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REVIEW 4 major objections 6 minor 22 references

Open-DiffLoco shows that differentiable simulation can train a deployable blind quadruped policy in about 20 minutes on one GPU, without reference gaits or privileged base-velocity observations, and the policy tracks commands below 0.2 m/s

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2026-08-04 15:47 UTC pith:PZNWVZGV

load-bearing objection A genuinely useful open-source framework with a real hardware demo, but the central claim that PPO fails under the same minimal-reward setup is not backed by data in the paper. the 4 major comments →

arxiv 2608.02069 v1 pith:PZNWVZGV submitted 2026-08-03 cs.RO cs.LGcs.SYeess.SY

Open-DiffLoco: Open-Source Differentiable Learning for Deployable Blind Quadruped Locomotion

Martin Opat This is my paper
classification cs.RO cs.LGcs.SYeess.SY
keywords differentiable simulationquadruped locomotionblind locomotionSHACMuJoCo XLAJAVEsim-to-real transfervelocity tracking
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

This paper argues that deployable blind quadruped locomotion can be learned entirely through differentiable simulation, without kinematic reference gaits and without a privileged base-velocity sensor. The author implements SHAC in MuJoCo XLA, adds JAVE to keep the critic's Jacobian accurate during early training, and shows the resulting proprioceptive policy transfers to a Unitree Go2. On hardware the policy tracks omnidirectional velocity commands with RMSE below 0.2 m/s, reaches speeds above 1 m/s, and recovers from lateral pushes. Training takes about 20–60 minutes on a single consumer GPU using under 6 GB of VRAM. If the central argument is right, the reward engineering and large compute budgets typical of model-free locomotion learning are largely unnecessary for this class of tasks.

Core claim

The central claim is that the blind-locomotion objective is smooth enough for the bias introduced by contact discontinuities in first-order gradients to be outweighed by the substantial reduction in gradient variance. That trade-off is what makes a minimal differentiable reward set—velocity tracking, height, uprightness, and joint/action penalties—sufficient for gait discovery. The deployed policy removes reference trajectories and base linear velocity from actor observations, and still transfers to real hardware, tracking commanded velocities with RMSE below 0.2 m/s and reaching speeds above 1 m/s. The paper also introduces JAVE, which supervises the critic's Jacobian through a Bellman-grad

What carries the argument

Short-Horizon Actor-Critic (SHAC) truncated differentiable rollout—an actor loss that sums analytic rewards over a short horizon and bootstraps the tail with a learned value function—is the engine of the framework. JAVE (Jacobian-Augmented Value Estimation) augments critic training with a Bellman-gradient loss that supervises the gradient of the value function using a learned one-step dynamics model, correcting the critic's slope where it feeds back into the policy gradient. The minimal reward set carries the conceptual load: its sufficiency is what demonstrates that analytic gradients supply the shaping signal that model-free methods must obtain from auxiliary rewards.

Load-bearing premise

The entire result hinges on the claim that the blind-locomotion objective is smooth enough that contact-discontinuity bias in analytical gradients is smaller than the variance reduction those gradients provide; if that trade-off reverses, training fails to converge to a stable gait.

What would settle it

Reproduce the released training on a single RTX 5080 and deploy the exported policy on a Unitree Go2 with the provided stack. If the policy does not track a 1 m/s forward command on flat ground with RMSE below 0.2 m/s, or if repeated training runs with the default hyperparameters fail to converge to a stable gait, the paper's transfer and smoothness claims would be contradicted.

Watch this falsifier. Get emailed when new claim-graph text bears on it.

If this is right

  • With the released code, a Unitree Go2 policy trained without reference gaits or privileged velocity tracks omnidirectional commands with RMSE below 0.2 m/s and speeds above 1 m/s in real deployment.
  • The same policy withstands uneven terrain and external lateral pushes, recovering after disturbance.
  • Training requires under 6 GB of VRAM and about 20–60 minutes on a single RTX 5080, so differentiable locomotion training no longer needs a large cluster.
  • JAVE improves early-training gradient stability and allows longer analytical horizons, though its final-performance gains over SHAC are modest.
  • This is the first open-source differentiable-simulation framework claimed to produce deployable locomotion policies, making the recipe reproducible.

