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When Should a World Model Move? Loss-Conditioned State Execution

Jintao Xu, Zhengyu Chen, Ben Zhang, Yongzhi Qi, Jianshen Zhang

arXiv:2609.15801v1cs.AIcs.LGmath.OC

TL;DR

Predictive informativeness alone does not determine whether changing state reduces downstream loss. The paper constructs a loss-specific feasible proposal and uses independent calibration to decide when to execute it rather than persist. Across the evaluated settings, experiments distinguish supported movement from predictive signals that do not justify an update under the declared loss.

  • Problem

    Occurrence ranking can be nearly perfect while persistence remains optimal under absolute loss, and occurrence information with conditional variance may not identify the loss-optimal movement decision.

    Source: §1 · p. 1, §3.1 · p. 4

  • Method

    The method maps a predictive distribution’s loss-specific Bayes correction into the feasible set and executes the fixed proposal only in groups with positive simultaneous lower confidence bounds on bounded-loss gain over persistence.

    Source: §1 · p. 2, §3 · p. 3

  • Results

    Experiments across synthetic, forecasting, action-conditioned, and constrained inventory settings distinguish supported updates, absent fitted-proposal gain, and insufficient calibration evidence, while quantifying trade-offs among certification, coverage, and prediction error.

    Source: §1 · p. 2

  • Takeaways & Limitations

    The experiments distinguish supported state movement from predictive signals that do not justify an update under the declared loss.

    Source: §5 · p. 9

    The guarantee assumes pre-calibration choices are fixed, calibration units are i.i.d. draws from the target population, and unit losses are bounded.

    Source: §3.2 · p. 5

Abstract

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We introduce loss-conditioned state execution, a model-agnostic method that decides whether to execute a world model's fixed feasible proposal or retain the current state. Predictive informativeness alone, however, does not establish whether an update will reduce downstream loss. Occurrence ranking can approach perfection while persistence remains the unique absolute-loss Bayes action. Two transition laws can also share occurrence information and conditional variance yet require opposite absolute-loss decisions. We formalize state movability as the existence of a loss-reducing feasible correction and distinguish it from the benefit of a particular proposal. Our method constructs a loss-specific feasible proposal from a predictive distribution and evaluates its groupwise bounded-loss gain over persistence on independent calibration units. The proposal is executed only in groups with a positive simultaneous lower confidence bound. For fixed proposals and groups with bounded unit losses, we prove that every accepted group has lower expected loss than persistence with high probability when calibration units are i.i.d. draws from the target population. Experiments on public forecasting and action-conditioned dynamics benchmarks show supported updates and a trade-off between certification and coverage. On 28,684 held-out M4 Monthly series, the method executes the proposal for 14.0% of series and achieves bounded loss 0.588, compared with 0.599 for persistence and 0.621 for always executing the proposal. The paired 95% bootstrap intervals for both comparisons lie below zero. In constrained forecasting of six unhealthy-inventory types from JD$\mbox{.}$com, a leading e-retailer in China, strong occurrence-ranking signal coexists with a loss-based preference for persistence, illustrating why event predictability and state execution must be evaluated separately.

1 INTRODUCTION

World models predict future-state distributions, but selecting a state also requires deciding whether to move or persist under the downstream loss. Loss-conditioned state execution evaluates a fixed feasible proposal against persistence and uses independent calibration to support updates.

1 INTRODUCTION

  • Independent calibration executes a fixed feasible proposal only when its groupwise bounded-loss gain over persistence has a positive simultaneous lower confidence bound.Otherwise, the state prediction remains the current state.Source: §1 · p. 2, Figure 1 · p. 2
  • The paper separates state movability—the existence of a loss-reducing feasible correction—from the benefit of a particular fixed proposal.It also shows that identical occurrence information and conditional variance can imply opposite absolute-loss execution decisions.Source: §1 · p. 2
  • Experiments across synthetic, forecasting, action-conditioned, and constrained inventory settings distinguish supported updates, absent fitted-proposal gain, and insufficient calibration evidence.The experiments quantify trade-offs among certification, update coverage, and prediction error.Source: §1 · p. 2

2 RELATED WORK

Related work addresses predictive distributions, rollout reliability, selective prediction, and fallback or certification. This paper instead evaluates whether a fixed feasible state correction improves over persistence under a declared loss.

