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arxiv: 2606.25923 · v1 · pith:JHI7YOCNnew · submitted 2026-06-24 · 💻 cs.LG

DT²: Decision-Targeted Digital Twins

Harry Amad , Mihaela van der Schaar This is my paper

Pith reviewed 2026-06-25 20:06 UTC · model grok-4.3

classification 💻 cs.LG
keywords digital twinsdecision-targeted trainingpolicy rankingfitted Q-evaluationoffline reinforcement learningmodel-based decision making
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The pith

Digital twins trained to minimize transition errors can rank policies suboptimally, but DT² targets rankings to improve selection.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper proves that minimizing one-step transition errors in digital twins does not always produce the best models for ranking policies according to expected reward when model capacity is limited. This holds even with expressive model classes in empirical tests. DT² first applies fitted Q-evaluation to offline data to estimate candidate policy values, then trains the twin so its generated rollouts preserve the pairwise rankings implied by those estimates. The resulting models improve policy ranking accuracy and lower decision regret for both training policies and unseen ones, while keeping simulation fidelity comparable to standard training.

Core claim

When model capacity is limited, training DTs to minimise one-step transition errors can produce suboptimal models for ranking sets of policies according to a reward function. DT² uses fitted Q-evaluation to estimate values of candidate policies from offline data. A DT is then trained to generate rollouts that preserve pairwise policy rankings derived from these proxy ground-truth values with an architecture-agnostic loss function.

What carries the argument

Architecture-agnostic loss that trains the digital twin to preserve pairwise policy rankings obtained from fitted Q-evaluation on offline data.

If this is right

  • DT² yields higher accuracy when ranking policies by expected reward.
  • Decision regret drops during policy selection from the ranked set.
  • Gains appear for both policies present in the offline data and for new policies.
  • Simulation fidelity measured by raw transition error stays comparable to baseline training.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Training objectives for simulators used in decisions should align directly with downstream ranking or selection tasks rather than generic prediction metrics.
  • The ranking-preservation idea could apply to other model-based planning systems where the end goal is comparative evaluation of action sequences.
  • Testing the method on continuous policy parameterizations would show whether the pairwise approach scales beyond discrete candidate sets.

Load-bearing premise

Pairwise policy rankings from fitted Q-evaluation on offline data serve as a reliable proxy for true relative policy values.

What would settle it

A controlled benchmark with known true policy values where DT² produces higher decision regret than a transition-error trained twin on the same data and architecture.

Figures

Figures reproduced from arXiv: 2606.25923 by Harry Amad, Mihaela van der Schaar.

Figure 1
Figure 1. Figure 1: We visualise two diabetes DTs, Φˆ 1 (top) and Φˆ 2 (bottom), under treatment plans with high, low, and adaptive insulin levels, and we consider the ‘value’ of a treatment plan as the time it spends in the optimal glucose region. Φˆ 1 has lower MSE from the true rollouts, yet it leads to an incorrect treatment plan preference ordering (high ≈ low ≻ adaptive). In contrast, Φˆ 2 leads to a correct preference … view at source ↗
Figure 2
Figure 2. Figure 2: When Φ ∈ F/ , the Lsim-optimal DT, Φˆ θ∗ , may land in a region of low decision quality for some candidate policy set Π and reward function r (grey areas). With decision-targeted DT training, we wish to find Φˆ θ′ that resides in a better decision region (green areas), at a small simulation fidelity cost. Proof. See Appendix A.1. From Theorem 3.1 we can see that, when a DT cannot ex￾actly model its target … view at source ↗
Figure 3
Figure 3. Figure 3: State delta across action values, as determined by mecha￾nistic models learnt via L MSE sim and LDT2 , compared to the true Φ. Black dots represent constant-action policies in Π. 6.1.3. PARTIALLY OBSERVED DYNAMICS Finally, we investigate a system with partially observable dynamics, where an unobserved latent variable zt dictates 6 [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Regret and Spearman’s correlation for preference orderings from L NLL sim (hashed) and LDT2 (solid) DTs across base architectures in six continuous control environments. We report averages over 10 seeds, with 95% CIs. the transition distribution, ensuring Φ ∈ F/ even with an ex￾pressive hypothesis space of three-layer MLPs. We consider a one-dimensional system governed by xt+1 = xt +at +zt, where zt ∼ N (0… view at source ↗
Figure 5
Figure 5. Figure 5: plots the Spearman’s correlation and test MSE obtained across these λ settings (N.B. that the λ = 0 set￾ting is equivalent to standard training with L NLL sim only). As expected, we observe a consistent increase in ranking per￾formance and decrease in simulation fidelity as λ increases. Practitioners can therefore effectively use λ to navigate to their desired point along this trade-off during training. Ho… view at source ↗
Figure 6
Figure 6. Figure 6: Regret and Spearman’s correlation for preference orderings from L MSE sim (hashed) and LDT2 (solid) DTs across base architectures in six continuous control environments. We report averages over 10 seeds, with 95% CIs. For visual purposes, the top end of some error bars are cropped out. 25 [PITH_FULL_IMAGE:figures/full_fig_p025_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Regret and Spearman’s correlation for preference orderings from DTs trained via L NLL sim DTs (hashed) and LDT2 with ranking losses of our smoothed Kendall’s (solid), a hinge loss (circles), and a ListNet loss (dotted) across different base architectures. We report averages over 10 seeds, with 95% CIs. For visual purposes, the top end of some bars are cropped out. 27 [PITH_FULL_IMAGE:figures/full_fig_p027… view at source ↗
read the original abstract

