based learning.
In a mathematical sense, explanation-based learning isn't
learning at all. The new fact that the program learns
follows directly from other facts and inference rules
already in its database. In EBL, the program constructs a
proof of a new fact and adds the fact to its database, so
that it is ready-at-hand the next time it needs it. The
program has compiled a new fact, but in principle
it doesn't know anything more than it did before, because
it could always have deduced that fact from things it
already knows.
As I read the Epsilon Theory article, it struck me that EBL
helps a learner to surface unknown knowns by using
specific experiences as triggers to combine knowledge it
already into a piece of knowledge that is usable immediately
without having to repeat the (perhaps costly) chain of
inference ever again. Deducing deep truths every time you
need them can indeed be quite costly, as anyone who has ever
looked at the complexity of search in logical inference
systems can tell you.
When I begin to think about unknown knowns in this way,
perhaps it does make sense in some real-world scenarios to
think about things you don't know you know. If I can figure
it all out, maybe I can finally make my fortune in the stock
market.
-----