pith. machine review for the scientific record. sign in

arxiv: 2604.08036 · v1 · submitted 2026-04-09 · 💻 cs.LG · cs.RO

Recognition: 2 theorem links

· Lean Theorem

PriPG-RL: Privileged Planner-Guided Reinforcement Learning for Partially Observable Systems with Anytime-Feasible MPC

Mohsen Amiri , Ali Beikmohammadi , Sindri Magnu\'sson , Mehdi Hosseinzadeh
Authors on Pith no claims yet

Pith reviewed 2026-05-10 17:33 UTC · model grok-4.3

classification 💻 cs.LG cs.RO
keywords reinforcement learningpartial observabilitymodel predictive controlprivileged informationknowledge distillationPOMDPquadruped locomotion
0
0 comments X

The pith

A privileged anytime-feasible MPC planner can distill its full-state guidance to train a stronger RL policy despite the agent's partial observations.

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

The paper sets out to show that an RL agent facing only lossy state observations can still reach high performance and sample efficiency if, during training only, it receives guidance from a separate planner that sees the true state and runs an approximate dynamical model. The core mechanism is a distillation step inside Soft Actor-Critic that transfers the planner's decisions into the policy without requiring the planner at test time. If the transfer works, the resulting policy can be deployed on hardware that never has privileged information, such as a quadruped navigating obstacle fields with onboard sensors alone. The authors supply both a convergence-style analysis and hardware experiments to support the claim.

Core claim

In a POMDP where the learning agent receives only a lossy projection of the state, an anytime-feasible MPC planner that has access to the true state and an approximate model can be used exclusively during training to generate guidance; Planner-to-Policy Soft Actor-Critic then distills this guidance so that the final policy outperforms a standard SAC baseline in both sample efficiency and asymptotic return, with the framework validated in Isaac Lab simulation and on a physical Unitree Go2.

What carries the argument

Planner-to-Policy Soft Actor-Critic (P2P-SAC), which augments the standard SAC critic and actor updates with a distillation loss that aligns the policy's action distribution to the privileged planner's anytime-feasible MPC actions.

If this is right

  • The learned policy operates without the planner or full state at deployment time.
  • Sample efficiency rises because the planner supplies high-quality action targets during training.
  • The same distillation structure applies to any planner that can run in real time with privileged information.
  • Theoretical analysis guarantees convergence under standard POMDP and MPC assumptions.

Where Pith is reading between the lines

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

  • The approach could be combined with other privileged-information methods such as privileged simulation or teacher-student frameworks to further reduce the observability gap.
  • If the approximate model used by the planner is updated online from the learning agent's experience, the method might close the sim-to-real gap more tightly than static MPC.
  • The framework suggests a general recipe for any robotic task where full-state information is cheap in simulation or motion-capture but expensive on the physical platform.

Load-bearing premise

The planner's actions, computed from an approximate model and full state, will transfer to improve the partial-observation policy without causing instability or negative transfer.

What would settle it

A controlled ablation in which P2P-SAC shows no statistically significant gain in sample efficiency or final return over vanilla SAC on the same partial-observation quadruped tasks, or fails to transfer to hardware.

Figures

Figures reproduced from arXiv: 2604.08036 by Ali Beikmohammadi, Mehdi Hosseinzadeh, Mohsen Amiri, Sindri Magnu\'sson.

Figure 1
Figure 1. Figure 1: Illustration of the proposed PriPG-RL architecture during training. [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Training curves: mean episodic reward (solid lines, left y-axis) [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Hardware experiments using the Unitree Go2 quadruped. The [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
read the original abstract

This paper addresses the problem of training a reinforcement learning (RL) policy under partial observability by exploiting a privileged, anytime-feasible planner agent available exclusively during training. We formalize this as a Partially Observable Markov Decision Process (POMDP) in which a planner agent with access to an approximate dynamical model and privileged state information guides a learning agent that observes only a lossy projection of the true state. To realize this framework, we introduce an anytime-feasible Model Predictive Control (MPC) algorithm that serves as the planner agent. For the learning agent, we propose Planner-to-Policy Soft Actor-Critic (P2P-SAC), a method that distills the planner agent's privileged knowledge to mitigate partial observability and thereby improve both sample efficiency and final policy performance. We support this framework with rigorous theoretical analysis. Finally, we validate our approach in simulation using NVIDIA Isaac Lab and successfully deploy it on a real-world Unitree Go2 quadruped navigating complex, obstacle-rich environments.

