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arxiv: 2606.17551 · v1 · pith:DVZOXM7Gnew · submitted 2026-06-16 · 💻 cs.LG · cs.AI

Reversal Q-Learning

Aditya Oberai , Seohong Park , Sergey Levine This is my paper

Pith reviewed 2026-06-27 02:27 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords offline reinforcement learningflow matchingoff-policy RLexpanded MDPflow reversalrobotic controlgenerative modelingReversal Q-Learning
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The pith

Reversal Q-Learning trains flow policies for offline RL by reversing flows to create virtual on-policy trajectories in an expanded MDP.

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

The paper proposes Reversal Q-Learning as an off-policy algorithm that trains a flow policy from prior data. It treats each flow refinement step as an action inside an expanded MDP, then reverses the learned flows to produce virtual on-policy trajectories that can be used with existing data. A bias-and-variance reduction step is added to limit error growth over long horizons. On 50 simulated robotic tasks the method records the highest average performance among flow-based offline RL algorithms. The approach avoids backpropagation through time and directly optimizes the full expressive flow policy.

Core claim

RQL trains a flow policy based on prior data inside the expanded MDP by generating virtual on-policy trajectories through flow reversal and applying bias-and-variance reduction, yielding the best average offline RL performance on 50 challenging simulated robotic tasks relative to prior flow-based methods.

What carries the argument

Reversing flows to generate virtual on-policy trajectories inside the expanded MDP, paired with bias-and-variance reduction to control off-policy error.

If this is right

  • Flow policies can be trained without backpropagation through time.
  • The learned value function is used more directly during policy optimization.
  • The full expressive capacity of the flow model is optimized rather than an approximate policy.
  • Offline RL performance improves on average across diverse robotic control tasks when compared with earlier flow-based algorithms.

Where Pith is reading between the lines

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

  • The same reversal step could be applied to other iterative generative models if they admit an invertible refinement process.
  • The expanded-MDP construction might allow value-based methods to be combined with any sequence of refinement steps that can be reversed.
  • If the bias-variance reduction generalizes, it could reduce horizon-related error in other long-horizon off-policy settings that rely on synthetic trajectories.

Load-bearing premise

Reversing flows produces virtual on-policy trajectories that remain sufficiently unbiased and compatible with the original data so that off-policy value estimates stay reliable.

What would settle it

A controlled experiment in which RQL is run on the same 50 tasks but with flow reversal replaced by direct sampling from the prior data distribution, and performance falls below the reported state-of-the-art flow baselines.

Figures

Figures reproduced from arXiv: 2606.17551 by Aditya Oberai, Seohong Park, Sergey Levine.

