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Adaptive Complementarity in Human-AI Systems: Architecture as a State-Shaping Choice

Babak Heydari

arXiv:2609.07001v3cs.HC

TL;DR

Human–AI interaction can improve current performance while changing the capabilities and relationships that future performance depends on. The paper develops adaptive complementarity to evaluate architectural choices in light of those state changes. In a computational illustration, adaptive allocation improves net output over generic procedures and an optimal predetermined calendar, while a stable priority rule retains essentially all of its calendar-relative gain.

  • Problem

    Human–AI arrangements can improve present performance while changing future capabilities and relationships, complicating evaluation of which architecture will work best over time.

    Source: §1 · pp. 1–2

  • Method

    The paper develops a framework linking interaction architecture to state creation, history-dependent fit, and the value of responding to evolving states.

    Source: §3.2 · p. 11, §7 · p. 26

  • Results

    A priority rule derived from adaptive allocation retains essentially all of its gain over the optimal predetermined calendar, while the adaptive policy improves net output over generic procedures and that calendar.

    Source: §5.2 · p. 19, §7 · p. 26

  • Takeaways & Limitations

    Evaluation should account for the states interaction creates and how they alter later architectural fit, while distinguishing adaptive policy discovery from the stable rule used to implement it.

    Source: §7 · p. 26

    The strategic analysis fixes the evaluation objective; fully endogenous objectives require a further model.

    Source: §6.1 · p. 25

Abstract

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Human-AI interaction can improve current performance while changing the capabilities and relationships on which future performance depends. We develop adaptive complementarity, a framework for choosing interaction architecture with these state consequences in view. Access, information exposure, task allocation, timing, and communication can alter which arrangement will be valuable later; their settings can often be reset faster than the capabilities, search patterns, or conventions they create. Three mechanisms organize the argument: information exposure and collective search, delegation and capability evolution, and strategic interdependence and information governance. Their integration yields cross-mechanism implications, including conditions under which a loss of expertise heterogeneity increases the information differentiation required to preserve independent search. We distinguish strong human-AI complementarity from advantage over another workflow and from advantage over an evolving reference policy. A computational illustration examines scarce human review in a workflow whose success requires several specialized stages. Review develops human expertise and AI capabilities, changing where subsequent review is most valuable. Adaptive allocation improves net output over untailored procedures and the optimal predetermined calendar. An understandable priority rule derived from the adaptive solution retains essentially all of its gain: the procedure stays fixed while assignments respond to the capabilities that interaction creates. The framework directs evaluation toward the states present interaction creates, their consequences for later architectural fit, and the conditions under which observing and responding to them is worthwhile.

1 The complementarity puzzle

Human–AI interaction can improve current work while changing the capabilities and relationships that shape future performance. The paper frames this as a design problem: evaluate both what an arrangement achieves and what it leaves behind.

The complementarity puzzle

  • AI assistance can improve performance while changing what people learn, making assisted outcomes alone an incomplete account of an arrangement’s effects.In an education field experiment, conventional GPT-4 assistance improved performance while available but was followed by worse unaided performance; teacher-informed guidance largely mitigated that penalty.Source: §1 · pp. 1–2
  • Information exposure, delegation, and communication can change search, capabilities, and relationships, so an arrangement that works now may fit less well later.For example, more similar expertise after repeated delegation may require more differentiated information to preserve independent search.Source: §1 · pp. 1–2
  • Strong complementarity requires the combination to outperform both standalone participants, unlike augmentation or improvement over a status quo.A meta-analysis found combinations outperformed humans alone on average but underperformed the better standalone participant, with variation across tasks.Source: §1 · p. 2
  • The framework separates state creation, history-dependent fit, and the operational value of measuring evolving conditions and responding to them.A stable priority rule can leave the procedure unchanged while assignments adapt to experience.Source: §1 · p. 3
  • The paper integrates architectural choices, the conditions they create, and evaluation comparisons, connecting formal analysis to an implementable allocation rule.It distinguishes strong complementarity, advantage over another workflow, and advantage over time.Source: §1 · p. 3

2 Architecture, state, and evaluation

The framework distinguishes adjustable interaction architecture from the agent, problem, and relational states it helps create. It also separates evaluation benchmarks and treats architectural choice as a dynamic tradeoff between current performance and future value.