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 addresses RL under partial observability in POMDPs by introducing a privileged planner (anytime-feasible MPC with access to approximate dynamics and full state) available only during training. It proposes P2P-SAC to distill the planner's privileged actions and knowledge into the learning policy, claims rigorous theoretical analysis supporting the approach, and reports successful validation in NVIDIA Isaac Lab simulation plus real-world deployment on a Unitree Go2 quadruped navigating obstacle-rich environments.

Significance. If the distillation transfers reliably, the work could meaningfully advance hybrid planning-RL methods for POMDPs in robotics, where privileged information is often available at training but not deployment. The sim-to-real result on a physical quadruped and the provision of theoretical analysis are concrete strengths that would elevate the contribution beyond purely empirical distillation techniques.

major comments (2)
  1. [§4] §4 (Theoretical Analysis): The claimed rigorous theoretical analysis supporting P2P-SAC distillation does not appear to include explicit error bounds or Lipschitz-style analysis on the discrepancy between the MPC planner's approximate dynamics/privileged state and the true partially observed system; without this, the guarantee against negative transfer or instability remains unanchored and is load-bearing for the central transfer claim.
  2. [§5] §5.2–5.3 (Experiments): The reported improvements in sample efficiency and final performance on the Unitree Go2 lack reported statistical significance (e.g., error bars across seeds, p-values vs. baselines), ablation on the distillation loss terms, or quantification of model mismatch effects; this weakens the evidence that the planner guidance reliably mitigates partial observability rather than succeeding due to favorable simulation conditions.
minor comments (2)
  1. [Abstract] Abstract: The phrase 'rigorous theoretical analysis' could be strengthened by briefly indicating the nature of the result (e.g., convergence under bounded mismatch) to better set reader expectations.
  2. [§3] Notation and §3: Ensure the POMDP tuple and the exact form of the P2P-SAC objective (including how privileged actions are used as targets or regularizers) are defined with consistent symbols before the algorithm description.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments identify important opportunities to strengthen both the theoretical grounding and the empirical evidence. We address each major comment below and will incorporate the suggested revisions in the next version of the manuscript.

read point-by-point responses

  1. Referee: [§4] §4 (Theoretical Analysis): The claimed rigorous theoretical analysis supporting P2P-SAC distillation does not appear to include explicit error bounds or Lipschitz-style analysis on the discrepancy between the MPC planner's approximate dynamics/privileged state and the true partially observed system; without this, the guarantee against negative transfer or instability remains unanchored and is load-bearing for the central transfer claim.

    Authors: We appreciate the referee's observation. Section 4 presents a rigorous analysis establishing policy improvement and convergence of P2P-SAC when the planner provides privileged guidance, under the modeling assumption that the planner's approximate dynamics remain sufficiently close to the true system. However, we acknowledge that the manuscript does not derive explicit Lipschitz constants or quantitative error bounds on the specific dynamics mismatch. We will revise Section 4 to add a supporting lemma that bounds the propagation of model error into the value-function approximation and the resulting policy stability, thereby making the conditions for avoiding negative transfer explicit. revision: yes

  2. Referee: [§5] §5.2–5.3 (Experiments): The reported improvements in sample efficiency and final performance on the Unitree Go2 lack reported statistical significance (e.g., error bars across seeds, p-values vs. baselines), ablation on the distillation loss terms, or quantification of model mismatch effects; this weakens the evidence that the planner guidance reliably mitigates partial observability rather than succeeding due to favorable simulation conditions.

