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arxiv: 2605.22376 · v1 · pith:P5CZ7ZIEnew · submitted 2026-05-21 · 💻 cs.LG

Target-Aligned Bellman Backup for Cross-domain Offline Reinforcement Learning

Wei Liu , Ting Long This is my paper

Pith reviewed 2026-05-22 07:59 UTC · model grok-4.3

classification 💻 cs.LG
keywords cross-domain offline reinforcement learningBellman targetsdata transferabilityselective backuppolicy optimizationvalue estimation
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The pith

Assessing source-domain transitions by their alignment with target-domain Bellman targets rather than surface similarity improves policy learning in cross-domain offline RL with scarce target data.

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

The paper claims that standard ways of transferring data from a source domain to a target domain in offline reinforcement learning rely on measuring how similar individual transitions look or behave, yet this can mislead because visually or dynamically similar transitions often produce different long-term returns once the policy is executed in the target environment. Because policy optimization depends on accurate Bellman targets to judge the quality of actions, the authors argue that transferability should instead be judged by how much each source transition helps produce reliable Bellman targets in the target domain. They introduce a selective backup procedure that keeps only those source transitions whose contribution improves target-domain value estimation. A reader would care because many practical RL problems have abundant source data but very little target data, and the mismatch between surface similarity and value consistency explains why prior transfer methods sometimes degrade performance.

Core claim

The central claim is that assessing the transferability of source-domain transitions based on their alignment with target-domain Bellman targets, rather than superficial transition similarity, enables more effective policy learning in cross-domain offline RL with limited target data.

What carries the argument

Target-Aligned Bellman Backup (TABB), which selectively leverages source-domain data by measuring their contribution to accurate Bellman target estimation in the target domain.

If this is right

  • Source data that produces inconsistent long-term returns in the target domain is down-weighted even if the transitions appear similar.
  • Policy optimization receives higher-quality value estimates when target data is highly limited.
  • The method produces consistent performance gains across a broad range of cross-domain offline RL settings.

Where Pith is reading between the lines

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

  • The same alignment principle could be tested in online cross-domain transfer where new target samples can be collected adaptively.
  • It raises the question of whether other transfer problems in sequential decision-making should replace state-action similarity with value-function alignment.
  • If the alignment score can be computed without extra target samples, the approach may lower the data requirements for safe deployment in new environments.

Load-bearing premise

Alignment with target-domain Bellman targets can be measured reliably from source data alone and used for selective backup without introducing new biases or requiring extra target-domain samples for calibration.

What would settle it

An experiment in which source transitions are selected by measured alignment with target Bellman targets yet the resulting policy performs no better than, or worse than, a policy trained with similarity-based selection on the same limited target data.

Figures

Figures reproduced from arXiv: 2605.22376 by Ting Long, Wei Liu.

Figure 1
Figure 1. Figure 1: Transition and return distribution However, such strategies can be problematic. As il￾lustrated in [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Results under different levels. We evaluate the robustness of TABB from two per￾spectives: varying dynamics-shift intensities and heterogeneous source-target data quality. Varying dynamics-shift intensities. We construct cross-domain tasks with varying friction levels in the Hopper and Walker2D environments. The fric￾tion level is selected from {0.1, 0.5, 2.0, 5.0}, cov￾ering a broad range of dynamics vari… view at source ↗
Figure 3
Figure 3. Figure 3: Oracle Bellman Error of source tran￾sitions ranked by TBM and transition similarity. TABB uses TBM to estimate the target-domain Bellman target for each source transition, and measures its mismatch with the original source Bellman target. The resulting mismatch is then used to reweight source transitions according to their consis￾tency with target-domain Bellman learning. To empirically examine whether the… view at source ↗
read the original abstract

Cross-domain offline reinforcement learning (CDRL) aims to improve policy learning in a target domain by leveraging data collected from a source domain. Existing works typically assess the transferability of source-domain data by measuring its similarity to target-domain transitions, and implicitly perform transition-level selection. Transitions that are considered similar are assigned higher weights or rewards, while dissimilar ones are down-weighted. However, transition-level similarity does not necessarily imply consistency in long-term returns. Even visually or dynamically similar transitions may lead to significantly different outcomes in the target domain, which can mislead policy learning and degrade performance. To address this issue, we revisit the fundamental objective of policy learning. Since policy optimization ultimately relies on Bellman targets to evaluate the quality of decisions, we propose to assess the transferability of source-domain transitions based on their alignment with target-domain Bellman targets, rather than superficial transition similarity. Based on this insight, we propose a method termed Target-Aligned Bellman Backup (TABB), which selectively leverages source-domain data by measuring their contribution to accurate Bellman target estimation in the target domain. We evaluate TABB across a broad range of cross-domain offline RL settings with highly limited target-domain data. Experimental results show that TABB consistently achieves strong performance.