2.1 What architecture changes

  • Interaction architecture governs access, information, allocation, decision rights, timing, and communication, while agent, problem, and relational states capture conditions interaction can change.Architecture is often only partly controllable, and changing a setting does not directly reset learned skills, representations, or routines.Source: §2.1 · p. 4
  • A fixed rule can produce state-responsive assignments: the rule stays unchanged while its choices condition on observed circumstances or available history.The value of responsiveness and the complexity of implementing it are separate questions.Source: §2.1 · p. 4

2.2 Three comparisons that answer different questions

  • Strong complementarity, workflow advantage, and trajectory policy advantage answer different questions and require distinct reference classes and conditions.Only the first row of Table 1 necessarily tests strong complementarity; the MASAI comparison instead evaluates an AI-supported workflow against two-radiologist reading.Source: §2.2 · p. 5, Table 1 · p. 5
  • The initial MASAI safety analysis reported a 44.3% reduction in screen-reading workload with a similar cancer detection rate.Follow-up reported higher sensitivity with unchanged specificity and met the prespecified non-inferiority criterion for interval cancers.Source: §2.2 · p. 6
  • A benchmark gap can rise while system value falls when the benchmark deteriorates faster, so benchmark movement alone does not establish stronger complementarity.Comparisons over time must let each alternative generate its own learning history.Source: §2.2 · p. 6

2.3 A compact dynamic comparison

  • Dynamic architectural choice weighs current performance against continuation value, including the state left behind and the cost of switching.Equation (7) applies standard dynamic-programming logic rather than supplying a new optimization method.Source: §2.3 · pp. 6, 8
  • Trajectory policy advantage compares policies from common initial conditions while allowing each to generate its own subsequent states.Implementable policies may rely on history or beliefs, and noisy measurements, limited control, or costly adjustment can favor a stable architecture.Source: §2.3 · p. 8

3 Three mechanisms

The section traces how information exposure, delegation, and strategic information governance shape both immediate behavior and the states that influence later interaction. It identifies mechanisms, evaluation boundaries, and evidence needed to distinguish immediate effects from consequences carried forward.

3 Three mechanisms

  • Each mechanism links an architectural choice to behavior, an accumulated state, and the value of a later architecture; the mechanisms can operate together but are not exhaustive.Information exposure shapes collective search, delegation shapes capability and reliance, and strategic governance shapes cooperation and competition.Source: §3 · p. 8

3.1 Information exposure and collective search

  • Common AI exposure can improve an individual decision while narrowing collective exploration, so whether to pool or differentiate information depends on current search conditions.The value of independence can fall as uncertainty resolves and rise again with new evidence or a regime change; there is no universal explore-early, exploit-late schedule.Source: §3.1 · pp. 9–10
  • A collective loss arises only when the cost of reduced independent search to others exceeds the user’s gain; diagnose it with novelty and unresolved search opportunity, not similarity alone.A longitudinal test can randomize early exposure and then impose the same architecture to test whether earlier exposure leaves a consequential state.Source: §3.1 · p. 10

3.2 Delegation, capability, and reliance

  • Delegation allocates both current work and opportunities to learn; human involvement can build expertise and improve AI feedback, changing which allocation is valuable later.Continued practice may be needed to sustain capabilities that support later collaboration.Source: §3.2 · pp. 10, 12
  • Capability composition matters alongside level: two people with 68% unaided accuracy can differ in coverage of AI failures, reversing the preferred next workflow.The value of human contribution depends on how human knowledge complements AI capabilities.Source: §3.2 · p. 11

3.3 Strategic interdependence and information governance

  • Strategic information governance changes disclosure and interaction conditions that can shape behavioral histories, reputations, conventions, and competitive positions.The relevant value depends on the evaluation objective; communication can create both useful integration and external costs, and mediation is worthwhile only if its improvement covers its cost.Source: §3.3 · pp. 12, 14
  • In AIM, a learned, state-conditioned disclosure policy improved cooperation and aggregate payoffs relative to the fixed-disclosure baselines tested.Disclosure varied with neighborhood history: pairwise actions sometimes came first, while neighborhood information became dominant as cooperation developed; the policy was trained offline.Source: §3.3 · p. 13
  • The cited mechanisms are demonstrated in controlled environments, not deployed institutions; the studies do not establish which effects persist under identical later rules.Testing whether earlier architecture changes which later rule performs best requires comparing alternative later rules within each inherited-history condition.Source: §3.3 · pp. 14–15

4 What the mechanisms imply together

The mechanisms share a structure: architecture changes a state whose value can differ under future conditions. Their connections also yield a conditional result: losing expertise heterogeneity can increase the information differentiation needed to maintain a fixed level of search independence.