A digital twin (DT) is a virtual model of a real-world system that can assist decision-making by simulating scenarios induced by different policies. However, typical machine learning-based DTs do not optimise for this use case. We prove that, when model capacity is limited, training DTs to minimise one-step transition errors can produce suboptimal models for ranking sets of policies according to a reward function. We further show that this holds empirically, even with expressive model classes. To address this, we introduce $\text{DT}^2$, a decision-targeted DT training paradigm. Firstly, $\text{DT}^2$ uses fitted Q-evaluation to estimate values of candidate policies from offline data. A DT is then trained to generate rollouts that preserve pairwise policy rankings derived from these proxy ground-truth values with an architecture-agnostic loss function. We empirically demonstrate the efficacy of our method across a range of settings and architectures. $\text{DT}^2$ consistently improves policy ranking and reduces decision regret during policy selection relative to conventional DT training, both for policies used during training and for unseen policies, while maintaining a good level of raw simulation fidelity.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 2 minor

Summary. The manuscript claims that conventional digital twin (DT) training via one-step transition error minimization can lead to suboptimal models for ranking policies by their values under a reward function, with a proof provided for limited model capacity and empirical evidence even for expressive models. To address this, DT² is introduced, which first applies fitted Q-evaluation (FQE) to offline data to obtain proxy policy values, then trains the DT using an architecture-agnostic loss to preserve the pairwise rankings induced by these proxies. Empirical results demonstrate that DT² improves policy ranking accuracy and reduces decision regret for both in-training and unseen policies compared to standard training, while preserving simulation fidelity.

Significance. If the results hold, this paper makes a significant contribution by highlighting the misalignment between standard simulation objectives and decision-making utility in digital twins, offering a targeted training approach that directly optimizes for policy ranking. The provision of a proof for the limited-capacity case and consistent empirical improvements across multiple settings and architectures are strengths that could guide future work in model-based RL and digital twin applications. The architecture-agnostic nature of the loss is particularly practical.

major comments (2)
  1. [Abstract and method description] The central claim that DT² yields better policy selection relies on the assumption that FQE-derived pairwise rankings serve as a reliable proxy for true policy values. However, the manuscript does not appear to include an independent validation of this proxy (e.g., via on-policy rollouts in environments with known ground truth), which is load-bearing for the decision-targeted objective and the reported reductions in decision regret.
  2. [Proof section (referenced in abstract)] The proof establishes suboptimality only under limited model capacity; the extension to expressive model classes is purely empirical. If the proof technique cannot be extended, this should be explicitly discussed as a limitation of the theoretical contribution.
minor comments (2)
  1. [Abstract] The abstract states that DT² 'consistently improves' but does not quantify the improvements or mention the number of environments/architectures tested; adding such details would strengthen the summary.
  2. [Notation] Ensure that the definition of the loss function in the DT² paradigm is clearly distinguished from standard transition losses, perhaps with an equation number for easy reference.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive comments, which highlight important aspects of our theoretical and empirical claims. We address each major comment below and outline planned revisions.

read point-by-point responses

  1. Referee: [Abstract and method description] The central claim that DT² yields better policy selection relies on the assumption that FQE-derived pairwise rankings serve as a reliable proxy for true policy values. However, the manuscript does not appear to include an independent validation of this proxy (e.g., via on-policy rollouts in environments with known ground truth), which is load-bearing for the decision-targeted objective and the reported reductions in decision regret.

    Authors: We agree that validating the FQE proxy is important for the decision-targeted objective. While our empirical results already measure final policy selection quality and decision regret using ground-truth values (via on-policy evaluation in the benchmark environments), we did not explicitly compare FQE estimates against these ground-truth values in the original manuscript. In the revision, we will add a dedicated validation subsection reporting the correlation between FQE-derived rankings and true policy values across the environments, thereby confirming the proxy's reliability in the settings studied. revision: yes

  2. Referee: [Proof section (referenced in abstract)] The proof establishes suboptimality only under limited model capacity; the extension to expressive model classes is purely empirical. If the proof technique cannot be extended, this should be explicitly discussed as a limitation of the theoretical contribution.

    Authors: The referee is correct: the formal proof applies only to limited-capacity models, with the expressive-model case supported solely by experiments. We will revise the manuscript to explicitly state this scope as a limitation of the theoretical contribution and note that extending the proof technique to general function classes is left for future work. revision: yes

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper's central derivation consists of a capacity-limited proof that one-step transition minimization can be suboptimal for policy ranking, plus an empirical method that explicitly trains on FQE-derived pairwise rankings as an external proxy target via a new loss. This does not reduce any claimed result to its inputs by construction, nor does it involve self-definitional mappings, fitted inputs renamed as predictions, load-bearing self-citations, imported uniqueness theorems, smuggled ansatzes, or renamed known results. The FQE proxy is treated as an independent (if imperfect) benchmark rather than being generated from the DT itself, leaving the derivation self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review based on abstract only. The central claim rests on the domain assumption that fitted Q-evaluation yields usable proxy rankings and that preserving those rankings improves decisions more than transition accuracy.

axioms (1)
  • domain assumption Fitted Q-evaluation on offline data produces reliable pairwise policy rankings that should be preserved by the digital twin.
    Invoked to generate the proxy ground-truth values used in the DT² loss.

pith-pipeline@v0.9.1-grok · 5730 in / 1311 out tokens · 23866 ms · 2026-06-25T20:06:02.339399+00:00 · methodology

discussion (0)

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Reference graph

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