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7.9 Relation to GIRL

GIRL is not a synonym for infinitesimal decision making. It chooses a particular decision modality and makes its structures concrete.

Dimension	Infinitesimal Decisions	GIRL
Scope	planning, optimization, games, causal and online decisions, and RL	reinforcement learning
Base declaration	left/right Kan decision semantics	Bellman factorization for values and policies
Typical probe	evidence, preference, constraint, mechanism, or context direction	state, transition, reward, replay, or policy direction
Decision quotient	declared behavioral equivalence of the modality	action-common value variation and advantage contrasts
Consistency test	right Kan compatibility, feasibility, equilibrium, or fixed point	Bellman and policy consistency
Empirical realization	problem-specific and not fixed by the abstraction	GTD, Mirror–Prox, sampled transport, ESS and recovery gates

Table 7.3 GIRL is the reinforcement-learning realization of a broader infinitesimal decision layer.

The distinction also clarifies the architecture of the book. UDL supplies the general base semantics; this chapter tangent-lifts that semantics; Deep LINCS compiles such typed diagrams into differentiable systems; and GIRL instantiates the resulting pattern for Bellman decision making.