Further reading

Universal Decision Learning and its left/right Kan formulation are developed in Mahadevan [ 2026l ] . Standard accounts of Kan extensions and their pointwise formulas are given by Mac Lane [ 1971 ] and Riehl [ 2017 ] . The categorical background in Chapter 0 explains the universal properties used here, while Chapters 4 and 5 supply the tangent and intervention semantics.

For the reinforcement-learning specialization, see Sutton and Barto [ 2018 ] and the GIRL development in Chapter 15. Pearl’s intervention hierarchy [ Pearl , 2009b ] is essential for separating an ordinary parameter perturbation from a causally grounded mechanism change. The nonsmooth boundary connects to the generalized derivative and subdifferential discussion in Chapter 1; its central lesson is that a switching or set-valued decision requires a richer tangent object, not an arbitrary choice of one gradient.