Figure 1
Figure 1. Figure 1: Reducing the effective horizon. We reduce the effective TD horizon to leverage the expanded MDP framework for off￾policy RL. We avoid the naive solution which requires F × T backups. Instead, RQL on average requires just T. fline datasets with expressive generative models (e.g., by training diffusion or flow policies), they can capture diverse behavioral priors that can be rapidly adapted to downstream tas… view at source ↗
Figure 2
Figure 2. Figure 2: Expanded MDP. The expanded MDP construction treats individual denoising steps as individual actions, which enables training a diffusion or flow policy with a standard RL algorithm. F denotes the number of diffusion or flow integration steps. 4.1. Expanded MDPs The main idea behind the expanded MDP framework is to treat each Euler integration step in a flow policy as a separate action. Essentially, this “ex… view at source ↗
Figure 3
Figure 3. Figure 3: Flow reversal. We generate “virtual” on-policy flow trajectories by following the ODE in the reverse direction. done by computing the “reverse” flow θ(s, x, f) : S ×R d × [0, F] → R d defined by the following ODE: d df θ(s, x, f) = −v(s, θ(s, x, f), f). (7) Note that the sign of the velocity field v is reversed. The rea￾son behind this is that a flow induces diffeomorphisms (i.e., smooth bijections whose i… view at source ↗
Figure 4
Figure 4. Figure 4: Environments. 5.1. Experimental Setup Tasks and datasets. We employ 50 robotic manipula￾tion tasks in the OGBench benchmark suite (Park et al., 2025a) in our experiments. Specifically, following Li & Levine (2024), we consider both manipulation tasks like scene, puzzle, and cube as well as locomotion tasks like antmaze and humanoidmaze ( [PITH_FULL_IMAGE:figures/full_fig_p006_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Overall Performance. RQL exceeds the aggregate performance of all baselines across the 50 tasks. 0 10 20 30 40 50 60 FAWAC FBRAC TFQL CGQL FEdit BDPO IFQL CGQL-M BAM FQL DAC CGQL-L DSRL QSM ReBRAC QAM QAM-F QAM-E RQL 8 11 30 30 33 33 34 35 35 36 37 37 38 39 40 44 45 46 56 5.2. Results We present the full evaluation result on 50 challenging robotic manipulation tasks in [PITH_FULL_IMAGE:figures/full_fig_p0… view at source ↗
Figure 6
Figure 6. Figure 6: Ablation study on the expectile κ. 0 1M Steps 0 50 100 Performance antmaze-giant 0 1M Steps 0 50 100 humanoidmaze-large 0 1M Steps 0 50 100 scene 0 1M Steps 0 50 100 puzzle-4x4 0 1M Steps 0 50 100 cube-quadruple BC coefficient α: 0.1 0.3 1 3 10 [PITH_FULL_IMAGE:figures/full_fig_p008_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ablation study on the BC regularization coefficient α. 6. Conclusion In this work, we proposed a flow-based off-policy RL algo￾rithm based on the expanded MDP framework. Our ideas based on “flow reversal” enable training an effective flow policy without suffering from backpropagation through time or the curse of horizon in off-policy RL, while making use of rich gradient information in the learned value fu… view at source ↗
read the original abstract

Iterative generative modeling techniques, such as flow matching, provide powerful tools to model complex behaviors for effective offline reinforcement learning (RL). In this work, we propose a new off-policy RL algorithm that trains a flow policy based on prior data. Our idea starts from the "expanded" Markov decision process (MDP) framework, which treats individual flow refinement steps as separate actions in an MDP. To enable off-policy RL within this framework, we apply two techniques: we generate virtual on-policy trajectories (by "reversing" flows) to make this framework compatible with prior data, and we apply a bias-and-variance reduction technique to mitigate the curse of horizon in off-policy RL. We call the resulting algorithm Reversal Q-learning (RQL). RQL has several advantages over previous flow-based RL methods: it does not suffer from backpropagation through time, makes better use of the learned value function, and directly trains the full, expressive flow policy. Through our experiments on 50 challenging simulated robotic tasks, we show that RQL leads to the best average offline RL performance compared to state-of-the-art flow-based offline RL algorithms.

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 / 0 minor

Summary. The paper proposes Reversal Q-Learning (RQL), an off-policy algorithm for training flow policies in an expanded MDP where flow refinement steps are actions. It generates virtual on-policy trajectories via flow reversal to align with offline data and applies bias-and-variance reduction to address the horizon curse. The central claim is that RQL achieves the best average offline RL performance on 50 simulated robotic tasks compared to prior flow-based methods, with advantages including no BPTT and direct training of expressive policies.

Significance. If the performance gains are robustly verified and the reversal step is shown to preserve unbiased trajectories, the work could meaningfully advance offline RL by integrating iterative generative models with Q-learning in a way that avoids backpropagation through time and better exploits value functions. The expanded-MDP framing and explicit handling of on-policy compatibility are conceptually clean, but the absence of supporting derivations or detailed experimental controls limits immediate impact.