4 What the mechanisms imply together

  • Across mechanisms, architecture changes independent search, a capability portfolio, or strategic behavior and position, each of which can alter the value of a later arrangement.State changes may help or harm; the relevant comparison depends on future problem conditions.Source: §4 · p. 15, Table 3 · p. 15

4.1 The same current lever can leave different future values

  • Under a specified decay process and common continuation architecture, an inherited state difference has a discounted residual value whose absolute magnitude increases with persistence.Its sign depends on the value of the inherited state, not persistence itself; the calculation assumes other expected reward differences cancel and a stable local state-to-value mapping.Source: §4.1 · pp. 15–16

4.2 A state change can alter requirements in another design dimension

  • When expertise heterogeneity and differentiated AI input both reduce search correlation, losing heterogeneity locally increases the differentiation required to maintain a feasible fixed search-independence target.The result identifies a compensation requirement, not whether maintaining that target is optimal.Source: §4.2 · p. 16
  • The compensation result requires that delegation actually lower relevant heterogeneity; productive specialization could instead increase it, and maintaining the target may be costly or less valuable.Monotonicity assumptions alone do not establish that optimal information differentiation falls with heterogeneity.Source: §4.2 · pp. 16–17
  • Differentiated exposure may preserve oversight representations, while strategic histories can change responses to later information policies; measuring both channels is needed to identify their interaction.This is a proposed cross-mechanism connection, not evidence that strategic studies test collective search.Source: §4.2 · p. 17

5 Adaptive review in interdependent workflows

Scarce review can correct current work while building human and AI capabilities that change where later review is most valuable. The section models this feedback and shows that allocation can respond through an understandable rule whose procedure stays fixed.

5.1 The organizational problem

  • Each workflow requires three correct stage outputs, while one review opportunity can correct one stage and build human expertise or shared AI capability.The model treats the stages as necessary components whose outputs must all be correct for workflow success.Source: §5.1 · p. 17, Figure 2 · p. 18

5.2 Discovering the adaptive allocation

  • The preferred review target changes with realized learning: stage A may receive review at AI accuracy 0.60, but priority shifts to B or C at 0.75.A predetermined calendar can anticipate average development but cannot condition the next assignment on whether improvement actually occurred.Source: §5.2 · p. 19
  • Adaptive allocation produces 29.151 discounted net workflows versus 26.621 under the optimized calendar, a 9.50% gain after review costs.It also uses 28.07 reviews on average rather than 30, with the same available capacity.Source: §5.2 · p. 19, Figure 3 · p. 20
  • With both learning channels active, adaptation adds 2.529 net workflows over the calendar; without human practice it adds 1.041, and without AI learning less than 0.001.With both channels disabled, the increment is zero.Source: §5.2 · p. 19, Figure 3 · p. 20

5.3 From an adaptive policy to a meaningful operating rule

  • The priority rule yields 29.150737 net workflows versus 29.150776 for the exact adaptive policy, retaining 99.998% of its gain over the calendar.The rule prioritizes the least accurate AI stage, then the specialist with the highest correction capability among ties.Source: §5.3 · pp. 20–21

5.4 More interdependent teams

  • The five-team gain over uniform allocation is 30.08%, but the comparison reflects lower baseline reliability as well as developing capabilities.When component accuracy is raised to hold reliability constant, adaptive gains over uniform allocation remain between 10.85% and 11.32%.Source: §5.4 · pp. 21–22
  • With five teams, adaptive review yields 15.067 net workflows versus 11.965 under the optimized calendar; the priority rule yields 15.066.The five-team adaptive policy gains 25.92% over the calendar.Source: §5.4 · p. 21, Figure 4 · p. 22

5.5 What the illustration establishes

  • The illustration shows that responding to capabilities created by review can improve output, while its comparisons assume an established review-and-feedback system.Creating that infrastructure is a separate intervention with its own benefits and implementation costs.Source: §5.5 · pp. 22–23

6 Evaluation and implementation

The evaluation framework separates state creation, changes in later architectural fit, and the operational value of observing and responding to state. It also shows how adaptive policies can inform simpler procedures, while emphasizing that evaluation depends on benchmarks, available information, and organizational scope.