2 RELATED WORK

  • World-model research limits unreliable simulation through ensembles, short rollouts, pessimism, unknown-region penalties, and uncertainty-aware rollout adaptation.Other approaches adapt imagination depth or action-chunk length; this paper instead evaluates a fixed feasible correction against persistence.Source: §2 · p. 2
  • Proper scoring rules evaluate predictive distributions, while point forecasts target loss-specific functionals and AUROC summarizes ranking rather than a fixed-cost decision.The paper compares a post-feasibility state correction with persistence under the declared loss.Source: §2 · p. 2
  • Selective prediction withholds uncertain outputs, whereas this method assigns persistence as the feasible baseline whenever a proposal is rejected.Coverage depends on evidence that the fixed candidate improves over persistence under the declared loss.Source: §2 · p. 3
  • Safe policy improvement and runtime-assurance methods also use baseline fallbacks, but this method uses independent calibration and learn-then-test to certify groupwise gain for a proposal fixed before calibration.The comparison distinguishes its evaluation target and fallback behavior from related approaches.Source: §2 · p. 3

3 LOSS-CONDITIONED STATE EXECUTION

The section defines loss-conditioned proposals and distinguishes whether any feasible correction can improve on persistence from whether the model’s proposal does. It characterizes persistence under common losses, then uses independent grouped calibration to certify proposal gains.

3 LOSS-CONDITIONED STATE EXECUTION

  • The executed proposal maps a predictive distribution’s Bayes correction into the feasible state set, while persistence is the zero correction.State movability is the best feasible risk reduction over persistence; proposal benefit is the gain from the particular executed correction, and proposal benefit cannot exceed movability.Source: §3 · p. 3

3.1 PERSISTENCE REGIONS AND RANKING–MOVEMENT SEPARATION

  • Under squared loss, persistence is uniquely optimal exactly when the conditional mean correction is zero; pinball and asymmetric linear losses select loss-specific quantile conditions.Under absolute loss, persistence is optimal when zero is a conditional median, and unique when it is the unique median.Source: §3.1 · p. 4
  • Occurrence-ranking AUROC can exceed 1 − ε even when persistence is the unique absolute-loss Bayes correction at every context.Thus, strong occurrence ranking alone does not establish loss-reducing movement.Source: §3.1 · p. 4
  • Two transition laws can share occurrence information and conditional variance yet have opposite absolute-loss optima: persistence under one and a positive correction under the other.Directly evaluating a common fixed candidate’s loss gain distinguishes the laws; empirical-sign and lower-confidence-bound rules recover opposite decisions as calibration grows.Source: §3.1 · p. 4

3.2 INDEPENDENT LOSS-SPECIFIC CALIBRATION

  • Calibration treats the proposal, groups, and bounded unit-loss definition as fixed, with units sampled independently from the target population.Units may represent transitions, series blocks, episodes, or complete training runs; groups use pre-outcome information.Source: §3.2 · p. 5
  • The selector applies the fixed proposal only in represented groups whose lower confidence bound on gain is positive; otherwise, it uses persistence.The simultaneous guarantee states that every accepted group has positive expected improvement over persistence with probability at least 1 − δ.Source: §3.2 · p. 5
  • Sufficient per-group sample size scales as B^2 log(G/δ)/µ_g^2, tying certification requirements to the loss bound, number of groups, and population gain.This rate makes the calibration burden explicit for simultaneous certification.Source: §3.2 · p. 6

4 EXPERIMENTS

The experiments test whether calibration identifies when a fixed proposal improves on persistence across forecasting and action-conditioned settings. Results show supported updates as well as cases where occurrence or predictive signals do not justify execution under the evaluated loss.