Where Pith is reading between the lines

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

  • If the smoothness/variance explanation generalizes, the same minimal-reward recipe may transfer to other contact-rich skills such as object manipulation or stair climbing, where reward engineering currently bottlenecks progress.
  • JAVE's idea—supervising the critic's Jacobian rather than only its value—could be applied to adaptive-horizon methods, where the truncation boundary changes every step and critic-gradient errors are likely more damaging.
  • The implicit terrain model (tilted gravity plus Ornstein–Uhlenbeck foot perturbations) is a cheap, differentiable substitute for mesh terrains; an ablation against explicit heightfields could show whether it is sufficient for robust sim-to-real transfer or if harder terrain requires real geometry.
  • Removing base linear velocity from actor observations suggests that the resulting proprioceptive policy could run on robots without velocity estimators, potentially lowering hardware cost for deployment.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The paper presents Open-DiffLoco, an open-source framework that implements the Short-Horizon Actor-Critic (SHAC) algorithm in MuJoCo XLA (MJX) for blind quadruped locomotion. The claimed contributions are: a simplified differentiable reward set with no reference trajectories and no privileged base linear velocity in the actor; a hardware transfer to a Unitree Go2 with reported tracking RMSE below 0.2 m/s, speeds above 1 m/s, and robustness to terrain and pushes; low training cost (about 20-60 minutes, under 6 GB VRAM on an RTX 5080); and an algorithmic extension, Jacobian-Augmented Value Estimation (JAVE), which supervises critic Jacobians via a Bellman-gradient target built from a learned dynamics model. The paper argues that differentiable simulation's first-order gradients provide a dense signal that PPO's high-variance zeroth-order gradients cannot, enabling convergence with minimal rewards. The central hardware result is plausible and potentially valuable, but several load-bearing comparisons and quantitative claims require strengthening.

Significance. If the empirical claims are fully supported, this would be a useful contribution: an open, reproducible differentiable-simulation pipeline for deployable legged locomotion, with substantially reduced reward engineering and computation. The release of code and hardware videos is a concrete strength, as is the demonstration that a modern differentiable simulator can produce deployable blind locomotion on commodity hardware. The JAVE idea of supervising value-function Jacobians is interesting and sensibly motivated by the SHAC truncation-boundary analysis, though the paper appropriately stops short of claiming convergence guarantees. The significance is reduced by the fact that the headline explanatory claim about why PPO fails in this setting is not backed by a same-configuration comparison, and the hardware evaluation lacks the quantitative detail needed to verify the RMSE and robustness claims. Still, the core framework demonstration is a worthwhile result if the missing evidence is supplied.

major comments (4)
  1. [Section II-B and Figure 2] The central explanatory claim is that PPO cannot learn under the deployed minimal-reward/no-reference/no-privileged-velocity setup, and that differentiable simulation succeeds because of reduced gradient variance. This is not supported by the evidence. Section II-B asserts 'we were unable to replicate these results when using PPO's implementation in MuJoCo Playground under the same setup,' but gives no data. More importantly, Section III states that in Figure 2 PPO uses its native reward set and the FoG methods use reference-based parameterisations; this is explicitly not the deployed configuration. Thus the comparison does not test the actual claimed setting. Please either run PPO in the exact deployed configuration (Table I rewards, no reference, no base linear velocity) and report learning curves and deployment metrics, or clearly restrict the claims to a framework demonstration and r
  2. [Section IV, Figure 4] The hardware section reports 'a root-mean-square error below 0.2 m/s' but provides no numerical RMSE values, no per-component (forward, lateral, yaw) breakdown, no number of trials, no standard deviations or error bars, and no protocol for the terrain and disturbance tests. Figure 4 appears to be a single representative trace. This is load-bearing for the paper's central hardware claim. Please add a table with per-axis RMSE, trial counts, command profiles, and, for robustness claims, quantitative perturbation magnitudes and recovery statistics. If results vary across runs, report mean plus or minus standard deviation over multiple deployments.
  3. [Section IV and Table II] The manuscript does not specify which trained policy was deployed on hardware: SHAC or JAVE. It also does not state the exact horizon, number of parallel environments, reward weights, action noise, or domain-randomisation ranges used for the deployed policy. Table II gives ranges, not the configuration responsible for Figure 4 and the videos. This is essential for reproducibility and for interpreting the relative contributions of SHAC and JAVE. Please state the exact training configuration for the deployed policy in the text or in Table II.
  4. [Section II-D and Appendix I] The JAVE target in Eq. (17) is built with a learned dynamics model and a frozen sampled action. As the appendix acknowledges, this removes the policy-feedback term from the Jacobian target when eta = 0 (the current implementation). The theoretical conditions for contraction of the Bellman-gradient operator are explicitly left to future work, which is acceptable. However, the claim that JAVE 'improves early training stability' is supported only by Figure 5, which appears to show single runs without error bars or quantitative gradient-stability metrics. Please provide multi-seed statistics or clearly label Figure 5 as illustrative rather than as evidence.
minor comments (6)
  1. [Abstract and Section II-D] The acronym JAVE is rendered as 'JA VE' in several places; please use a consistent representation.
  2. [Figure 2] The figure layout is confusing: the inset with a secondary PPO axis appears duplicated, and the main curves use a reward scale that the caption says is not comparable across methods. Consider splitting into separate panels or using normalized improvement to make the sample-efficiency claim readable.
  3. [Section II-D] The sentence 'See Appendix II for a full proof' is misleading: Appendix II proves that an L2-bounded value error does not bound the gradient error, which is related but not a proof of the preceding claim about a pointwise-accurate critic biasing policy updates. Please tighten the cross-reference.
  4. [Equation (9) and Appendix I] The notation for the estimated observation map is inconsistent: Eq. (7) writes G_beta(o_c), while Eq. (14) writes hat_G_beta(o_c, bar_a_t). Clarify the arguments and the role of the learned model in Eq. (9).
  5. [Section III] The statement 'FoG methods retain the velocity estimator and kinematic reference parameterisations' should be justified: if these are not the deployed configuration, why are they used for the optimizer comparison? A sentence explaining the design of the ablation would help.
  6. [Section V] The claim that FoG methods are 'approximately 100x more sample efficient' should specify the denominator (e.g., total environment steps for PPO vs. SHAC/JAVE in Figure 2) and note that reward scales differ, so the comparison is qualitative.