6 Evaluation and implementation

  • Evaluate state creation, history-dependent fit, and feedback value as distinct claims: manipulate architecture, measure the changed state, and test its effect on later choices.A positive result for one target does not establish the others.Source: §6 · p. 23, Table 4 · p. 23

6.1 Identifying state creation and feedback value

  • To identify state creation, use a common continuation regime after randomizing earlier architecture, and account for experience, channels, incentives, and task difficulty that may remain unequal.Repeated state measurements help establish temporal order; a randomized intervention on a proposed mediator can provide stronger evidence than statistical mediation alone.Source: §6.1 · p. 23
  • Measure capability composition and cross-mechanism changes, not just average skill: equal accuracy can conceal different human–AI error overlap, and reduced expertise heterogeneity may require more information differentiation to preserve a correlation target.Testing optimal compensation also requires measuring differentiation costs and the target’s value.Source: §6.1 · p. 24
  • Compare feasible policies using matched controls, resources, horizons, and information access, while reporting absolute, contemporaneous, and longitudinal outcomes separately.A bundled intervention may show a policy effect without identifying which architectural lever caused it; a task-limited result may leave longer-term rankings unresolved.Source: §6.1 · pp. 24–25
  • Governance evaluations should state whose objective is assessed, which channels are controlled, and what response assumptions support policy rankings; the analysis fixes the evaluation objective.Fully endogenous objectives require a further model, though contestability can be represented as a state variable or constraint.Source: §6.1 · p. 25

6.2 Discovering adaptive policies and implementing stable rules

  • Policy discovery can be translated into a stable procedure: the competing-platforms heuristic retained 81.5% of the learned policy’s competitive lead, while remaining more robust to observation noise.It achieved a 23.2 percentage-point market-share lead against the fixed-recommendation opponent, versus 28.5 points for the learned policy.Source: §6.2 · p. 25
  • In the workflow illustration, a rule derived from the adaptive policy reviews the least accurate AI stage, prioritizing the more capable specialist on ties, and retains essentially all gain over the best preplanned calendar.The rule requires current capability information; its extraction was manual, while policy learning and rule response are distinct activities.Source: §6.2 · pp. 25–26
  • Simpler extracted procedures should be tested on new initial conditions, measurement error, and structural changes; transfer selection must avoid destination outcomes.The workflow example assumes a specified learning process, so learning that process remains a separate empirical task.Source: §6.2 · p. 26

7 Conclusion

Adaptive complementarity treats interaction architecture as a choice that shapes the conditions for its own future success. The conclusion connects that framework to responsive review allocation and to empirical evaluation that follows states as well as outcomes.

7 Conclusion

  • Interaction architecture changes dependence among searchers, the capability portfolio available to collaborate, and strategic behavior and competitive conditions.These consequences can outlast the settings that produced them and alter requirements in another design dimension.Source: §7 · p. 26
  • In the workflow illustration, review develops human expertise and stage-specific AI capabilities, so responsive assignment improves net output over generic procedures and the optimal predetermined calendar.A stable priority rule retains essentially all of its calendar-relative gain while assignments adapt to capabilities.Source: §7 · p. 26
  • Empirical evaluation should follow state changes as well as outcomes, testing what later alternatives are worth and reporting absolute performance separately from evolving benchmarks.Counterfactual policies should be allowed to generate their own trajectories.Source: §7 · p. 26

Appendices

The governance appendix models feasible architecture as a choice whose consequences include behavioral responses and state transitions. It distinguishes full-information analysis from implementable policies and identifies limits on policy ranking and objective specification.

A Governance, information, and dynamic consistency

  • The governance formulation integrates behavioral or equilibrium responses into expected rewards and transition dynamics rather than assuming governance directly sets behavior.The realized configuration can include choices shaped by agents, users, institutions, or external constraints.Source: A Governance, information, and dynamic… · p. 30
  • With switching costs, the inherited choice matters because it determines later adjustment costs; learning and reliance effects belong in transitions and continuation rewards.The discounted formulation assumes bounded rewards and costs, nonempty feasible choices, and standard measurability conditions.Source: A Governance, information, and dynamic… · p. 30
  • An implementable policy generally acts on beliefs formed from the information history, not the true state, and cannot condition on unobserved skill or conventions.Interventions may change what is learned about state, and beliefs can include unknown parameters.Source: A Governance, information, and dynamic… · p. 30
  • Policy rankings may vary across plausible behavioral responses, and positive switching costs alone do not guarantee a simple hysteresis band.The framework supplies no equilibrium-selection theorem; robust evaluation requires an ambiguity set and dynamically consistent uncertainty treatment.Source: A Governance, information, and dynamic… · p. 30
  • Strategic comparisons should use a shared stakeholder boundary: private rewards can rise while group reward falls, and constraints can represent autonomy, fairness, safety, or contestability.Source: A Governance, information, and dynamic… · p. 30