    Authors: We agree that additional statistical rigor and targeted ablations would strengthen the experimental claims. In the revised manuscript we will: (i) report mean performance with standard-deviation error bars computed over at least five independent random seeds for all learning curves and final metrics; (ii) include ablation studies that isolate the contribution of each term in the P2P-SAC distillation loss; and (iii) add a sensitivity analysis that systematically varies the accuracy of the planner's dynamics model and quantifies the resulting degradation in policy performance. These changes will provide clearer evidence that the observed gains arise from the planner's mitigation of partial observability. revision: yes

Circularity Check

0 steps flagged

No significant circularity; P2P-SAC distillation and theoretical support remain independent of self-referential fits

full rationale

The paper presents P2P-SAC as a new distillation procedure from an anytime-feasible MPC planner (with privileged state and approximate model) to a policy under partial observability. No equations, derivations, or self-citations are shown that reduce the claimed performance gains or transfer guarantees to fitted parameters renamed as predictions, self-definitions, or load-bearing prior results by the same authors. The 'rigorous theoretical analysis' is invoked as external support rather than a closed loop. This matches the default expectation of non-circularity for a method paper whose central contribution is a novel training procedure.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The framework rests on standard POMDP modeling and RL assumptions plus the domain assumption that a privileged planner can be constructed and will provide transferable guidance.

axioms (2)
  • domain assumption The environment is a POMDP where the learning agent receives only a lossy projection of the true state while a planner has privileged full-state access during training.
    Explicitly stated in the problem formalization in the abstract.
  • domain assumption An approximate dynamical model suffices for the MPC planner to generate useful guidance despite model mismatch.
    Implicit in the choice of MPC as the planner agent.

pith-pipeline@v0.9.0 · 5493 in / 1320 out tokens · 85601 ms · 2026-05-10T17:33:48.955211+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

36 extracted references · 9 canonical work pages · 4 internal anchors

  1. [1]

    Ta-explore: Teacher-assisted exploration for facilitating fast reinforcement learning,

    A. Beikmohammadi and S. Magn ´usson, “Ta-explore: Teacher-assisted exploration for facilitating fast reinforcement learning,” inProceedings of the 2023 International Conference on Autonomous Agents and Multiagent Systems, 2023, pp. 2412–2414

    2023

  2. [2]

    Human-level control through deep reinforcement learning,

    V . Mnih, K. Kavukcuoglu, D. Silver, A. A. Rusu, J. Veness, M. G. Bellemare, A. Graves, M. Riedmiller, A. K. Fidjeland, G. Ostrovski et al., “Human-level control through deep reinforcement learning,” nature, vol. 518, no. 7540, pp. 529–533, 2015

    2015

  3. [3]

    Benchmarking deep reinforcement learning for continuous control,

    Y . Duan, X. Chen, R. Houthooft, J. Schulman, and P. Abbeel, “Benchmarking deep reinforcement learning for continuous control,” inInternational conference on machine learning. PMLR, 2016, pp. 1329–1338

    2016

  4. [4]

    Partially observable markov decision processes in robotics: A survey,

    M. Lauri, D. Hsu, and J. Pajarinen, “Partially observable markov decision processes in robotics: A survey,”IEEE Transactions on Robotics, vol. 39, no. 1, pp. 21–40, 2022

    2022

  5. [5]

    Proximal Policy Optimization Algorithms

    J. Schulman, F. Wolski, P. Dhariwal, A. Radford, and O. Klimov, “Proximal policy optimization algorithms,”arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  6. [6]

    Addressing function approxi- mation error in actor-critic methods,

    S. Fujimoto, H. Hoof, and D. Meger, “Addressing function approxi- mation error in actor-critic methods,” inInternational conference on machine learning. PMLR, 2018, pp. 1587–1596

    2018

  7. [7]

    Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor,

    T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine, “Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor,” inInternational conference on machine learning. Pmlr, 2018, pp. 1861–1870

    2018

  8. [8]

    Accelerating actor-critic- based algorithms via pseudo-labels derived from prior knowledge,

    A. Beikmohammadi and S. Magn ´usson, “Accelerating actor-critic- based algorithms via pseudo-labels derived from prior knowledge,” Information Sciences, vol. 661, p. 120182, 2024

    2024

  9. [9]

    When to trust your model: Model-based policy optimization,

    M. Janner, J. Fu, M. Zhang, and S. Levine, “When to trust your model: Model-based policy optimization,”Advances in neural information processing systems, vol. 32, 2019

    2019

  10. [10]

    Concrete Problems in AI Safety

    D. Amodei, C. Olah, J. Steinhardt, P. Christiano, J. Schulman, and D. Man ´e, “Concrete problems in ai safety,”arXiv preprint arXiv:1606.06565, 2016

    work page internal anchor Pith review arXiv 2016

  11. [11]

    Rigorous agent evaluation: An adversarial approach to uncover catastrophic failures,