4 EXPERIMENTS

  • The experimental overview covers questions, selection outcomes, and held-out empirical losses, with lower loss and regret indicating better results.The experiments compare proposal benefit and the trade-off between confidence correction, update coverage, and prediction loss.Source: Table 1 · p. 6, §4 · p. 6

4.1 CONTROLLED PHASE TRANSITION

  • Across 500 controlled repetitions, increasing calibration units per group from 50 to 1,000 raised beneficial-group power from 0.452 to 0.888 and lowered regret from 0.0566 to 0.0051.With 200 observations per group, confidence correction reduced the probability of accepting any harmful group from 6.96% to 0.00010%, while beneficial-group acceptance fell from 98.2% to 66.6%.Source: §4.1 · p. 6, Figure 2 · p. 7

4.2 SUPPORTED MOVEMENT ON INTERMITTENT DEMAND

  • On intermittent-demand series, both groups were accepted and test MAE was 0.391, versus 0.573 for persistence, 0.626 for seasonal naive, and 0.539 for a trailing mean.Selective-minus-persistence MAE was −0.182, with a 95% bootstrap interval of [−0.194, −0.170].Source: §4.2 · p. 7

4.3 SELECTIVE EXECUTION UNDER HETEROGENEOUS GAIN

  • On 28,684 held-out M4 Monthly series, selective loss was 0.588 versus 0.599 for persistence and 0.621 for always executing; paired 95% bootstrap intervals favored selective execution in both comparisons.The gate covered 14.0% of test series; confidence correction reduced coverage from 22.2% to 14.0% while test loss rose from 0.586 to 0.588 versus the empirical-sign rule.Source: §4.3 · p. 7

4.4 CERTIFIED SELECTION IN DISCRETE-ACTION DYNAMICS

  • In discrete-action dynamics, only the turn group was certified, with mean held-out gain 0.2964; across all transitions, selective loss was 0.122 versus 0.185 for persistence but 0.0277 higher than always-execute loss.The turn-group gain interval was [0.2625, 0.3292]; the forward group’s simultaneous lower confidence bound was −0.218.Source: §4.4 · p. 8

4.5 SELECTIVE EXECUTION IN NEURAL MULTI-STEP DYNAMICS

  • In neural multi-step dynamics, selective macro NMSE beat persistence at every horizon, while a calibration-tuned uncertainty baseline did better at h = 1 and 5.Persistence-to-selective NMSE was 0.481→0.073, 0.793→0.077, 1.401→0.082, and 1.919→0.552 for h = 1, 5, 10, and 20; coverage was 33.3/86.2/100/100%.Source: §4.5 · pp. 8–9, Figure 3 · p. 8

4.6 CONSTRAINED FORECASTING OF SIX UNHEALTHY-INVENTORY TYPES

  • For unhealthy-inventory forecasting, the shared proposal had higher MAE than persistence at all four horizons despite occurrence-probe macro AUROC values of 0.819, 0.792, 0.791, and 0.794.No signed-delta probe beat zero-change persistence in at least four of five entity-held-out folds.Source: §4.6 · p. 9, Figure 4 · p. 9

5 CONCLUSION

The paper frames state execution as a loss-conditioned choice between a fixed feasible proposal and persistence, with independent calibration supporting movement. Its methodological foundations position this interface alongside related approaches and establish decision and calibration guarantees.

