A KL-regularization Framework for Learning to Plan with Adaptive Priors

\'Alvaro Serra-Gomez; Daniel Jarne Ornia; Dhruva Tirumala; Thomas Moerland

arxiv: 2510.04280 · v2 · pith:OEZM3DVHnew · submitted 2025-10-05 · 💻 cs.LG · cs.AI· cs.RO

A KL-regularization Framework for Learning to Plan with Adaptive Priors

\'Alvaro Serra-Gomez , Daniel Jarne Ornia , Dhruva Tirumala , Thomas Moerland This is my paper

Pith reviewed 2026-05-22 13:21 UTC · model grok-4.3

classification 💻 cs.LG cs.AIcs.RO

keywords KL regularizationmodel-based reinforcement learningMPPI planningpolicy optimizationadaptive priorscontinuous control

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The pith

PO-MPC unifies MPPI-based reinforcement learning by using the planner's action distribution as an adaptive prior in policy optimization.

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

This paper introduces PO-MPC, a family of KL-regularized methods for model-based reinforcement learning that treat the planner's distribution as a prior when updating the policy. The key idea is that since the states seen in training come from the MPPI planner, making the policy match the planner's behavior leads to better value estimates and overall performance. The framework shows how earlier methods fit as special cases and tests new ways to balance return maximization against the KL term, with experiments indicating clear gains on continuous control tasks.

Core claim

PO-MPC is a family of KL-regularized MBRL methods that integrate the planner's action distribution as a prior in policy optimization. By aligning the learned policy with the planner's behavior, PO-MPC allows more flexibility in the policy updates to trade off Return maximization and KL divergence minimization. We clarify how prior approaches emerge as special cases of this family, and we explore previously unstudied variations. Our experiments show that these extended configurations yield significant performance improvements, advancing the state of the art in MPPI-based RL.

What carries the argument

PO-MPC, the family of KL-regularized MBRL methods that incorporate the MPPI planner's distribution as a prior during policy updates to align sampling policy with planning behavior.

If this is right

Prior MPPI-based RL approaches emerge as special cases of the PO-MPC family.
New variations in the KL-regularized updates lead to significant performance improvements.
Alignment improves accuracy of value estimation and long-term performance.
The framework advances the state of the art in MPPI-based reinforcement learning.

Where Pith is reading between the lines

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

The unification points to a systematic way to combine planning and learning that may extend to planners other than MPPI.
Different weightings of the return versus KL terms could be tested to find task-specific optima.
Similar adaptive priors might stabilize training in other model-based or hybrid algorithms.

Load-bearing premise

The states encountered during training depend on the MPPI planner, so aligning the sampling policy with the planner improves the accuracy of value estimation and long-term performance.

What would settle it

An experiment showing that updating the policy independently without KL alignment to the planner achieves equal or better value estimation accuracy and task performance would challenge the core motivation.

Figures

Figures reproduced from arXiv: 2510.04280 by \'Alvaro Serra-Gomez, Daniel Jarne Ornia, Dhruva Tirumala, Thomas Moerland.

**Figure 3.** Figure 3: Effects of approximating the Planning policy with the intermediate prior through different cost functions. Mean of 3 runs; shaded areas are 95% CI. We report the average across tasks, and environments showing a clear effect of training with loss in Eq. 5 instead of Eq. 4. See Appendix D for results on all tasks. 8 [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Performance comparison of PO-MPC and the baselines on 7 state-based high-dimensional [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗

**Figure 5.** Figure 5: Performance comparison in 14 state-based high-dimensional control tasks from Hu [PITH_FULL_IMAGE:figures/full_fig_p018_5.png] view at source ↗

**Figure 6.** Figure 6: Top: Mean and, Bottom:Standard deviation of the KL divergence term in Equation 13 for both PO-MPC using an intermediate policy prior and the Planning policy. Experiments are done in the HumanoidBench Locomotion suite (Sferrazza et al., 2024). Mean of 3 runs. We show empirical evidence on how the mean and standard deviation of the KL term are significantly larger when the Planning policy samples are used in… view at source ↗

