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Measuring Goal-Directedness

NeurIPS 2024 · Learning theory and algorithms › Prediction and decision losses · approach: Adaptive testing and experiments · 0 citations (OpenAlex)

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Defines maximum entropy goal-directedness (MEG), a causal, scale-invariant measure of how well a utility function predicts a policy's behaviour via maximum causal entropy, with algorithms for MDPs and small CliffWorld experiments.

Problem

Measuring how goal-directed a system's decision variables are, i.e., to what extent a policy can be predicted as optimising some utility function, in causal models and MDPs.

Approach

Adapts maximum causal entropy IRL: for each attainable expected utility, take the maximum-entropy policy attaining it (a soft-optimal Boltzmann policy with rationality beta), and define goal-directedness as the best predictive log-likelihood gain over the uniform policy. This yields scale and translation invariance, works with known or hypothesised utility classes, and handles arbitrary (nonlinear

Key results

• Known-utility MEG for epsilon-greedy policies in CliffWorld falls from 2.4 at epsilon=0.1 to 0.001 at epsilon=0.8, tracking reduced optimality.
• Known-utility MEG decreases as the goal region grows from k=1 (37.8) to k=3 (16.8), while unknown-utility MEG stays around 32-35 across k.
• Proves MEG is translation and scale invariant, bounded between 0 and sum of log domain sizes, and zero for variables the decision cannot influence.

Measured effects reported in the paper

Surprising findings

• A policy that pessimises a utility function can be just as goal-directed as one that optimises it.
• Naively plugging a utility into the MCE policy is not scale-invariant (predictive accuracy -0.018 vs -0.13 for 2U vs U).

Limitations

• Requires environment access to run policies; cannot compute from purely observational data.
• Gradient-based unknown-utility algorithm may be computationally intractable in high dimensions and only gives a lower bound for non-convex classes.
• Results depend heavily on chosen variables and distributional shifts; only small-scale experiments.

Experimental setup

Datasets: CliffWorld (seals suite)

Benchmarks: CliffWorld

Metrics: MEG (predictive accuracy relative to uniform, nats) cross-entropy

Baselines: MCE IRL discovering agents causal discovery

Builds on: maximum causal entropy IRL causal influence diagrams maximum entropy reinforcement learning Discovering Agents

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