Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.hsvi

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

AHoF D73 HSVI (Heuristic Search Value Iteration for POMDPs): maintain an upper and a lower bound on the optimal value function and search belief points to tighten them; the algorithm has converged at a belief when the bound gap is within the target precision: converged? gap epsilon = decide (gap <= epsilon). A gap 1/4 within precision 1/2 is converged; a gap exactly at precision is converged; a gap 3/4 above precision is not. Proved native and axiom-free (decision, converged and boundary instances, at-most gap certificate, unconverged). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound. 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.hsvi` prints this classification.

hsvi/converged? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

hsvi/small-gap-converged :
  → ce-is/elite? 1/4 1/2 = data/true

hsvi/boundary-gap-converged :
  → ce-is/elite? 1/2 1/2 = data/true

hsvi/gap-certificate :
  → 1/4 ≤ 1/2

hsvi/large-gap-unconverged :
  → ce-is/elite? 3/4 1/2 = data/false