THEORY-091: Command-to-outcome mutual information scores an interface because it measures how reliably the operator's input determines what happens at the chosen horizon, which rewards a learnable channel rather than an intuitive one

Source

Reddy, Levine and Dragan (2022), LIT-503, read as NOTE-250.

The account

The paper’s version. Whatever the user is trying to do, an intuitive interface produces less noisy commands, so the mutual information I(x_t, (s_t, s_{t+Δ})) between command and induced state change rises with interface quality and needs no knowledge of the task.

That is LIT-503’s proposal, and the results this account rereads are its own. Offline, on 540K examples of keyboard and eye-gaze interfaces, the score predicted task reward in 4 of 5 domains at an average Spearman ρ = 0.43. Online, maximized by human-in-the-loop RL over an 8-parameter cursor interface with 12 users, it correlated with task reward at ρ = 0.87.

The version its results support. The quantity measured is how much the operator’s input determines the state Δ steps later: how reliable the channel from what they do to what happens is. That tracks task success whenever success requires the operator to steer, which is why it ranks interfaces without labels. It is not a measure of intuitiveness, because the operator adapts. A mapping they find unnatural but consistent becomes one they can steer through, and it scores as well as a natural one.

What it explains

The practice is SOTA-309, and this account explains both of its instructions: why the score ranks interfaces with no labels, and why the horizon Δ has to be chosen deliberately, since it sets which states the operator’s input is being credited with determining.

• The bimodal convergence. Over 12 users, learned cursor interfaces settle on no perturbation (θ ≈ 0) and on exact inversion (θ ≈ π). Both are consistent. Only one is intuitive. The score cannot prefer it, and the result shows it does not.
• The sign flip. In shared-autonomy Lunar Lander the assistant overrides commands to prevent crashes. Commands then determine less of the next state and more of the states that follow, because the lander is still flying. One-step influence falls and long-horizon influence rises, so the correlation with reward is strongly negative at Δ = 1 and positive at episode length. The paper’s version does not predict this: the interface did not become less intuitive.
• Why online beats offline (ρ = 0.87 against 0.43). In the online study one user adapts to one interface family on one task, so steerability and success are close to the same thing. Across heterogeneous offline domains they come apart more.

Where it is weak

• It is a reading of one paper’s results, not something the paper tests. The bimodal convergence is the evidence for it, and it comes from one 8-parameter cursor task with 12 users.
• Consistency and intuitiveness were not separated by design. No condition compares an equally consistent but unnatural mapping against a natural one before adaptation, which is the test in promote_when.
• “Determines the outcome” hides the choice of Δ. The account says why the horizon matters. It does not say how to pick one without knowing the user’s timescale, which the source names as its main limitation.

What it does not say

It does not say the score is wrong to prefer a consistent channel. For a prosthesis used every day, a mapping the user can learn may be the right target. The claim is that the score measures learnability, and a reader who takes it as a measure of intuitiveness will be surprised by an inverted mouse.