    J. Uesato, A. Kumar, C. Szepesvari, T. Erez, A. Ruderman, K. An- derson, N. Heess, P. Kohliet al., “Rigorous agent evaluation: An adversarial approach to uncover catastrophic failures,”arXiv preprint arXiv:1812.01647, 2018

    work page arXiv 2018

  12. [12]

    Discovering state-of-the-art reinforcement learning algorithms,

    J. Oh, G. Farquhar, I. Kemaev, D. A. Calian, M. Hessel, L. Zintgraf, S. Singh, H. Van Hasselt, and D. Silver, “Discovering state-of-the-art reinforcement learning algorithms,”Nature, vol. 648, no. 8093, pp. 312–319, 2025

    2025

  13. [13]

    Reinforcement learning algorithms: A brief survey,

    A. K. Shakya, G. Pillai, and S. Chakrabarty, “Reinforcement learning algorithms: A brief survey,”Expert Systems with Applications, vol. 231, p. 120495, 2023

    2023

  14. [14]

    R. S. Sutton, A. G. Bartoet al.,Reinforcement learning: An introduc- tion. MIT press Cambridge, 1998, vol. 1, no. 1

    1998

  15. [15]

    Learning without state- estimation in partially observable markovian decision processes,

    S. P. Singh, T. Jaakkola, and M. I. Jordan, “Learning without state- estimation in partially observable markovian decision processes,” ICML, 1994

    1994

  16. [16]

    On the convergence of td-learning on markov reward processes with hidden states,

    M. Amiri and S. Magn ´usson, “On the convergence of td-learning on markov reward processes with hidden states,” in2024 European Control Conference (ECC). IEEE, 2024, pp. 2097–2104

    2024

  17. [17]

    Reinforcement learning in switching non-stationary markov decision processes: Algorithms and conver- gence analysis,

    M. Amiri and S. Magn ´usson, “Reinforcement learning in switching non-stationary markov decision processes: Algorithms and conver- gence analysis,”arXiv preprint arXiv:2503.18607, 2025

    work page arXiv 2025

  18. [18]

    Learning by cheating,

    D. Chen, B. Zhou, V . Koltun, and P. Kr ¨ahenb¨uhl, “Learning by cheating,” inProc. Conference on Robot Learning (CoRL), 2020, pp. 66–75

    2020

  19. [19]

    Learning quadrupedal locomotion over challenging terrain,

    J. Lee, J. Hwangbo, L. Wellhausen, V . Koltun, and M. Hutter, “Learning quadrupedal locomotion over challenging terrain,”Science robotics, vol. 5, no. 47, p. eabc5986, 2020

    2020

  20. [20]

    Rapid locomotion via reinforcement learning,

    G. B. Margolis, G. Yang, L. Paull, and P. Agrawal, “Rapid locomotion via reinforcement learning,” inRobotics: Science and Systems, 2022

    2022

  21. [21]

    RMA: Rapid motor adaptation for legged robots,

    A. Kumar, Z. Fu, D. Pathak, and J. Malik, “RMA: Rapid motor adaptation for legged robots,” inProc. Robotics: Science and Systems (RSS), 2021

    2021

  22. [22]

    Deep q-learning from demonstrations,

    T. Hester, M. Vecerik, O. Pietquin, M. Lanctot, T. Schaul, B. Piot, D. Horgan, J. Quan, A. Sendonaris, I. Osbandet al., “Deep q-learning from demonstrations,” inProceedings of the AAAI conference on artificial intelligence, vol. 32, no. 1, 2018

    2018

  23. [23]

    Leveraging Demonstrations for Deep Reinforcement Learning on Robotics Problems with Sparse Rewards

    M. Vecerik, T. Hester, J. Scholz, F. Wang, O. Pietquin, B. Piot, N. Heess, T. Roth ¨orl, T. Lampe, and M. Riedmiller, “Leveraging demonstrations for deep reinforcement learning on robotics problems with sparse rewards,”arXiv preprint arXiv:1707.08817, 2017

    work page Pith review arXiv 2017

  24. [24]

    AWAC: Accelerating Online Reinforcement Learning with Offline Datasets

    A. Nair, A. Gupta, M. Dalal, and S. Levine, “Awac: Accelerating online reinforcement learning with offline datasets,”arXiv preprint arXiv:2006.09359, 2020

    work page internal anchor Pith review arXiv 2006

  25. [25]

