Skill Mutual Information

Problem

Compute the mutual information between skills and states for unsupervised skill discovery.

With a uniform state distribution, MI = (1 / n_states) * sum over states and skills of p(z|s) * ln(p(z|s) / p(z)), counting only terms with positive probability. Empty inputs return 0.0.

Hint

Maximizing this objective makes skills distinguishable from the states they visit.

Test cases

case 1

in: [[0.5,0.5],[[1,0]]]

expected: 0.6931471805599453

case 2

in: [[0.5,0.5],[[0.5,0.5],[0.5,0.5]]]

expected: 0

case 3

in: [[0.25,0.75],[[0.25,0.75],[0.5,0.5]]]

expected: 0.07192051811294521

case 4

in: [[],[]]

expected: 0

Starter codePython

import math
def skill_mutual_information(skill_probs, posteriors):
    # Your code here
    pass

4 test cases · run your code against them in the editor