5 CONCLUSION

  • The conclusion presents state execution as a loss-conditioned choice between a fixed feasible proposal and persistence, with independent calibration certifying when movement is supported.Across the studied settings, experiments distinguish supported movement from predictive signals that do not justify an update under the declared loss.Source: §5 · p. 9
  • The conclusion identifies recursive rollouts, online recalibration, and policy-aware proposal construction as future work.Source: §5 · p. 9

A METHODOLOGICAL FOUNDATIONS

  • The methodological foundations position the interface among related methods before establishing loss-conditioned decisions, proposal-quality bounds, and calibration guarantees.Source: A METHODOLOGICAL FOUNDATIONS · p. 13

A.1 COMPARISON WITH RELATED METHODS

The related-method comparison distinguishes what is selected and what is evaluated. This interface selects a feasible correction or persistence according to group-average loss reduction and calibrates the proposal after feasibility mapping.

A.1 COMPARISON WITH RELATED METHODS

  • The interface selects between a feasible state correction and persistence using the correction’s group-average loss reduction.Evaluating after the feasibility map aligns the calibration target with the update actually executed.Source: §A.1 · p. 13
  • The calibration construction tests each group’s null of nonpositive gain and uses simultaneous error control to certify accepted groups under bounded-loss, conditional-i.i.d. sampling.Hoeffding bounds are one valid choice; other simultaneous bounds can use the same proposal, loss, and persistence baseline.Source: §A.1 · p. 13
  • Table 2 compares representative selection methods by their decision objects and evaluation targets.Source: Table 2 · p. 13

A.2 LOSS-CONDITIONED DECISIONS

The section characterizes state corrections under a declared loss and separates the existence of a loss-reducing feasible correction from the benefit of a model’s particular proposal. It shows that shared occurrence information and conditional variance can still yield opposite absolute-loss decisions.

A.2 LOSS-CONDITIONED DECISIONS

  • The section distinguishes population state movability, Mℓ > 0, from the benefit Vℓ of the model’s particular feasible proposal; positive Vℓ supports that proposal.The executed correction is obtained by mapping the model’s proposal into the feasible state set, while persistence is correction zero.Source: §A.2 · pp. 13–14
  • Absolute-loss Bayes corrections are conditional medians, while squared loss targets the conditional mean and asymmetric linear loss targets a task-specific quantile.The zero correction is an absolute-loss minimizer exactly when zero is a conditional median.Source: §A.2 · p. 14
  • Under absolute loss, persistence is the unique Bayes correction when the conditional zero-change probability exceeds 1/2.Every nonzero correction then has strictly greater conditional risk.Source: §A.2 · p. 14
  • Occurrence ranking can approach perfect AUROC even when persistence is optimal at every context under absolute loss.The example has P(∆ = 1 | H) < 1/2, making zero the unique conditional median.Source: §A.2 · p. 14
  • Two transition laws with identical occurrence information and conditional variance can have different absolute-loss Bayes corrections, so those summaries cannot determine both execution decisions.Under one law zero is the unique conditional median; under the other, β is the unique conditional median.Source: §A.2 · p. 15

A.3 CALIBRATION GUARANTEES

The calibration guarantee certifies positive expected bounded-loss improvement for every accepted group under fixed-design, i.i.d. sampling assumptions. Additional analyses examine certification power, decision-summary non-identification, feasible inventory geometry, and selector sensitivity.

A.3 CALIBRATION GUARANTEES

  • With fixed proposals, groups, and bounded unit losses, every accepted group has positive expected improvement over persistence with probability at least 1 − δ under conditional i.i.d. calibration sampling.The guarantee applies to the target population covered by the sampling law; the declared unit loss includes its aggregation and clipping.Source: §A.3 · p. 15
  • Groups with population gain µ_g > 2r_g are accepted simultaneously with probability at least 1 − δ, where r_g is the group’s Hoeffding radius.The sufficient sample-size threshold is n_g > 8B^2 log(G/δ)/µ_g^2.Source: §A.3 · p. 16
  • When episodes contribute to multiple groups, the certificate concerns mean gain among episodes containing each group; a union bound permits dependence between groupwise tests.Empty groups receive persistence.Source: §A.3 · p. 16