    Lowrey, A

    K. Lowrey, A. Rajeswaran, S. Kakade, E. Todorov, and I. Mordatch, “Plan online, learn offline: Efficient learning and exploration via model-based control,”arXiv preprint arXiv:1811.01848, 2018

    work page arXiv 2018

  26. [26]

    Neural network dynamics for model-based deep reinforcement learning with model- free fine-tuning,

    A. Nagabandi, G. Kahn, R. S. Fearing, and S. Levine, “Neural network dynamics for model-based deep reinforcement learning with model- free fine-tuning,” in2018 IEEE international conference on robotics and automation (ICRA). IEEE, 2018, pp. 7559–7566

    2018

  27. [27]

    Robust-to-early termination model predictive control,

    M. Hosseinzadeh, B. Sinopoli, I. Kolmanovsky, and S. Baruah, “Robust-to-early termination model predictive control,”IEEE trans- actions on automatic control, vol. 69, no. 4, pp. 2507–2513, 2023

    2023

  28. [28]

    REAP-T: A MATLAB toolbox for implementing robust-to-early termination model predictive control,

    M. Amiri and M. Hosseinzadeh, “REAP-T: A MATLAB toolbox for implementing robust-to-early termination model predictive control,” IFAC-PapersOnLine, vol. 59, no. 30, pp. 1096–1101, 2025

    2025

  29. [29]

    Practical considerations for imple- menting robust-to-early termination model predictive control,

    M. Amiri and M. Hosseinzadeh, “Practical considerations for imple- menting robust-to-early termination model predictive control,”Systems & Control Letters, vol. 196, p. 106018, 2025

    2025

  30. [30]

    A tutorial review of neural network modeling approaches for model predictive control,

    Y . M. Ren, M. S. Alhajeri, J. Luo, S. Chen, F. Abdullah, Z. Wu, and P. D. Christofides, “A tutorial review of neural network modeling approaches for model predictive control,”Computers & Chemical Engineering, vol. 165, p. 107956, 2022

    2022

  31. [31]

    A dynamic em- bedding method for the real-time solution of time-varying constrained convex optimization problems,

    M. Amiri, I. Kolmanovsky, and M. Hosseinzadeh, “A dynamic em- bedding method for the real-time solution of time-varying constrained convex optimization problems,”Systems & Control Letters, vol. 209, p. 106352, 2026

    2026

  32. [32]

    Overcoming exploration in reinforcement learning with demonstra- tions,

    A. Nair, B. McGrew, M. Andrychowicz, W. Zaremba, and P. Abbeel, “Overcoming exploration in reinforcement learning with demonstra- tions,” in2018 IEEE international conference on robotics and automa- tion (ICRA). IEEE, 2018, pp. 6292–6299

    2018

  33. [33]

    arXiv preprint arXiv:2509.10771 , year=

    C. Schwarke, M. Mittal, N. Rudin, D. Hoeller, and M. Hutter, “Rsl-rl: A learning library for robotics research,”arXiv preprint arXiv:2509.10771, 2025

    work page arXiv 2025

  34. [34]

    Blind bipedal stair traversal via sim-to-real reinforcement learning,

    J. Siekmann, Y . Godse, A. Fern, and J. Hurst, “Blind bipedal stair traversal via sim-to-real reinforcement learning,” inRobotics: Science and Systems, 2021

    2021

  35. [35]

    Isaac Lab: A GPU-Accelerated Simulation Framework for Multi-Modal Robot Learning

    M. Mittal, P. Roth, J. Tigue, A. Richard, O. Zhang, P. Du, A. Serrano- Munoz, X. Yao, R. Zurbr ¨ugg, N. Rudinet al., “Isaac lab: A gpu- accelerated simulation framework for multi-modal robot learning,” arXiv preprint arXiv:2511.04831, 2025

    work page internal anchor Pith review arXiv 2025

  36. [36]

    Adaptive rejection sampling for gibbs sampling,

    W. R. Gilks and P. Wild, “Adaptive rejection sampling for gibbs sampling,”Journal of the Royal Statistical Society: Series C (Applied Statistics), vol. 41, no. 2, pp. 337–348, 1992

    1992