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An audit budget is most useful when each new reference label is chosen for the decision it can change. A robust knowledge gradient values the next audit across a declared ambiguity set, while a decision-stability rule stops when plausible updates no longer alter the action enough to justify their cost.
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Chapter contents
Choose the route closest to the decision, or read from Chapter 1. The chapters remain open; these grouped routes are a navigable index.
Route 1 · Define the decision
Route 2 · Work the ledgers
Route 3 · Transfer the method
Route 4 · Check limits and evidence
Route 5 · Ask and continue
CHAPTER 1 OF 12 · DEFINE THE DECISION
1. Sequential allocation is a decision problem
At round n, choose a scene class x, observe a costly reference label and update the estimated loss of each deployment action. The classical knowledge gradient values x by the expected increase in the best terminal value after that observation.
A robust version replaces one predictive model with a worst-case or lower-envelope value across a credible set. That makes the choice conservative, but only relative to the models and losses included.
CHAPTER 2 OF 12 · DEFINE THE DECISION
2. Separate learning value from sample count
A scene has high audit value when plausible outcomes could reorder actions, shrink costly regret or eliminate an ambiguity-set corner. A large stratum can have low value when all outcomes lead to the same deployment decision.
Audit units must respect scene or acquisition clusters. Hundreds of pixels from one image do not provide hundreds of independent opportunities to learn cross-scene risk.
CHAPTER 3 OF 12 · WORK THE LEDGERS
3. A sequential allocation ledger
A team can audit one of three scene classes. Values are expected reductions in robust deployment loss before cost.
| Candidate class | Expected robust loss reduction | Audit cost | Robust knowledge gradient |
|---|---|---|---|
| Ordinary cropland | 0.006 | 0.004 | 0.002 |
| Cloud-edge scenes | 0.024 | 0.010 | 0.014 |
| Mountain shadow | 0.018 | 0.009 | 0.009 |
After observing the result, recompute the ledger. A fixed allocation planned from round zero cannot react when one ambiguity is resolved earlier than expected.
CHAPTER 4 OF 12 · WORK THE LEDGERS
4. Worked two-round update
Suppose the cloud-edge audit reveals a reference error, reducing its next expected loss reduction from 0.024 to 0.011 while the mountain-shadow value rises to 0.020 as dependence estimates update.
| Round | Chosen audit | Net value before audit | Updated best action | Worst-case regret gap |
|---|---|---|---|---|
| 0 | Cloud edge | 0.014 | Keep A | 0.031 |
| 1 | Mountain shadow | 0.011 | Targeted deployment | 0.014 |
| 2 | Candidate stop | Best remaining 0.003 | Targeted deployment | 0.006 |
The regret gap compares the chosen action with the best action inside each credible model. It is a decision diagnostic, not a confidence interval by itself.
CHAPTER 5 OF 12 · WORK THE LEDGERS
5. Define stability across plausible updates
A decision-stability stop can require the same action across all retained models, worst-case regret below epsilon and maximum net value of any next audit below its cost threshold.
Add persistence over several rounds or a time-uniform evidence rule when monitoring is continuous. Do not stop simply because the point estimate has not changed after one uninformative audit.
CHAPTER 6 OF 12 · TRANSFER THE METHOD
6. Protect exploration and rare harms
Pure one-step value can neglect a rare scene whose first audit unlocks future learning. Reserve exploration, use a longer lookahead or require minimum coverage for safety-critical strata.
A robust lower envelope may be overly conservative when the ambiguity set contains implausible corners. Tighten the set with auditable assumptions rather than silently replacing the worst case.
CHAPTER 7 OF 12 · TRANSFER THE METHOD
7. Changed-context transfer: flood mapping
Transfer the workflow to flood-extent products across urban, forest and cloud-obscured scenes. Reference collection may use field reports, very-high-resolution imagery or expert interpretation, each with different cost and error.
The transfer check models event-level clustering, delayed labels and acquisition selection. A scene unavailable after the flood cannot be treated as a freely selectable next audit.
CHAPTER 8 OF 12 · TRANSFER THE METHOD
8. Connect the audit branch
The robust-value guide quantifies uncertainty in the value and least-favourable dependence model. The dependence-region guide defines the ambiguity set.
Use the heterogeneity-bounds guide when the decision depends on the distribution of scene effects rather than one average.
CHAPTER 9 OF 12 · CHECK LIMITS AND EVIDENCE
9. Limits and common misconceptions
A knowledge gradient is a policy based on a predictive model; it does not guarantee that the realised next audit improves the decision. Myopic policies can miss multi-step information paths.
Decision stability is not parameter certainty. Several models can disagree scientifically while recommending the same current action, especially when costs dominate.
CHAPTER 10 OF 12 · CHECK LIMITS AND EVIDENCE
10. Practical evidence checklist
Archive the action set, scene candidates, audit costs, predictive label models, ambiguity set, loss function, knowledge-gradient computation, clustering, exploration rule, regret tolerance and stopping history.
Report each round’s candidate ledger, chosen audit, realised label, model update, robust action, near-best alternatives and sensitivity of the stop to cost and epsilon.
CHAPTER 11 OF 12 · ASK AND CONTINUE
11. Frequently asked questions
Why not audit the most uncertain scene?
Uncertainty matters only through the decision. A highly uncertain scene can have little value if all plausible labels leave the action unchanged.
Can the stop be reopened?
Yes. New sensors, seasons, policies or loss weights can invalidate stability. Record the conditions under which monitoring restarts.
Is robust knowledge gradient a single formula?
No. Robustness may use worst-case, distributionally robust or risk-averse objectives; the exact definition and ambiguity set must be stated.
CHAPTER 12 OF 12 · ASK AND CONTINUE
12. Sources and next reading
Frazier, Powell and Dayanik introduce the knowledge-gradient policy for correlated normal beliefs. Krause and colleagues develop robust observation selection under multiple objectives and sensor placement by information gain. The sequential remote-sensing ledgers and robust stopping rule above are original teaching adaptations whose guarantees depend on the declared model and design.
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