B SIX-TYPE INVENTORY MODEL

  • The six inventory types are overlapping marginals, each bounded by active inventory without a constraint on their sum; replacing this feasible box with a disjoint simplex creates representation error when overlap is positive.Figure 5 illustrates the geometry in a three-type projection.Source: B SIX-TYPE INVENTORY MODEL · p. 16, Figure 5 · p. 17

C.1 EVALUATION LOSSES; C.1.2 CALIBRATION AND DEPLOYMENT ASSUMPTIONS

  • Calibration evaluates each fixed candidate against persistence under the same bounded unit loss, which may differ from the candidate’s construction loss; deployment transfer requires positive gain to persist in accepted groups.A common calibration and deployment population is sufficient for the stated alignment condition.Source: §C.1.1 · p. 17, §C.1.2 · p. 18

C.2.1 CONFIDENCE CORRECTION AT THE MOVEMENT BOUNDARY; C.2.3 CALIBRATION COUNTS AND CERTIFICATION THRESHOLDS

  • At the movement boundary, confidence correction can avoid accepting harmful groups; calibration groups with positive mean gain below their radius may nevertheless remain uncertified.The boundary analysis compares empirical-sign and LCB acceptance probabilities, while Table 7 distinguishes empirical acceptance from the sufficient population-gain condition.Source: §C.2.1 · p. 20, §C.2.3 · p. 20

C.2.2 NUMERICAL ILLUSTRATION OF SUMMARY NON-IDENTIFICATION

  • Two transition laws can share occurrence probability, Bernoulli entropy, and conditional variance yet require opposite absolute-loss decisions; direct loss-gain evaluation distinguishes them.With the same candidate, population gain is −0.3867 under P0 and 0.1885 under P1.Source: §C.2.2 · p. 20

C.3.1 SELECTOR COMPARISON WITH FIXED CANDIDATES; C.3.2 MONASH GROUPING SENSITIVITY

  • Confidence correction reduces coverage in M4 Monthly, Quarterly, FourRooms, and short-horizon MuJoCo, while the empirical-sign and LCB rules make the same decisions on Monash, M4 Daily, and Web Traffic.In M4 Monthly, the additionally accepted ambiguous group has positive test gain 0.0227; in Monash’s four- and eight-stratum configurations, Hoeffding selection rejects every group.Source: §C.3.1 · p. 21, §C.3.2 · pp. 21–22

C.4 INVENTORY RESULTS ACROSS METRICS AND TIME

The shared inventory candidate has higher mean error than persistence across the reported metrics, with paired bootstrap intervals excluding zero at horizons 7, 14, and 30. The same error ordering holds at a later historical forecast origin.

C.4 INVENTORY RESULTS ACROSS METRICS AND TIME

  • The shared inventory candidate has higher mean error than persistence across raw MAE, inventory-normalized MAE, and inventory WAPE.Table 10 covers the reported scales and a later-window historical forecast origin.Source: §C.4 · p. 22, Table 10 · p. 22
  • At horizons 7, 14, and 30, the paired 95% bootstrap intervals for shared-minus-persistence raw MAE lie above zero; only the horizon-1 interval includes zero.The intervals are [0.0005, 0.0187], [0.0007, 0.0309], and [0.0002, 0.0512] at horizons 7, 14, and 30, respectively; the horizon-1 interval is [−0.0006, 0.0061].Source: §C.4 · p. 22

C.4 INVENTORY RESULTS ACROSS METRICS AND TIME; C.5 ADDITIONAL BENCHMARK RESULTS

  • The shared candidate retains the higher-error ordering at a later historical forecast origin using only earlier transitions for training.The appendix also reports additional forecasting, FourRooms, and MuJoCo evaluations.Source: §C.4 · p. 22, §C.5 · p. 22

C.5.1 CROSS-FREQUENCY AND EXTERNAL EVALUATION

The Quarterly empirical-sign comparator improves on both extreme policies, while the frozen Daily and Web Traffic protocols reject all groups. On Quarterly, the empirical-Bernstein radius certifies a group that the Hoeffding radius does not.