B Derivations and qualifications

The appendices qualify the framework’s comparative statics and specify the interdependent-workflow illustration, its computation, and its scope. They show that adaptive allocation and an extracted rule perform well in the stated environment, while clarifying which assumptions and comparisons those results support.

B.1 Residual value

  • Under a common continuation, a harmful successor-state residual outweighs a current gain only when the gain falls below the stated persistence threshold, before switching-cost differences.The simple residual-value multiplier does not suffice when rewards vary over time or other state differences remain.Source: §B.1 · p. 31

B.2 Required and optimal compensation

  • A loss of expertise heterogeneity can increase the information differentiation required to meet a fixed correlation target, but the result is local and can fail when differentiation limits make the target infeasible.Optimal differentiation requires additional objective and cost assumptions; signs of the separate effects alone do not determine the optimal-policy conclusion.Source: §B.2 · p. 31

B.3 Local architectural comparisons

  • Local architectural comparisons rely on controlled approximation remainders, and a ranking reversal requires a threshold crossing among feasible, reachable states.A mean correlation difference need not determine expected continuation value when distributions also differ.Source: §B.3 · p. 31

C Interdependent workflows: specification and computation

  • The workflow illustration allocates scarce review among specialized human–AI teams whose stage-specific capabilities develop through review; its numerical levels are illustrative, not calibrated effect estimates.The model assumes fully observed capabilities, known transitions, no forgetting, and no exogenous task change, isolating allocation in response to prior learning.Source: C Interdependent workflows:… · p. 32, Table 5 · p. 32, §C.1 · p. 33

C.2 Exact policy and calendar calculations

  • Exact dynamic programming chooses a stage or idles based on current capabilities, while symmetry reduction exploits interchangeable team labels without merging different capability states.Predetermined calendars are separately optimized over assignment sequences and stopping decisions.Source: §C.2 · p. 33

C.3 Rule extraction and learning channels

  • For the three-team reference, the extracted rule yields 29.1507367411 net workflows versus 29.1507761699 for the adaptive policy, retaining 99.998441% of the adaptive-calendar increment.With both learning channels operating, the adaptive-calendar increment is 2.5293809; the two single-channel increments are 1.0414298 and 0.0000145, with an interaction adding 1.4879367 net workflows beyond their sum.Source: §C.3 · p. 34

C.4 Scaling, denominators, and additional checks

  • The reported size comparison holds operating duration and expected incoming cases fixed while increasing the number of specialties and review capacity; total review spending is not fixed across organization sizes.Reported gains are net-output quantities after cost, and matched-reliability controls also change feedback probabilities.Source: §C.4 · p. 34
  • Additional workflow comparisons use named benchmarks within the same environment, reoptimize adaptive policy and calendar, and maintain the review cap on every history.Source: Table 6 · p. 35, §C.4 · p. 35

C.5 Numerical checks and reproducibility

Numerical checks validate the adaptive policy and its extracted rule against independent simulations and solver comparisons. The independent-output illustration also changes the production objective while retaining learning.

C.5 Numerical checks and reproducibility

  • The exchangeability-reduced and labeled solvers agree to numerical precision, and direct calendar and adaptive-policy evaluations match their optimization and Bellman values.A short-horizon exhaustive-calendar check and comparisons of reduced and labeled transition calculations are included.Source: §C.5 · p. 35
  • Across 200,000 histories, simulated and exact discounted values were 15.06094 and 15.06658 for adaptive allocation, with deviations below 2.3 standard errors.The simulated adaptive-minus-uniform difference was 3.49881, with a 95% interval of [3.47610, 3.52152], containing the exact difference of 3.48390.Source: §C.5 · p. 35

D Independent outputs and alternative implementations

  • The independent-output control gives three domains four outputs each per period, shares one review opportunity, and divides rewards by three without changing policies or percentage gains.It retains the workflow illustration’s human and AI levels, learning rates, initial states, horizon, and discount factor.Source: D Independent outputs and alternative… · p. 36

D.1 What interdependence adds

Adaptive allocation gains more over uniform allocation and the exact calendar when production requires stages to succeed together. This identifies production interdependence, rather than agent count alone, as an amplifier of the allocation mechanism.

