Protected floor$44.24
Nominal value$44.24
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Decision Lab 03 · Robust planning under preference shift
Pay a little now. Protect the decision later.
Freeze a synthetic nominal choice model, declare how far future preferences may move, and choose the assortment with the strongest protected floor—before the stress test is revealed.
Known synthetic MNLGlobal KL prior ballExact small-instance search
M2W · Model the world → simulate uncertainty → decide before reveal → test toward transfer
- 01Freezenominal model input
- 02Declareglobal KL shift budget
- 03Protectmaximize the worst-case floor
- 04Stressreveal one shared future
- 05Judgeprice, floor, and shifted benefit
Live robustness experiment
Choose the protection. Then reveal the future.
The robust planner uses the frozen baseline and your KL budget; it does not use the stress endpoint or slider. Both policies are then judged in the same shifted MNL world.
Global KL distance0.078 / 0.10
Inside declared setKL(qα || p₀)
Three different roles
Choose blind. Evaluate after reveal.
Nominal and robust decisions are frozen without using α or the stress endpoint. The shifted oracle is displayed only to measure the opportunity left after the reveal.
PolicyAssortmentNominalProtected floorRevealed stressRole
Nominal leaderPro + Everyday$44.24$27.27$35.31Optimizes the frozen nominal baseline
Robust leaderPlus + Everyday$42.60$27.72$44.87Optimizes the declared floor
Shifted oraclePlus + Everyday——$44.87Evaluator only · sees the stress
Nominal price of robustness$1.643.7% of nominal value
→Protected-floor gain+$0.45against the nominal policy
→Shifted benefit at α = 1.00+$9.56synthetic comparison
Shared-world stress test
Follow both frozen policies.
Nominal policyRobust policy
$44.24$42.60
0%α = 0.00$42.36$43.16
25%α = 0.25$40.27$43.72
50%α = 0.50$37.94$44.29
75%α = 0.75$35.31$44.87
100%α = 1.00The stress endpoint softens Pro demand while strengthening Plus and Entry. It is curated to interrogate the policy—not fitted from customer data.
Inside the certificate
How the adversary moves choice.
OutcomeNominalWorst caseMovement
No purchase29.2%52.5%↑ 23.3%
Plus12.3%5.4%↓ 6.9%
Everyday58.5%42.1%↓ 16.4%
Effective conditional radius for this shelf: 0.125. The adverse mix exhausts the allowed KL budget unless zero revenue is already reachable.
Robustness frontier
Watch the decision switch.
Protected floor$33.41
Nominal value$44.24
Protected floor$32.16
Nominal value$42.60
Protected floor$27.72
Nominal value$42.60
Protected floor$21.39
Nominal value$42.60
Protected floor$18.84
Nominal value$42.60
Disclosed synthetic model
Nothing hidden in the stress path.
Outside attraction stays at 1. Capacity stays at 2. At intermediate α, each preference weight moves linearly between its two disclosed values.
Pro$120.00
Nominal v0.300
→Stress-end v0.045
fallsPlus$85.00
Nominal v0.420
→Stress-end v0.714
risesEveryday$55.00
Nominal v2.000
→Stress-end v1.600
fallsEntry$20.00
Nominal v0.500
→Stress-end v0.650
risesExact small-instance search
Every feasible nonempty shelf.
RankAssortmentNominalProtectedStress
01Plus + Everyday$42.60$27.72$44.87
02Pro + Everyday$44.24$27.27$35.31
03Everyday$36.67$22.23$33.85
04Everyday + Entry$34.29$21.87$31.08
05Pro + Plus$41.69$8.88$37.57
06Plus + Entry$23.80$5.11$31.17
07Pro + Entry$25.56$3.32$10.86
08Entry$6.67$0.46$7.88
09Plus$25.14$0.26$35.41
10Pro$27.69$0.00$5.17
Enumeration is exact for 4 products and capacity 2; it is not a claim of scalable optimization.
Research foundation
One uncertain prior. Coherent choices across every shelf.
The experiment implements the known-model planning objective in Example 2.2 of the robust assortment work by Miao Lu, Yuxuan Han, Han Zhong, Zhengyuan Zhou, and José Blanchet. It perturbs one global preference prior inside a Kullback–Leibler ball, then conditions that prior on each offered shelf.
The product names and prices provide continuity with Decision Lab 02. This lab specifies a new synthetic preference prior so the robustness mechanism can be examined in isolation. Connecting D2's learned model directly to the robust planner is the next end-to-end integration step. The global construction preserves multinomial-logit coherence across assortments; exhaustive search is exact here only because there are four products.
Read the robustness paperPath to autonomy transfer
The nouns change. The decision architecture survives.
A later autonomy prototype can apply the same freeze–protect–stress pattern to warehouse task and charging decisions under operating-regime drift.
To establish this transfer, the next prototype must specify the warehouse model, validate the adapter, and evaluate operating-regime shifts.
Evidence passport
What the robustness prototype establishes—and what comes next.
A global preference-shift budget can change the selected assortment; its nominal cost and protected floor are computed exactly for this tiny model; a separate in-set stress path tests the frozen policies.
Learn the nominal model from logged choices, calibrate the shift budget, extend the optimizer beyond this small MNL instance, and validate the resulting policy with held-out and experimental evidence.
What goes next?