Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.lp-mdp

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/lp_mdp.clj1 definitions, 4 theorems

AHoF D24 LP Formulation of an MDP: the optimal value function is the solution of a linear program that minimizes the total value subject to the Bellman inequality constraints -- for every state-action pair the value must be at least its one-step backup R + gamma * E[V']: satisfies-bellman? backup value = decide (backup <= value). A value that meets or exceeds its backup is LP-feasible for that constraint; a value below its backup violates it. Proved native and axiom-free: the constraint decision, a feasible and a tight instance, the native at-most feasibility certificate, and a violated instance. Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.lp-mdp` prints this classification.

lp-mdp/satisfies-bellman? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

lp-mdp/feasible-value :
  → lis/extends? 1/2 3/4 = data/true

lp-mdp/tight-constraint :
  → lis/extends? 3/4 3/4 = data/true

lp-mdp/feasibility-certificate :
  → 1/2 ≤ 3/4

lp-mdp/violated-constraint :
  → lis/extends? 3/4 1/2 = data/false