D.1 What interdependence adds

  • Adaptive allocation earns 55.83307, gaining 2.80% over uniform allocation and 2.43% over the exact calendar; joint completion raises those gains to 10.85% and 9.50%.The output values across objectives are not directly comparable as welfare levels because the experiment changes what successful production requires.Source: §D.1 · p. 36
  • Joint completion makes component improvements interact, so allocation must coordinate realized development; mixed outputs provide an intermediate case.The comparison identifies production interdependence, rather than a larger agent count alone, as an amplifier of the allocation mechanism.Source: §D.1 · p. 36

D.2 Standing procedures can already be adaptive

Standing procedures can retain adaptive assignments without continually changing institutional rules, while transfer across model structures depends on how the source environment shapes feedback. A separate illustration holds AI competence fixed to examine how human knowledge composition affects workflow fit.

D.2 Standing procedures can already be adaptive

  • Reservation and polling procedures use current capabilities and forward-looking acceptance, so their realized allocations adapt under stable institutional rules.Their performance measures those implementations, not wholly unresponsive allocation.Source: §D.2 · p. 36
  • The best tested procedure reaches 166.187 against 167.499 for the full allocation optimum, while local review scores retain 98.70% of the adaptive-calendar increment.The institutional search is not a global-optimality claim; the local score assigns review to the highest positive domain score.Source: §D.2 · pp. 36–37, Table 7 · p. 37

D.3 Structural transfer has a separate interpretation

  • A shared-AI source feedback rule transfers 0.32% below its paired calendar, whereas the batch-source rule exceeds its paired calendar by 4.17%.The shared-AI calendar is the best found in a documented multistart search, while the batch-source calendar is exact; source designs were informed by the destination rather than blindly preregistered.Source: §D.3 · p. 37

E Knowledge composition and architectural fit

  • The knowledge-composition illustration fixes the AI and has one human knowledge state, isolating how human knowledge composition changes architectural fit at identical aggregate accuracy.Unlike review allocation, it has no competition among domains for a shared resource.Source: E Knowledge composition and… · pp. 37–38

E.1 Primitives, timing, and interpretation

  • The baseline partitions 25 equiprobable types into 20 AI-covered and five blind-spot types, starts at mastery counts (10, 1), and charges .06 effort per independent-work case.The AI is fixed, transitions are known, and the dynamic optimum assumes perfectly observed mastery; independent work enables blind-spot learning at rate η, while AI-led use supplies it at ωη.Source: §E.1 · pp. 38–39
  • Independent work requires a human attempt before answer combination, and its ideal combination retains any correct constituent answer; this is a favorable integration assumption.Both workflows provide learning opportunities on AI-covered types, while independent attempts and corrective feedback provide them on blind spots.Source: §E.1 · p. 38

E.2 History experiments and analytical boundaries

Different learning histories can reverse the preferred next workflow even at equal human accuracy. The reversal depends on learning access, effort cost, and the resulting distribution of mastered blind-spot types.

E.2 History experiments and analytical boundaries

  • At baseline with n = 30, the reversal bounds are .04000 and .1127225; independent work is strictly better when mB ≥2, occurring on 91.8034% of independent-work histories and no AI-led histories.The historical contrast is mediated by mastery rather than an additional history label.Source: §E.2 · p. 39
  • After 30 training cases, human accuracy is 62.18% following AI-led work and 69.45% following independent work, so this history comparison does not isolate knowledge composition at equal competence.Expected stopping times to mastery gains are 42.2817 AI-led cases and 26.6853 independent-work cases, with expected independent-work effort cost 1.6011.Source: §E.2 · pp. 39–40
  • When ω = 1, learning kernels are identical and fixed histories generate identical distributions, though random mastery can still make state-responsive choices useful.The same absence of history differences holds when n = 0 or η = 0; very low or high effort costs can also leave the same workflow preferred after both histories.Source: §E.2 · p. 39
  • The equal-attainment experiment stops each path at 17 mastered types without discarding paths; independent-work paths draw six newly mastered types from the remaining covered and blind-spot types.The independent-work blind-spot count follows a hypergeometric distribution, yielding a mean next independent-work value of .8485714.Source: §E.2 · pp. 39–40
  • At 68% human accuracy, independent work is worth .78000 after AI-led training and .84857 after independent training, while AI-led work remains .80000; the preferred next workflow reverses.Figure 5 shows the reversal at equal competence; every path reaches mastery of 17 of 25 types, though training duration and effort differ.Source: Figure 5 · p. 40, §E.2 · p. 40