Circularity Check

0 steps flagged

No circularity: the paper's central claims are empirical, JAVE is a bootstrapped auxiliary loss rather than a definitional restatement, and the PPO-comparison confound is an evidence issue, not a circular reduction.

full rationale

Open-DiffLoco's derivation chain is empirical and self-contained. The central results—that SHAC in MJX with a minimal differentiable reward set, no reference trajectories, and no privileged base linear velocity yields policies that transfer to a Unitree Go2—are established by training curves, simulation tracking plots, and hardware measurements. The reward terms in Table I directly define the task objective (velocity tracking, height, uprightness, etc.), and the reported RMSE below 0.2 m/s is an evaluation of the same commanded-velocity tracking objective. This is standard RL practice, not a constructional equivalence: the policy is not fitted to the hardware evaluation data, and the reward weights/scales are fixed training hyperparameters rather than fitted to the reported metrics. JAVE's critic-Jacobian supervision is a bootstrapped self-consistency objective (Eqs. 9–17), not a restatement of the actor update or of the task reward; the paper explicitly acknowledges the contractiveness conditions are unproven and that the learned dynamics model shifts rather than eliminates the gradient-error problem (Appendix I). The only notable weakness is that the PPO comparison in Figure 2 is explicitly not run in the deployed configuration ('PPO uses its native reward set and the FoG methods use ... reference-based parameterisations'), and the Section II-B statement that PPO could not replicate the results 'under the same setup' is therefore not documented by Figure 2. This is a correctness/evidence confound about the explanatory claim, not a circularity: no equation reduces to its inputs by construction, no fitted parameter is renamed as a prediction, and there are no load-bearing self-citations (the paper has essentially no self-citations).

Axiom & Free-Parameter Ledger

4 free parameters · 5 axioms · 0 invented entities

The central training result rests on hand-chosen reward weights, unspecified JAVE/OU hyperparameters, and strong domain assumptions about gradient bias, terrain adequacy, and differentiability of the observation dynamics. These are not derived or externally benchmarked.