C.5.1 CROSS-FREQUENCY AND EXTERNAL EVALUATION

  • Quarterly Q-Sign’s bounded-loss difference is −0.00817 against persistence and −0.03844 against always accepting, with paired 95% intervals below zero for both comparisons.Table 11 reports forecasting replication results and identifies whether a method has lower test loss than both baselines.Source: §C.5.1 · p. 22, Table 11 · p. 23
  • For the Quarterly candidate-favored group, the Hoeffding and empirical-Bernstein LCBs are −0.0227 and 0.0254, respectively, with 1,540 calibration units.The group’s mean gain is 0.0502 and sample variance is 0.0169.Source: §C.5.1 · p. 23
  • Daily rejects every group because all three calibration mean gains are nonpositive, and the selector matches persistence, which has lower test loss than always executing the candidate.The candidate-favored, ambiguous, and persistence-favored groups have calibration counts of 1, 19, and 1,640.Source: §C.5.1 · p. 23
  • On Web Traffic Weekly, all three groups are rejected and selective execution matches persistence; its paired 95% interval for the loss difference against always executing is [−0.1120, −0.1092].The annual-seasonal proposal was evaluated on 57,841 calibration and 87,222 held-out test page series.Source: §C.5.1 · p. 23

C.5.2 FOURROOMS GROUPWISE GAINS AND CLOSED-LOOP EVALUATION

In FourRooms, both groups have positive test gains and calibration selects the turn group, but the closed-loop pilot shows similarly low navigation success across execution rules. In MuJoCo, all reported groupwise bounded-gain intervals have positive lower endpoints.

C.5.2 FOURROOMS GROUPWISE GAINS AND CLOSED-LOOP EVALUATION

  • Both FourRooms groups have positive test gains under the episode–group loss, with calibration selecting the turn group.Table 12 reports test gains equally weighted across episodes containing each group.Source: §C.5.2 · p. 23, Table 12 · p. 23
  • Across 30 FourRooms evaluation seeds, persistence and LCB execution each succeed in 2/30 episodes, versus 1/30 for always executing; LCB coverage averages 23.9%.The paired success-rate difference against persistence is 0.000, with a 95% interval of [−0.100, 0.100]; the pilot shows similarly low navigation success across all three rules.Source: §C.5.2 · p. 23

C.5.3 MUJOCO GROUPWISE BOUNDED-LOSS GAINS

  • All 324 MuJoCo groupwise bounded-gain bootstrap intervals have positive lower endpoints; seven groups with negative unclipped gains have positive bounded gains ranging from 0.3688 to 0.7560.Table 13 reports groupwise bounded-loss gains across 27 repeated runs.Source: §C.5.3 · p. 23, Table 13 · p. 24

D EXPERIMENT CONFIGURATIONS

The experiment configurations fix architectures and optimizers before test-result aggregation, while candidate fitting and gate selection use separate training and calibration splits. Forecasting, inventory, and action-conditioned configurations are summarized, with complete episodes serving as action-conditioned sampling units.

D EXPERIMENT CONFIGURATIONS

  • Architectures and optimizers were fixed before test-result aggregation; candidate fitting used training data, and gate selection used calibration data.Test-oracle rules provide diagnostic reference values.Source: D EXPERIMENT CONFIGURATIONS · p. 24
  • Table 14 summarizes forecasting and inventory configurations, with counts referring to paired calibration and test units.Source: Table 14 · p. 24
  • Table 15 summarizes action-conditioned configurations, using complete episodes as sampling units.Source: Table 15 · p. 25
  • MuJoCo ensembles use independent Bernoulli bootstraps of training transitions, and normalization statistics and uncertainty tertiles use training units only.Window strides are 10/5/5 for training/calibration/test; each gate horizon uses at most 50,000 training windows, with evaluation batches of 8,192.Source: D EXPERIMENT CONFIGURATIONS · p. 25

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