E.3 Policy classes, horizon, and terminal value

The section compares fixed, predetermined, and state-contingent policies, then tests how their relative value depends on learning, observation, and the continuation after the study horizon.

E.3 Policy classes, horizon, and terminal value

  • The full policy conditions on time and mastery, whereas the myopic state policy chooses the larger current net reward and ignores investment returns.The comparisons also include the best fixed workflow and a schedule chosen before learning outcomes are observed.Source: §E.3 · p. 40
  • Observing mastery of blind spots suffices for the optimum, while average unaided accuracy generally does not.Average unaided accuracy combines mastery of ordinary and blind-spot types.Source: §E.3 · p. 41
  • With the common-continuation terminal rule, the best schedule is also the best fixed workflow in all six rows.It is AI-led for T = 14 with zero terminal reward and independent work otherwise.Source: Table 9 · p. 41
  • Over 30 cases, the full policy gains .351315 over myopic choice but only .007874 over the best schedule.The larger difference largely reflects forward-looking learning investment, not the incremental value of observing state over an informed predetermined design.Source: §E.3 · p. 41
  • With common continuation after the horizon, independent work throughout the controlled interval attains the full optimum at all three reported horizons.The feedback premium is sensitive to what happens after the study ends.Source: §E.3 · p. 41
  • After 30-case histories, first actions differ with one or five cases remaining, but independent work is optimal at all reached states with 14 or 30 cases remaining.The policy reversal has a horizon boundary even though the histories still leave different knowledge states.Source: §E.3 · p. 41

E.4 Sensitivity and alternative information conditions

The sensitivity checks examine when history-dependent workflow comparisons persist or change under alternative information and learning conditions. The section also gives an exact schedule solver and reports its verification and reproducibility scope.

E.4 Sensitivity and alternative information conditions

  • 23 of 135 declared parameter-grid cells show a strict reversal of expected next-workflow rankings after 30-case histories.This grid count is not a probability of reversal in real systems.Source: §E.4 · p. 42
  • Under proportional scaling to K = 50, 100, and 200, the reversal survives, but the histories lengthen to 60, 120, and 240 cases.The comparison is not at a fixed number of cases.Source: §E.4 · p. 42
  • With imperfect combination and learning held fixed, six of nine checks retain the baseline fixed-case-count reversal; in other cells, integration loss makes independent work unattractive after both histories.The checks do not model learning from disagreement or endogenous verification effort.Source: §E.4 · p. 42
  • Replacing four of the AI’s blind-spot types makes the difference between histories’ independent-work values disappear, and replacing five changes its sign.AI accuracy remains 80%; this tests partner-specific complementary knowledge, not an optimal-workflow reversal or endogenous AI learning.Source: §E.4 · p. 42
  • A sufficiently informative free pre-review flag makes selective review best after both histories, while weakly informative flags preserve the original choice contrast.This is a one-case comparison, not a three-workflow learning solution.Source: §E.4 · p. 42
  • With a perfect free failure flag, always using fallback and the full optimum both earn 19.614906 over 30 cases with zero terminal value.The calculation does not show that practical AI confidence estimates are free or perfectly informative.Source: §E.4 · p. 43

E.5 Exact solution and released materials

  • Commuting learning kernels let the exact schedule dynamic program optimize over elapsed time and the count of independent-work actions without enumerating all 2^T schedules.Reward timing remains in the recursion, and terminal value is integrated over the complete endpoint distribution.Source: §E.5 · p. 43
  • Released code evaluates finite distributions exactly up to floating-point arithmetic, and the solver matches exhaustive enumeration for three passive-learning rates under both terminal specifications.The computation and tests establish the numerical illustration’s reproducibility; differential learning access and its consequences still require empirical tests.Source: §E.5 · p. 43
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