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A Theory of Cheap Control in Embodied Systems

Fig 5

Illustration of the exponential family Eq (11) of policies.

This figure shows an example with ∣𝒲∣ = 3 and ∣𝒜∣ = 2 and a policy-behavior map ψ with embodied behavior dimension d = 2. In this case, the polytope is the three-dimensional cube of 3 × 2 row stochastic matrices shown in the middle. The curved surface within is the exponential family , which is parametrized by two parameters. The exponential family is mapped by the policy behavior map ψ to the same set of behaviors (the hexagon illustrated in the right) as the set of all policies.

doi: https://doi.org/10.1371/journal.pcbi.1004427.g005