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dd14c26 | 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 | import OAI.Probability.MatroidSecretary.Labels.FiniteLabelingModel
namespace OAI
namespace MatroidProphet.Labeling
open Finset
/-- A hidden rule on arbitrary finite labels has the same online information
restriction as the canonical `Fin n` hidden rule. -/
structure LabeledHiddenRule (E : Type*) [Fintype E] [MeasurableSpace E]
(bits : ℕ) where
mask : Seed bits → Finset E
core : LabeledOnlineRule E bits
noncomputable def labeledObserved {E : Type*} [Fintype E] [MeasurableSpace E]
{bits : ℕ} (A : LabeledHiddenRule E bits) (r : Seed bits) (w : E → ℝ) :
E → ℝ := by
classical
exact fun e => if e ∈ A.mask r then w e else 0
noncomputable def labeledHiddenAcceptedThrough
{E : Type*} [Fintype E] [MeasurableSpace E] {bits : ℕ}
(A : LabeledHiddenRule E bits) (r : Seed bits) (w : E → ℝ)
(π : LabeledOrder E) (t : ℕ) : Finset E := by
classical
exact labeledAcceptedThrough A.core r (labeledObserved A r w) w π t \ A.mask r
noncomputable def labeledHiddenReward
{E : Type*} [Fintype E] [MeasurableSpace E] {bits : ℕ}
(A : LabeledHiddenRule E bits) (r : Seed bits) (w : E → ℝ)
(π : LabeledOrder E) : ℝ :=
∑ e ∈ labeledHiddenAcceptedThrough A r w π (Fintype.card E), w e
noncomputable def labeledHiddenWorstReward
{E : Type*} [Fintype E] [MeasurableSpace E] {bits : ℕ}
(A : LabeledHiddenRule E bits) (w : E → ℝ) (r : Seed bits) : ℝ := by
classical
exact Finset.univ.inf' ⟨(Fintype.equivFin E).symm, mem_univ _⟩
(labeledHiddenReward A r w)
end MatroidProphet.Labeling
end OAI
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