Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.deterministic-pg

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/deterministic_pg.clj3 definitions, 3 theorems

AHoF D55 Deterministic Policy Gradient: the DPG theorem gives the gradient as the chain product of the action-value gradient and the policy Jacobian, grad = ∇_a Q · ∇_θ μ: policy-gradient q-grad mu-grad = q-grad * mu-grad (over signed). Worked: 2 * 3 = 6. Values proved by signed cross-product equivalence. Proved native and axiom-free. Requires signed/multiply (from rainbow.math.rational.signed.multiply, chained), signed/from-nnrat, signed/equivalent. Scope (measured by the kernel): this module has 2 worked instances (statements about specific values) and 1 definitional unfoldings (true by unfolding a definition). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.deterministic-pg` prints this classification.

Depends onmath.rational.signed.multiply

det-pg/policy-gradient :
  (x₁ x₂ : ℚ)
  → ℚ

det-pg/gradient-example :
  → ℚ

det-pg/unit-jacobian :
  → ℚ

det-pg/policy-gradient-unfold :
  (a b : ℚ)
  → det-pg/policy-gradient a b = a · b

det-pg/gradient-example-is-6 :
  → det-pg/gradient-example = signed/from-nnrat 6

det-pg/unit-jacobian-is-3 :
  → det-pg/unit-jacobian = signed/from-nnrat 3