Which missing outcomes should you pay to recover?
Decision-focused de-censoring: selecting which already-censored historical outcomes to recover when their only purpose is to improve a later, globally constrained decision.
Abstract
Many organisations sit on incomplete history: interventions whose outcomes were never recorded. Recovering an outcome, a phone call, a chart pull, an inspection, a legal review, costs money and can fail. We study which censored outcomes to pay to recover when the only reason to recover them is to improve a later decision that allocates a separate, capacity-constrained portfolio of actions. We give an exact solver, together with certificates that prove when recovering nothing at all is the right call. It was internally reproduced on frozen synthetic populations at small scale (tens of cases) at up to a 2.37× end-to-end speed-up over our own scalar baseline, with exact decision agreement. The mechanism is not published here. We are candid about the boundary: the computational result holds; a claim of general method novelty does not.
Most organisations that make repeated, consequential decisions are sitting on incomplete history. A past intervention happened. Its outcome was never recorded, or was recorded and lost. You could recover it, make the call, pull the chart, run the inspection, commission the legal review, but recovery costs money, competes for the same scarce people who do the real work, and sometimes fails or comes back partial. Which missing outcomes are worth paying to recover?
The honest version of the question is narrower than “collect data for a downstream decision,” which decision-focused experimental design already answers well. The residual we study is the full discrete lifecycle: selected recovery of already-censored historical outcomes, uncertain recovery, a distinct future population to act on, and an exactly, globally coupled portfolio subject to capacity, specialist and service-floor constraints.
The closest modern work
Two recent lines come nearest, and neither solves the residual above. Huang et al. (2024), Amortized Bayesian Experimental Design for Decision-Making, learn an amortised policy that chooses which experiment to run next to improve a downstream decision, but their design space is prospective experiments over a shared model, not a one-off selection among specific, already-censored historical records whose recovery can fail, and their objective is not coupled to a separate, capacity-constrained integer portfolio. Benetti, Baio & Heath (2026), Calculating EVSI accounting for missing data, compute the expected value of sample information when data are missing. That is precisely our valuation primitive, but they price a study design. They do not solve the combinatorial question of which subset of censored outcomes to buy back subject to cost, uncertain recovery, and a globally coupled downstream allocation. The residual we study, selected recovery of already-censored outcomes feeding a separate constrained integer portfolio, sits in the gap between the two.
The result we can stand behind
The naïve approach re-solves a constrained portfolio for every candidate posterior. On a frozen 40-case synthetic population, 52% of those solves were exact repeats, structurally avoidable. Caching them was worth about 2× against that naive re-solver, but caching turned out not to be the right object at all.
The solver we built instead exploits structure specific to this decision. We are not publishing the mechanism. What we will state is what it achieves, and how hard we tried to break it. On a separately frozen twelve-seed population it reproduced every acquisition score and selected action, matched every selected portfolio, value and tie (12/12, zero mismatches), and certified 113 evidence sets as carrying no expected value at the root: cases where the optimal action does not change and the right move is to buy nothing. It ran 2.37× faster end-to-end than our scalar baseline, with the pre-declared gates of exactness, decision-agreement, structural reduction, runtime and breadth, all passing on the single permitted validation run.
Every speed-up on this page is against an internal baseline on synthetic, frozen populations at small scale (tens of cases). A comparison against a tuned external solver and a runtime-versus-instance-size curve are the stated next step, not a claim we make here. “Exact” refers to correctness, not polynomial time.
The boundaries we will not cross
The differentiator here is not a louder claim. It is a defended one. Several attractive extensions were negative results, and we keep them:
- Exact exchangeability compression reproduced all values but avoided only 3.5% of terminal cells, far below the bar to matter.
- One screen safely rejected most evidence sets yet ran at 0.97× the direct baseline: structural pruning is not a product when the exact solver is already cheaper than the certificate arithmetic.
- A joint portfolio-support bound was strictly tighter in 170,212/170,212 comparisons and still lost on wall-clock. Tighter-and-safe is not sufficient.
So the computational conjecture survived and the generic-novelty conjecture did not, yet. The open scientific question is whether a screen can be certified cheaply enough to pay for itself, and defended against strong published baselines rather than only against our own.
Why it is worth doing at all
Because the decision on the other side is expensive and constrained: which old cases to adjudicate before a scarce review team is allocated. Which incomplete files to pursue before a labelling, reimbursement or inspection decision. A method that lets you consider more candidate records, recovery actions and portfolio constraints inside a decision window is worth money, precisely where evidence collection is already costly and a refusal to buy low-value evidence is itself valuable. This paper is one project on a six-project research frontier; the others (decision-stability certificates, recoverability-aware adaptive recovery, distributionally-robust recovery, and online two-ledger allocation) build on this verified kernel, each adding a distinct, frozen scientific risk.
Method disclosure
The method is not published.
The kernel and the structural insight it rests on are not published.
We publish selectively and say which. Open-source, academic and pro bono work is published in full. Where the mechanism is the commercial asset we publish the result, the evidence grade and the boundary, and state that the mechanism is withheld, and never write around the gap.
Limitations & novelty boundary
The validated result is an exact application algorithm on an admitted generator, not a general theorem. Exact-posterior caching, multiobjective knapsack DP, alpha-vector pruning and value-directed belief compression are established prior art; our specialisation of them does not by itself constitute new method novelty. Several tempting extensions were negative results and are reported as such: one compression avoided too few cells to matter, and one screen ran slower than the direct approach it was meant to replace. Evidence is on frozen synthetic and semi-synthetic populations at small scale, and every speed-up is against our own internal baseline; a field claim would require prospective execution on operational recovery channels and a comparison against a tuned external solver.
References
- Avriel & Williams, The Value of Information and Stochastic Programming (1970).
- Bazgan et al., Solving efficiently the 0–1 multi-objective knapsack problem (2009).
- Boutilier & Poupart, Value-Directed Compression of POMDPs (2002).
- Blackwell, Comparison of Experiments (1951).
- Benetti, Baio & Heath, Calculating EVSI accounting for missing data (2026).
- Huang et al., Amortized Bayesian Experimental Design for Decision-Making (2024).