**Figure 7.** Figure 7: Performance comparison in 14 state-based high-dimensional control tasks from Hu [PITH_FULL_IMAGE:figures/full_fig_p020_7.png] view at source ↗

read the original abstract

Effective exploration remains a central challenge in model-based reinforcement learning (MBRL), particularly in high-dimensional continuous control tasks where sample efficiency is crucial. A prominent line of recent work leverages learned policies as proposal distributions for Model-Predictive Path Integral (MPPI) planning. Initial approaches update the sampling policy independently of the planner distribution, typically maximizing a learned value function with deterministic policy gradient and entropy regularization. However, because the states encountered during training depend on the MPPI planner, aligning the sampling policy with the planner improves the accuracy of value estimation and long-term performance. To this end, recent methods update the sampling policy by minimizing KL divergence to the planner distribution or by introducing planner-guided regularization into the policy update. In this work, we unify these MPPI-based reinforcement learning methods under a single framework by introducing Policy Optimization-Model Predictive Control (PO-MPC), a family of KL-regularized MBRL methods that integrate the planner's action distribution as a prior in policy optimization. By aligning the learned policy with the planner's behavior, PO-MPC allows more flexibility in the policy updates to trade off Return maximization and KL divergence minimization. We clarify how prior approaches emerge as special cases of this family, and we explore previously unstudied variations. Our experiments show that these extended configurations yield significant performance improvements, advancing the state of the art in MPPI-based RL.

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.

Desk Editor's Note private letter to a colleague

The paper unifies several MPPI-RL methods under one KL-regularized PO-MPC family and tests new variants that improve performance in the reported experiments.

read the letter

The main thing to know is that this paper organizes a cluster of recent MPPI-based reinforcement learning methods into a single framework called PO-MPC. It treats the planner's action distribution as a prior and uses KL regularization to align the learned policy with it. Earlier approaches drop out as special cases depending on how the regularization coefficient and the objective are set, and the authors try some previously unexamined balances between return and that KL term. The motivation is straightforward: since the states the policy sees come from the planner, keeping the two distributions close should make value estimates more accurate and improve long-term behavior. That framing is clean and makes the connections between papers easier to see. The experiments indicate that the new configurations deliver measurable gains on the continuous control tasks they tested. The work is incremental rather than foundational, but the unification itself is a useful organizational step that had not been written down this way before. On the softer side, the abstract leaves the exact experimental protocol, baseline details, and statistical tests implicit, so the strength of the performance claims will depend on how thoroughly those are documented in the full text. The core assumption about improved value estimation from alignment is reasonable but would benefit from a direct check or ablation rather than being read off final returns alone. Nothing in the presented material looks contradictory or circular. This paper is for people already working on model-based RL with sampling-based planners in continuous domains. Readers who follow the MPPI line will get a clearer map of the design space and some new knobs to try. It is not solving a long-standing theoretical question, but the framework is coherent and the results are positive enough that it deserves a serious referee. I would send it out for review.

Referee Report

0 major / 3 minor

Summary. The paper proposes PO-MPC, a family of KL-regularized model-based RL algorithms that treat the MPPI planner's action distribution as an adaptive prior during policy optimization. It shows that several prior MPPI-based methods arise as special cases by varying the KL coefficient and the form of the policy update, introduces previously unstudied configurations, and reports that these yield significant performance gains over baselines on continuous-control benchmarks.

