De Rerum Natura

One of my favorite games to play when I drive is to try to estimate the ideal throughput speed — the speed at which you can go through traffic without having to change your speed. This involves a couple of behavioral changes: you have to allow more space than normal between you and the car in front, you have to be aware of upcoming red lights, etc. Over the years I have found that some drivers behind me get really annoyed over the amount of space in front of me. They race around and drive as fast as they can to the red light ahead whereupon they have to immediately brake. Sometimes I get to go past these drivers since I approach the green light moving while they have to race me again from a dead stop.

It occurred to me the other day that if the driver behind me noticed that I was doing this, they could, in turn, engage in the same estimation game. Their estimate, however, would be better than mine since I am already smoothing out the flow in front of them. This computational chain could continue behind them, each time getting easier and easier to estimate the ideal throughput speed no matter how uncertain the traffic was in front of us. Is this a computation in series or in parallel? We are doing it at the same time so it is in parallel, but each driver depends on the estimate in front of them so it is in series.

This weekend I was talking to a friend from graduate school about how to stabilize errors in uncertain environments by sacrificing accuracy, the subject of the previous two posts. During the conversation, I realized another advantage of stabilizing errors: it makes it easier to modify your detector/classifier in an adversarial situation.

The “arms race” game is a common one in conflict situations. You have some technological advantage over an opponent. The opponent adapts and changes their strategy. This is different from the issue of a noisy environment. Here the signal used by your detector is intentionally modified to circumvent its performance level. The enemy camouflages their tanks better. New strategies are deployed. All of which leads to an increase in the error rate of your detector.

A user confronted with this situation would want to slow down their error rate increase so it can be below their learning rate. Such a user would be willing to sacrifice accuracy for the ability to adapt to an adversary. There is a strategic advantage to stabilizing errors.