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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 | import OAI.Probability.MatroidSecretary.Labels.LabeledTransportOneSample
import OAI.Probability.MatroidSecretary.Labels.RelabelingProphet
namespace OAI
/-! Exact agreement of two independently developed finite-label interfaces.
The bundled-rule presentation and the earlier canonical transport evaluate the
same concrete decisions, accepted prefixes, rewards, and offline benchmark. -/
namespace MatroidProphet.LabeledTransport
variable {α : Type*} [Fintype α] [MeasurableSpace α] [MeasurableSingletonClass α]
{n bits : ℕ}
omit [MeasurableSpace α] [MeasurableSingletonClass α] in
theorem optimum_eq_canonical (M : Matroid α) (w : α → ℝ) :
optimum M w = Relabeling.finiteOptimum M w := rfl
theorem decode_decide_eq_canonical (e : α ≃ Fin n)
(A : MatroidProphet.OnlineRule n bits) (k : Fin n) (r : Seed bits)
(s : α → ℝ) (h : History α k) :
(decodeRule e A).decide k r s h = Relabeling.transportedDecision e A k r s h := rfl
theorem decode_accepted_eq_canonical (e : α ≃ Fin n)
(A : MatroidProphet.OnlineRule n bits) (r : Seed bits) (s w : α → ℝ)
(π : ArrivalOrder α n) (t : ℕ) :
acceptedThrough (decodeRule e A) r s w π t =
Relabeling.transportedAcceptedThrough e A r s w π t := rfl
theorem decode_reward_eq_canonical (e : α ≃ Fin n)
(A : MatroidProphet.OnlineRule n bits) (r : Seed bits) (s w : α → ℝ)
(π : ArrivalOrder α n) :
reward (decodeRule e A) r s w π = Relabeling.transportedReward e A r s w π := rfl
end MatroidProphet.LabeledTransport
end OAI
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