File size: 1,811 Bytes
a2ee19a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 | import Mathlib
import OAI.Probability.GaussianRegression.Main
import OAI.Probability.MemoryPrecision.CoefficientStep
namespace OAI
open MeasureTheory ProbabilityTheory Set Filter EuclideanGeometry
open scoped ENNReal NNReal RealInnerProductSpace Topology Pointwise
noncomputable section
universe u v
open MeasureTheory ProbabilityTheory Set Filter
open scoped ENNReal NNReal RealInnerProductSpace Topology Pointwise
namespace MemoryPrecision.Kernel
namespace Policy
def ModelAdmissible {d M T : ℕ} {Ω : Type u} [MeasurableSpace Ω]
(K : Ω → Policy d M T) (ρ : Measure Ω) : Prop :=
∀ π : Measure (Sphere d), IsProbabilityMeasure π → Admissible K ρ π
def FixedSuccess {d M T : ℕ} {Ω : Type u} [MeasurableSpace Ω]
(K : Ω → Policy d M T) (ρ : Measure Ω) (ε : ℝ) (s : Sphere d) : ℝ≥0∞ :=
let rowMeasurable := @MeasurableSpace.pi (Fin T) (fun _ => Vector d)
(fun _ => @WithLp.measurableSpace
(@OfNat.ofNat ℝ≥0∞ 2
(@instOfNatAtLeastTwo ℝ≥0∞ 2 ENNReal.instAddCommMonoidWithOne.toNatCast inferInstance))
(Fin d → ℝ) inferInstance)
@lintegral (Ω × Rows d T)
(@Prod.instMeasurableSpace Ω (Rows d T) inferInstance rowMeasurable)
(@Measure.prod Ω (Rows d T) inferInstance rowMeasurable ρ (RowLaw d T))
(fun z => experiment K (angleTest ε) (s,z))
lemma modelAdmissible_of_measurable {d M T : ℕ} {Ω : Type u} [MeasurableSpace Ω]
(K : Ω → Policy d M T) (ρ : Measure Ω)
(hc : ∀ᵐ ω ∂ρ, (K ω).Completed)
(hm : ∀ f : Sphere d × Sphere d → ℝ≥0∞, Measurable f → (∀ x, f x ≤ 1) →
Measurable (experiment K f)) : ModelAdmissible K ρ := by
intro π hπ
exact ⟨hc, fun f hf h1 => (hm f hf h1).aemeasurable⟩
end Policy
end MemoryPrecision.Kernel
end
end OAI
|