PYTHON · NUMPY · IN-BROWSER

Linear Behavior Cloning

Fit the simplest possible policy — one linear map from observation to action — in closed form, and measure it on held-out episodes.

01Challenge

Solve a least-squares behavior-cloning policy and confirm it beats the mean baseline on the held-out episodes.

02Model

Behavior cloning is supervised learning on a robot: fit a function from observation to the action the expert took. Start with the simplest function there is, a straight line, solved in one shot by least squares. It will not be perfect, the expert's law curves, but a linear policy learned from data already leaves the hand-coded rule far behind. This is your floor; everything after this earns its keep by beating it.

03Guided practice

1. Fit on train only. Compute the normalization stats on the training frames, then z-score everything with them.

2. Least squares. Add a bias column of ones so the line can shift, then solve A · Wb ≈ actions with np.linalg.lstsq. That is behavior cloning in closed form.

3. Score it honestly. Report the mean squared error on the held-out episodes, and the fraction of the action variance it explains.

04Feedback

PASS WHEN PASS when the linear policy's held-out MSE is well under the mean baseline (it explains most of the action variance).

A cell errored — run them top to bottom.
The least-squares solve should clearly beat predict-the-mean.

05Retrieve & space

What does behavior cloning fit? (a function from observation to the expert's action).
How is a linear policy solved? (least squares, in closed form).
Why add a bias column of ones? (so the linear map can shift, not just rotate).

06Mastery & project

You can fit and honestly score a linear behavior-cloning policy — the floor every richer policy must beat.

A reflex worth keeping: always fit the simplest baseline first, so you know what 'better' has to mean.

← The Dataset Is the Program A Neural Policy, Trained by Gradient Descent →

action,\n# solved in closed form by least squares. Add a bias column so it can shift.\ndef fit_linear(Xtr, Ytr):\n A = np.concatenate([Xtr, np.ones((Xtr.shape[0],1))], axis=1)\n Wb, *_ = np.linalg.lstsq(A, Ytr, rcond=None) # (8,3)\n return Wb\ndef pred_linear(Wb, Xq):\n A = np.concatenate([Xq, np.ones((Xq.shape[0],1))], axis=1)\n return A @ Wb\nWb = fit_linear(X[tr], act[tr])\nval_mse = float(((pred_linear(Wb, X[val]) - act[val])**2).mean())\nbase = float(((act[val] - act[tr].mean(0))**2).mean())\nprint(f\"linear BC held-out MSE {val_mse:.2e} baseline {base:.2e} \"\n f\"variance explained {100*(1-val_mse/base):.1f}%\")","label":"Least-squares behavior cloning"},{"code":"# A linear policy already beats the mean baseline by a lot. It's our floor.\nassert val_mse < 0.35*base, \"linear BC should clearly beat the mean baseline\"\nprint(\"PASS - a linear policy, learned from data, beats the hand baseline.\")","label":"It beats the baseline"}],"intro":"Fit a linear behavior-cloning policy with least squares and evaluate it on held-out episodes.","key":"robot-learning/linear-behavior-cloning","kind":"python","title":"Linear Behavior Cloning"}">

PYTHON · NUMPY · IN-BROWSER

Linear Behavior Cloning

Fit a linear behavior-cloning policy with least squares and evaluate it on held-out episodes.

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