Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.pomcp

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/pomcp.clj2 definitions, 3 theorems

AHoF D75 Online POMDP (POMCP): Monte Carlo tree search in belief space, selecting actions at each node by their UCB score and keeping the higher-scoring action. With two actions the search prefers action 0 when its UCB is at least action 1's and the node value is the larger UCB: prefers-action-zero? u0 u1 = decide (u1 <= u0) node-value u0 u1 = if (u1 <= u0) then u0 else u1 (the larger UCB) over exact rationals. Proved native and axiom-free: the preference decision, the node value (max), and the switch when action 1 scores higher. Requires audit/decide-nnrat-at-most, logic/if-data (both in the D63 checkpoint). Scope (measured by the kernel): this module has 3 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.pomcp` prints this classification.

pomcp/prefers-action-zero? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

pomcp/node-value :
  (x₁ x₂ : ℚ≥0)
  → ℚ≥0

pomcp/prefers-higher-ucb :
  → bo/is-safe 3/4 1/2 = data/true

pomcp/node-value-is-maximum :
  → fsc/node-value 3/4 1/2 = 3/4

pomcp/switches-action :
  → bo/is-safe 1/2 3/4 = data/false