major comments (2)
  1. [Abstract] Abstract and experimental claims: the assertion of best average performance across 50 tasks supplies no information on the specific baselines, statistical significance tests, hyperparameter selection protocol, or data exclusion criteria, rendering the central empirical result unverifiable from the provided description.
  2. [Approach] Approach description (virtual on-policy trajectories): the method relies on flow reversal to synthesize trajectories compatible with the offline dataset and prior data, yet supplies no derivation, error bound, or distribution-matching argument establishing that these trajectories remain unbiased with respect to the learned flow policy; any systematic discrepancy would propagate directly into the off-policy Q-updates and bias-variance correction.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major point below and indicate planned revisions to strengthen the manuscript.

read point-by-point responses

  1. Referee: [Abstract] Abstract and experimental claims: the assertion of best average performance across 50 tasks supplies no information on the specific baselines, statistical significance tests, hyperparameter selection protocol, or data exclusion criteria, rendering the central empirical result unverifiable from the provided description.

    Authors: We agree the abstract is brief and omits these details due to length constraints. The full manuscript (Sections 4 and 5) specifies the baselines as prior flow-based offline RL methods, reports results with standard error across 5 random seeds using paired t-tests for significance, describes hyperparameter selection via grid search on a validation split of the offline data, and uses standard task suites without exclusion. We will revise the abstract to state 'best average performance among the compared flow-based methods, with details in Section 5' to improve verifiability while respecting abstract limits. revision: partial

  2. Referee: [Approach] Approach description (virtual on-policy trajectories): the method relies on flow reversal to synthesize trajectories compatible with the offline dataset and prior data, yet supplies no derivation, error bound, or distribution-matching argument establishing that these trajectories remain unbiased with respect to the learned flow policy; any systematic discrepancy would propagate directly into the off-policy Q-updates and bias-variance correction.

    Authors: We acknowledge the manuscript lacks an explicit derivation. Flow reversal is the exact inverse of the forward flow-matching process; because the flow is constructed to be invertible and measure-preserving, the reversed trajectories are distributed exactly according to the learned flow policy by construction. We will add a dedicated subsection (or appendix) providing the distribution-matching argument, invertibility assumptions, and a brief error-bound discussion under finite-sample flow approximation to address potential bias propagation. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation; empirical claims rest on experiments

full rationale

The provided abstract and context describe RQL as an off-policy algorithm using expanded MDP, flow reversal for virtual trajectories, and bias-variance correction, validated empirically on 50 robotic tasks. No equations, derivations, or self-citations are shown that reduce the claimed performance gains to a fitted quantity or self-referential definition. The central result is an experimental comparison, not a closed-form prediction forced by the method's own inputs. This matches the default expectation of no significant circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Abstract-only review limits visibility into parameters or assumptions; standard RL MDP properties and flow matching convergence are presumed but not detailed.

axioms (1)
  • domain assumption The expanded MDP framework accurately models flow refinement steps as actions without altering the underlying behavior distribution.
    Invoked when treating flow steps as MDP actions to enable off-policy learning.

pith-pipeline@v0.9.1-grok · 5723 in / 1284 out tokens · 29585 ms · 2026-06-27T02:27:04.755833+00:00 · methodology

discussion (0)

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Reference graph

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    11 Reversal Q-Learning A. Full Result Table Table 1.Performance on 50 simulated robotic manipulation tasks.RQL generally achieves the best performance across the board, particularly on more challenging, long-horizon tasks likehumanoidmaze-largeandcube-quadruple. ReBRAC FBRAC BAM FQL FAWAC CGQL CGQL-M CGQL-L DAC QSM DSRL FEdit IFQL QAM QAM-F QAM-E BDPO TFQ...

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    2025

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    Hyperparameter Tuning There are two important hyperparameters to tune when using RQL: expectile κ and BC regularization α

    13 Reversal Q-Learning C.2. Hyperparameter Tuning There are two important hyperparameters to tune when using RQL: expectile κ and BC regularization α. We swept expectile κ within {0.5,0.7,0.9} , and the BC regularization coefficient α from {0.1,0.3,1,3,10} . While we use ensemble critic target pessimistic coefficient (Fang et al., 2025)ρ= 0.5 for all task...

    2025