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April 23 - September 15, 2018
“optimal stopping”
Optimal stopping is the science of serial monogamy.
question of optimal stopping.
grapple with
anguish.
They don’t need a therapist; they need an algorithm. The therapist tells them to find the right, comfortable balance between impulsivity and overthinking. The algorithm tells them the balance is thirty-seven percent.
finite space and time.
What balance between new experiences and favored ones makes for the most fulfilling life?
how to live.
Alan Turing defined the very notion of computation by an analogy to a human mathematician who carefully works through the steps of
lengthy calculation, yielding an unmistakably right answer.
tackling real-world tasks requires being comfortable with chance, trading off time with accuracy, and using approximations.
Over the past decade or two, behavioral economics has told a very particular story about human beings: that we are irrational and error-prone, owing in large part to the buggy, idiosyncratic hardware of the brain. This self-deprecating story has become increasingly familiar, but certain questions remain vexing. Why are four-year-olds, for instance, still better than million-dollar supercomputers at a host of cognitive tasks, including vision, language, and causal reasoning?
And the mistakes made by people often say more about the intrinsic difficulties of the problem than about the fallibility of human brains.
Often, people need to make decisions while dealing with uncertainty, time constraints, partial information, and a rapidly changing world.
precepts
how to manage finite space, finite time, limited attention, unknown unknowns, incomplete information, and an unforeseeable future; how to do so with grace and confidence; and how to do so in a community with others who are all simultaneously trying to do the same.
simple to explain, devilish to solve, succinct in its answer, and intriguing in its implications.
“leap”
cost for search.
But this doesn’t make optimal stopping problems less important; it actually makes them more important, because the flow of time turns all decision-making into optimal stopping.
Intuitively, we think that rational decision-making means exhaustively enumerating our options, weighing each one carefully, and then selecting the best. But in practice, when the clock—or the ticker—is ticking, few aspects of decision-making (or of thinking more generally) are as important as one: when to stop.
But just as with the look-or-leap dilemma of the apartment hunt, the unanswered question is: what balance?
So is a bookworm settling into a reading chair with a hot cup of coffee and a beloved favorite, or a band playing their greatest hits to a crowd of adoring fans,
exploration can be a curse.
So explore when you will have time to use the resulting knowledge, exploit when you’re ready to cash in. The interval makes the strategy.
competing demands of the explore/exploit tradeoff. Companies want to invest R & D money into the discovery of new drugs, but also want to make sure their profitable current product lines are flourishing.
payoffs decreases geometrically:
exploring. The old adage tells us that “the grass is always greener on the other side of the fence,”
The untested rookie is worth more (early in the season, anyway) than the veteran of seemingly equal ability, precisely because we know less about him.
Exploration in itself has value, since trying new things increases our chances of finding the best. So taking the future into account, rather than focusing just on the present, drives us toward novelty.
“To try and fail is at least to learn; to fail to try is to suffer the inestimable loss of what might have been.”
In general, it seems that people tend to over-explore—to favor the new disproportionately over the best.
To live in a restless world requires a certain restlessness in oneself. So long as things continue to change, you must never fully cease exploring.
I had reached a juncture in my reading life that is familiar to those who have been there: in the allotted time left to me on earth, should I read more and more new books, or should I cease with that vain consumption—vain because it is endless—and begin to reread those books that had given me the intensest pleasure in my past.
aging—the result of diminished ability to contribute to social relationships, greater fragility, and general disengagement from society. But Carstensen has argued that, in fact, the elderly have fewer social relationships by choice. As she puts it, these decreases are “the result of lifelong selection processes by which people strategically and adaptively cultivate their social networks to maximize social and emotional gains and minimize social and emotional risks.”
The point is that these differences in social preference are not about age as such—they’re about where people perceive themselves to be on the interval relevant to their decision.
Being sensitive to how much time you have left is exactly what the computer science of the explore/exploit dilemma suggests.
The explore/exploit tradeoff also tells us how to think about advice from our elders. When your grandfather tells you which restaurants are good, you should listen—these are pearls gleaned from decades of searching.
“To lower costs per unit of output, people usually increase the size of their operations,”
Big-O notation provides a way to talk about the kind of relationship that holds between the size of the problem and the program’s running time.
Computer science, as undergraduates
are taught, is all about tradeoffs.
Sorting something that you will never search is a complete waste; searching something you never sorted is merely inefficient.
Computer science shows that the hazards of mess and the hazards of order are quantifiable and that their costs can be measured in the same currency: time.
Sometimes mess is more than just the easy choice. It’s the optimal choice.
If NCAA basketball games, say, are won by the stronger team 70% of the time, and winning the tournament involves prevailing in 6 straight games, then the best team has only a 0.70 to the 6th power—less than 12%—chance of winning the tournament! Put another way, the tournament would crown the league’s truly best team just once a decade.
but it’s exceptionally fault-tolerant. This algorithm’s workings
In many animal societies, resources and opportunities—food, mates, preferred spaces, and so forth—are scarce, and somehow it must be decided who gets what.
They must make a tradeoff between size and speed.
