You Will Know Them by Their Fruits

People seek to optimize on a daily basis. For example, I spend a great deal of my time fretting over (I wouldn't go so far as to call what I do thinking) how best to use my time. In my working memory, I have a finite set of activities I could undertake, and I wonder which one is 'best' given the constraints of my present surroundings, energy level, motivation, etc.

This optimization 'model' thus assumes I have some sort of objective function (if we're feeling grandiose, we could call it a utility function) that I want to maximize, call it \(f\), a set of possible activities, call them \(\mathcal{X} = \{ x_{1}, x_{2}, \ldots, x_{|\mathcal{X}|}\}\), and some current 'state,' call this \(s\), and then I'm looking to find

\[ x^{*} = \arg \max_{x \in \mathcal{X}} \ \ f(x; s) \text{ subject to } R(s) = c.\]

Of course, I stand no chance of enumerating \(\mathcal{X}\), no chance of finding a mapping \(f\) from activities to some sort of objective function that would determine the 'best' activity, and no reasonable constraint function \(R\) that determines what things I am capable with a given state \(s\).

The fact that this sort of optimization view of human activity is intractable is not news. Herbert Simon addressed this issue in his work. Some relevant quotes:

At each step toward realism, the problem gradually changes from choosing the right course of action (substantive rationality) to finding a way of calculating, very approximately, where a good course of action lies (procedural rationality).

— Herbert Simon, The Sciences of the Artificial

I am an adaptive system, whose survival and success, whatever my goals, depend on maintaining a reasonably veridical picture of my environment of things and people. Since my world picture approximates reality only crudely, I cannot aspire to optimize anything; at most, I can aim at satisficing. Searching for the best can only dissipate scarce cognitive resources; the best is enemy of the good.

— Herbert Simon, Models of My Life, p. 360

The life is in the moving through that garden or castle, experiencing surprises along the path you follow, wondering (but not too solemnly) where the other paths would have led: a heuristic search for the solution of an ill-structured problem. If there are goals, they do not so much guide the search as emerge from it. It needs no summing up beyond the living of it.

— Herbert Simon, Models of My Life, p. 367

In other words, the best we can hope for is an approximate (heuristic) solution to a weakened phrasing of the optimization problem above.

One way to solve that problem is to look at how other people have tried to solve it. But then we run into a another issue: we frequently don't have access to \(x^{*}\), but rather \(f(x^{*})\). And presumably many, many of the \(x \in \mathcal{X}\) will lead to very similar \(f(x; s)\) (it's doubtful that \(f\) isn't many-to-one). So, we judge people by outcomes, while we'd like to emulate their actions.

Add in the fact that there's a large stochastic component to all of this (imaginatively, let's call it luck), and the 'optimization via imitation' program also fails.

Of course, the best we can do (and what we ultimately do, in the absence of any particular plan) is sample \(\mathcal{X}\) more or less at random. Most of the time, this will give us suboptimal \(f(x; s)\). But sometimes we'll happen on a reasonable solution. We can do better than sampling at random if we use some other heuristic. For instance, we might record what action we took and our current state, and then note any quantifiable outcomes. Any heuristic for optimization will most likely do better than sampling at random (especially if we perform our sampling in a biased manor, like getting stuck in a rut), and this heuristic quantification approach seems like a reasonable step up from random sampling.

All of this is, of course, more or less useless. I can't think of many useful things that might come from this viewpoint of life. Or perhaps I am just in a pessimistic mood at the moment.