Significance. If the unification and empirical gains hold, the work supplies a clean, extensible framework that makes the policy-planner alignment explicit and tunable. This could streamline future MPPI-based MBRL research by replacing ad-hoc regularizers with a single KL-regularized objective. The explicit recovery of prior methods as special cases and the exploration of new variants are useful contributions; the reported state-of-the-art improvements, if statistically robust, would strengthen the practical case for planner-guided policy learning.

minor comments (3)

The abstract and introduction motivate the KL alignment by noting that training states depend on the MPPI planner, yet the precise mechanism by which this dependence affects value estimation accuracy is not quantified (e.g., no distribution-shift metric or ablation on state coverage).
Experimental section: baseline implementations and hyper-parameter selection protocols for the compared MPPI variants should be stated explicitly so that the claimed improvements can be reproduced without ambiguity.
Notation: the distinction between the planner distribution π_planner and the learned policy π_θ is clear in the abstract but would benefit from a single consolidated table of symbols and their roles in the PO-MPC objective.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of our work, the recognition of the unifying KL-regularized framework, and the recommendation for minor revision. We are pleased that the explicit recovery of prior methods and the exploration of new variants are viewed as useful contributions.

Circularity Check

0 steps flagged

No significant circularity detected in PO-MPC unification

full rationale

The paper introduces PO-MPC as a KL-regularized framework that recovers prior MPPI-based methods as special cases of a family trading off return maximization and KL minimization. This is presented as a generalization rather than a derivation that reduces to its own fitted parameters or self-referential definitions. The motivating assumption—that states encountered depend on the MPPI planner and alignment improves value estimation—is stated explicitly in the abstract without forming a closed loop or relying on unverified self-citations. No equations, uniqueness theorems, or ansatzes are shown to be smuggled in or renamed from known results in a way that forces the claimed improvements by construction. The framework remains self-contained against external benchmarks with independent experimental claims.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The framework rests on the domain assumption that planner-guided regularization improves value estimation because training states are planner-dependent; no new physical entities or free parameters are explicitly introduced in the abstract beyond standard RL hyperparameters.

free parameters (1)

KL regularization coefficient
Controls the trade-off between return maximization and divergence to the planner distribution; must be chosen or tuned per task.

axioms (1)

domain assumption States visited during policy training are generated by the MPPI planner distribution
Invoked to justify why aligning policy and planner improves value accuracy.

pith-pipeline@v0.9.0 · 5792 in / 1385 out tokens · 38652 ms · 2026-05-22T13:21:12.976836+00:00 · methodology

discussion (0)

Forward citations

Cited by 1 Pith paper

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Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages · cited by 1 Pith paper · 3 internal anchors

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Guangyao Zhou, Sivaramakrishnan Swaminathan, Rajkumar Vasudeva Raju, J Swaroop Guntupalli, Wolfgang Lehrach, Joseph Ortiz, Antoine Dedieu, Miguel L ´azaro-Gredilla, and Kevin Murphy. Diffusion model predictive control.arXiv preprint arXiv:2410.05364,

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A HYPERPARAMETERS In table 3 we share the hyperparameters employed for both our method (PO-MPC) and the baseline TD-MPC

12 Preprint. A HYPERPARAMETERS In table 3 we share the hyperparameters employed for both our method (PO-MPC) and the baseline TD-MPC. Both methods share all parameters except for the ones exclusive to PO-MPC. Table 3: Hyperparameter configuration. Hyperparameters Values General Num. steps 1 000 000 Replay buffer 1 000 000 Learning rate 3e-4 Max. Gradient ...

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We inherit all architectural choices from TD-MPC2

by Flandermeyer (2024a). We inherit all architectural choices from TD-MPC2. The architecture ofQ πθs ,λ ˆθQ follows the same design of its counterpartQ πθs θQ . De- spite updating an additional policy and action value function, training times do not differ signifi- cantly from the baselines. Baselines.For our experiments, we employ the implementations in ...

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26:θ − Q ←τ θ Q + (1−τ)θ − Q 27: ˜θ− Q ←τ ˜θQ + (1−τ) ˜θ− Q 28:end if 29:end for 17 Preprint. D ADDITIONALRESULTS D.1 RESULTS INDMCONTROLSUITE Figure 4: Performance comparison of PO-MPC and the baselines on 7 state-based high-dimensional control tasks from DMControl Suite (Tassa et al., 2018). Mean of 3 runs; shaded areas are 95% confidence intervals. In ...

