PYTHON · NUMPY

The average of two good answers

Show that minimising squared error against a set-valued demonstration returns the mean, and that the mean can be invalid.

01Challenge

Demonstrations show a robot going left and right around an obstacle in equal numbers. Fit the squared-error optimum and check whether it is a legal action.

Predict firstSixty demonstrations, half at minus 0.55 and half at plus 0.55 radians. Where does the squared-error optimum land?

02Model

A robot faces an obstacle. Going left is correct. Going right is correct. A human demonstrates both, roughly equally, because both are fine. Now fit a policy by minimising mean squared error against those demonstrations. The value that minimises squared error against a set of numbers is their mean, and that is not a modelling accident, it is what the loss is defined to do. The mean of go-left and go-right is go-straight, which is the one action that is certainly wrong. The important part is what does not fix it. More demonstrations do not fix it; they make the mean more precisely wrong. A bigger network does not fix it either, because the network is being asked to output one number and one number is the wrong type of answer. The correct answer here is a set, and the loss can only represent a point.

03Guided practice

Compute the squared-error optimum over all demonstrations, then test it against the obstacle.

04Feedback

PASS WHEN You found that the optimum is illegal while every demonstration is legal.

If your run fails, check:

Every single training example is a valid action. Their average is not. That gap is structural, not statistical.
More data drives the optimum toward exactly zero, which is the centre of the obstacle. Scale makes it worse, not better.
The loss is doing precisely what it was asked to do. The error is in asking a point-valued model to represent a set.

05Retrieve & space

Why does adding demonstrations fail to help here?
State the type error in one sentence: what type is the correct answer, and what type does the model return?
Name a task from your own work where the correct answer is a set rather than a point.

06Mastery & project

Given a set-valued demonstration distribution, predict where a squared-error policy lands and whether it is valid.

Find a real behaviour in your domain with two equally good executions. Ask what a regression model trained on both would output, and whether that output is safe.

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PYTHON · NUMPY

The average of two good answers

Sixty demonstrations, half going left, half going right. Find the value squared error selects and check it.

You read

the arrays and values already in scope

You change

the code you write in each cell

Fixed

the dataset and the checks that grade you