free parameters (4)
  • Reward weights (Table I) = height 10 (target height 0.3 m), vertical velocity 0.5, upright 0.5, joint deviation 0.3, action rate 0.02, action magni
    Hand-chosen weights in the simplified reward; no sensitivity analysis reported, and the claim that minimal rewards suffice depends on them.
  • JAVE loss weights alpha_TD, alpha_GB = not reported
    Balance TD and gradient losses in Eq. (10); JAVE's measured improvement depends on these values, which are not given.
  • OU terrain perturbation parameters gamma, sigma = not reported (repository only)
    Defines implicit terrain bumps in Eq. (25); the robustness-to-uneven-terrain claim depends on the choice of these parameters.
  • Core training hyperparameters = action noise sigma=0.5, action scale 0.5, actor LR 5e-3, critic LR 5e-4, horizon h=16-32, discount 0.99, GAE lambda 0.95
    Standard SHAC/JAVE hyperparameters chosen by the author; not derived and not swept.
axioms (5)
  • domain assumption Analytical gradients through contact-rich MJX dynamics provide useful descent directions despite unbiasedness loss from contact discontinuities.
    Invoked in Section II-B; the entire training depends on the bias-variance tradeoff favoring first-order gradients.
  • domain assumption Implicit terrain (tilted gravity plus contact-scaled OU foot forces) adequately approximates real uneven terrain for policy transfer.
    Appendix III; used to claim robustness to uneven terrain, but no mesh height field or real terrain geometry is used.
  • domain assumption The Bellman equation is differentiable w.r.t. critic observations and the one-step observation map G_beta exists and is differentiable where used.
    Differentiating Eq. (8) to obtain Eq. (9) requires the value function and G_beta to be differentiable; the paper does not prove this.
  • domain assumption The learned dynamics model F_psi is accurate enough for the JAVE gradient target to improve critic Jacobians.
    Appendix I acknowledges L2 fit does not control Jacobians and requires a curvature bound; this is assumed for the method to help.
  • standard math Gagliardo-Nirenberg interpolation inequality
    Used in Appendix I, Eq. (20); standard functional analysis result.

reviewed 2026-08-04 · how reviews work

0 comments
read the original abstract

Developing deployable locomotion policies through conventional reinforcement learning often requires complex reward engineering and expensive training times. While differentiable simulation offers a highly efficient alternative, open-source tools capable of end-to-end transfer of these policies to physical hardware remain limited. This paper introduces Open-DiffLoco, an open-source framework for training deployable blind quadruped locomotion policies with differentiable simulation. The framework implements the Short-Horizon Actor-Critic (SHAC) algorithm in MuJoCo XLA (MJX) and trains a proprioceptive policy that transfers to real-world hardware. The deployed policy removes privileged actor observations, including base linear velocity, and does not rely on reference trajectories. It also uses a substantially simplified reward function, enabling the robot to discover walking patterns without the complex auxiliary rewards typically used in conventional reinforcement learning pipelines. When deployed on physical hardware (a Unitree Go2 quadruped), the trained policy tracks omnidirectional velocity commands with root-mean-square error below 0.2 m/s, reaches speeds above 1 m/s, and remains robust to uneven terrain and external physical disturbances, such as lateral pushes. Across the reported configurations, training uses under 6 GB of VRAM on a single NVIDIA GeForce RTX 5080 GPU and completes in approximately 20-60 minutes. As an algorithmic extension to SHAC, we propose Jacobian-Augmented Value Estimation (JAVE), which supervises the critic Jacobians to improve early first-order policy-gradient training. To our knowledge, Open-DiffLoco is the first open-source framework for training deployable locomotion policies using differentiable simulation. Deployment videos and source code are available at: https://diffloco.martin-opat.com/

Figures

Figures reproduced from arXiv: 2608.02069 by Martin Opat.

Figure 1
Figure 1. Figure 1: High-level system architecture of the Open-DiffLoco framework. TABLE I: Simplistic reward terms used to train omnidirec￾tional blind locomotion. Term Expression x velocity tracking −(vx − v cmd x ) 2 y velocity tracking −(vy − v cmd y ) 2 Yaw-rate tracking −(ωz − ω cmd z ) 2 Height exp −10(h − 0.3)2  Vertical velocity −0.5v 2 z Upright 0.5(−gz) Joint deviation −0.3 P i (qi − q 0 i ) 2 Action rate −0.02P i… view at source ↗
Figure 2
Figure 2. Figure 2: Comparison of JAVE, SHAC, and PPO in terms of training exponential moving average (EMA) reward as a function of training iterations (left) and number of training steps across all environments (right). PPO uses its native reward implementation, so absolute reward values are not directly comparable across methods. V. DISCUSSION AND LIMITATIONS The proposed methodology can discover different gaits, e.g. trott… view at source ↗
Figure 4
Figure 4. Figure 4: Real-world velocity tracking evaluation. been shown to be capable of training robust policies with a simplified differentiable reward set, without kinematic refer￾ence trajectories and without privileged base linear velocity in the actor observations. The resulting policies transfer to hardware, track omnidirectional velocity commands, and re￾main robust to terrain variation and external disturbances. We a… view at source ↗
Figure 5
Figure 5. Figure 5: compares SHAC and JAVE. The actor gradients in JAVE are more stable than those in SHAC, resulting in better overall convergence and lower tracking errors. This performance gain is especially visible in early training. (a) SHAC (b) JAVE [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗

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This paper was first reviewed by deepseek-v4-flash on August 4, 2026.