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 paper proposes Target-Aligned Bellman Backup (TABB) for cross-domain offline RL. It claims that evaluating source-domain transition transferability via alignment with target-domain Bellman targets (rather than transition-level similarity) enables more effective policy learning when target data is highly limited. The method selectively backs up source data according to its contribution to accurate target Bellman estimation, and experiments across a range of CDRL settings are reported to show consistent strong performance.

Significance. If the central claim holds, the work offers a conceptually clean shift from superficial similarity metrics to value-consistent selection in CDRL. This could reduce bias from mismatched long-term returns and improve data efficiency in low-target-data regimes. The emphasis on Bellman-target alignment is a strength relative to prior transition-similarity approaches.

major comments (2)
  1. [Method / Target Bellman target estimation] The skeptic concern is load-bearing: with highly limited target data, any estimate of the target value function or Bellman residual necessarily has high variance and coverage gaps. The paper must show (e.g., via ablation or theoretical bound) that the alignment score does not systematically prefer source transitions that fit estimation error rather than true target dynamics; otherwise the claimed advantage over similarity-based selection collapses.
  2. [Experiments] Experimental claims of 'strong performance' and 'consistent' gains require concrete support. The manuscript should report statistical significance, number of seeds, exact baselines (including recent similarity-based CDRL methods), and ablations isolating the Bellman-alignment component versus naive weighting.
minor comments (2)
  1. [Method] Notation for the alignment score and the selective backup operator should be introduced with a clear equation early in the method section to avoid ambiguity when reading the algorithm.
  2. [Abstract / Introduction] The abstract states results across 'a broad range of cross-domain offline RL settings' but does not enumerate the domains or difficulty levels; a short table or list in the introduction would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and insightful comments. We address each major comment below and describe the revisions we will make to strengthen the paper.

read point-by-point responses

  1. Referee: [Method / Target Bellman target estimation] The skeptic concern is load-bearing: with highly limited target data, any estimate of the target value function or Bellman residual necessarily has high variance and coverage gaps. The paper must show (e.g., via ablation or theoretical bound) that the alignment score does not systematically prefer source transitions that fit estimation error rather than true target dynamics; otherwise the claimed advantage over similarity-based selection collapses.

    Authors: We appreciate this important concern. Our alignment score is explicitly defined to measure contribution to accurate target-domain Bellman target estimation rather than raw transition similarity. While we acknowledge that limited target data introduces variance, the selection criterion prioritizes source transitions whose inclusion reduces the estimated Bellman residual on the observed target samples. In the revision we add an ablation that perturbs the target value estimates with controlled noise and shows that TABB retains its advantage over similarity baselines, indicating that the method is not simply fitting estimation artifacts. A full theoretical guarantee remains difficult in the fully offline cross-domain setting, but the added empirical analysis directly tests the skeptic scenario raised. revision: yes

  2. Referee: [Experiments] Experimental claims of 'strong performance' and 'consistent' gains require concrete support. The manuscript should report statistical significance, number of seeds, exact baselines (including recent similarity-based CDRL methods), and ablations isolating the Bellman-alignment component versus naive weighting.

    Authors: We agree that the experimental section would benefit from greater rigor. In the revised manuscript we report results over 10 random seeds with mean and standard deviation, include paired t-test p-values for all comparisons, and explicitly list all baselines (including the most recent similarity-based CDRL approaches). We also add an ablation that replaces the Bellman-alignment weighting with a naive transition-similarity weighting scheme while keeping all other components fixed; the performance drop confirms the contribution of the alignment component. These changes directly address the request for concrete support of the reported gains. revision: yes

Circularity Check

0 steps flagged

No significant circularity; derivation remains self-contained

full rationale

The paper defines TABB by measuring source transitions' contribution to target-domain Bellman target accuracy, using an external target value estimate rather than fitting parameters to the same quantity being predicted. No step reduces a claimed prediction to a fitted input by construction, nor relies on self-citation for a uniqueness theorem or ansatz. The central method is specified via explicit alignment scoring on Bellman residuals, which is independent of the final policy performance metric. This qualifies as a normal non-finding under the guidelines.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The report is based solely on the abstract; no specific free parameters, axioms, or invented entities can be extracted or verified from the provided text.

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Reference graph

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