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Amisha Bhaskar, Zahiruddin Mahammad, Sachin R Jadhav, and Pratap Tokekar

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Model-Based Value Estimation for Efficient Model-Free Reinforcement Learning

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Shane Flandermeyer. tdmpc2-jax: Jax/flax implementation of TD-MPC2.https://github. com/ShaneFlandermeyer/tdmpc2-jax, 2024a. Accessed: 2025-08-28. Shane Flandermeyer. bmpc-jax: Jax/flax implementation of BMPC.https://github.com/ ShaneFlandermeyer/bmpc-jax, 2024b. Accessed: 2025-08-28. Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft act...

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Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review

Sergey Levine. Reinforcement learning and control as probabilistic inference: Tutorial and review. arXiv preprint arXiv:1805.00909,

work page internal anchor Pith review Pith/arXiv arXiv

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Proximal Policy Optimization Algorithms

John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms.arXiv preprint arXiv:1707.06347,

work page internal anchor Pith review Pith/arXiv arXiv

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Noah Siegel, Jost Tobias Springenberg, Felix Berkenkamp, Abbas Abdolmaleki, Michael Ne- unert, Thomas Lampe, Roland Hafner, Nicolas Heess, and Martin Riedmiller

doi: 10.15607/RSS.2024.XX.061. Noah Siegel, Jost Tobias Springenberg, Felix Berkenkamp, Abbas Abdolmaleki, Michael Ne- unert, Thomas Lampe, Roland Hafner, Nicolas Heess, and Martin Riedmiller. Keep doing what worked: Behavior modelling priors for offline reinforcement learning. InInternational Confer- ence on Learning Representations,

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ISBN 1595933832

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work page doi:10.1145/1143844.1143963

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Yuhang Wang, Hanwei Guo, Sizhe Wang, Long Qian, and Xuguang Lan

URLhttps://openreview.net/forum?id=LHGMXcr6zx. Yuhang Wang, Hanwei Guo, Sizhe Wang, Long Qian, and Xuguang Lan. Bootstrapped model predictive control.arXiv preprint arXiv:2503.18871,

work page arXiv

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Diffusion model predictive control.arXiv preprint arXiv:2410.05364,

Guangyao Zhou, Sivaramakrishnan Swaminathan, Rajkumar Vasudeva Raju, J Swaroop Guntupalli, Wolfgang Lehrach, Joseph Ortiz, Antoine Dedieu, Miguel L ´azaro-Gredilla, and Kevin Murphy. Diffusion model predictive control.arXiv preprint arXiv:2410.05364,

work page arXiv

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A HYPERPARAMETERS In table 3 we share the hyperparameters employed for both our method (PO-MPC) and the baseline TD-MPC

12 Preprint. A HYPERPARAMETERS In table 3 we share the hyperparameters employed for both our method (PO-MPC) and the baseline TD-MPC. Both methods share all parameters except for the ones exclusive to PO-MPC. Table 3: Hyperparameter configuration. Hyperparameters Values General Num. steps 1 000 000 Replay buffer 1 000 000 Learning rate 3e-4 Max. Gradient ...

work page 2024

[12] [12]

We inherit all architectural choices from TD-MPC2

by Flandermeyer (2024a). We inherit all architectural choices from TD-MPC2. The architecture ofQ πθs ,λ ˆθQ follows the same design of its counterpartQ πθs θQ . De- spite updating an additional policy and action value function, training times do not differ signifi- cantly from the baselines. Baselines.For our experiments, we employ the implementations in ...

work page 2025

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26:θ − Q ←τ θ Q + (1−τ)θ − Q 27: ˜θ− Q ←τ ˜θQ + (1−τ) ˜θ− Q 28:end if 29:end for 17 Preprint. D ADDITIONALRESULTS D.1 RESULTS INDMCONTROLSUITE Figure 4: Performance comparison of PO-MPC and the baselines on 7 state-based high-dimensional control tasks from DMControl Suite (Tassa et al., 2018). Mean of 3 runs; shaded areas are 95% confidence intervals. In ...

work page 2018