arxiv: 2604.25534 · v1 · submitted 2026-04-28 · 💻 cs.AI

Recognition: unknown

Sample-efficient Neuro-symbolic Proximal Policy Optimization

Simone Murari , Celeste Veronese , Daniele Meli

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Pith reviewed 2026-05-07 16:32 UTC · model grok-4.3

classification 💻 cs.AI

keywords neuro-symbolic reinforcement learningproximal policy optimizationsymbolic guidancesample efficiencysparse rewardspolicy transferlogical specificationsreinforcement learning

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The pith

Partial logical policy specifications transferred from easier tasks guide a neuro-symbolic extension of PPO to faster learning and higher returns in sparse-reward environments with long horizons.

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

The paper establishes that augmenting Proximal Policy Optimization with symbolic guidance derived from partial logical policy specifications learned on simpler problems enables more sample-efficient learning in environments featuring long planning horizons and sparse rewards. A sympathetic reader would care because standard deep reinforcement learning methods typically demand large amounts of interaction data and falter when rewards are infrequent and goals require multiple steps. The authors introduce two specific mechanisms for incorporating this guidance: one that modifies the action distribution during sampling and another that adds a regularization term based on symbolic knowledge to the training loss. Evaluations across three standard benchmarks demonstrate consistent advantages in learning speed and final performance over both vanilla PPO and a reward machine approach, and these gains persist even when the symbolic information is imperfect.

Core claim

The central discovery is a neuro-symbolic extension of PPO that transfers partial logical policy specifications from easier task instances to more difficult ones. This is achieved through H-PPO-Product, which biases the policy's action distribution at sampling time, and H-PPO-SymLoss, which incorporates a symbolic regularization term into the PPO objective. The approach yields faster learning and higher returns at convergence on the OfficeWorld, WaterWorld, and DoorKey environments compared to standard PPO and reward machine baselines, and remains effective under imperfect symbolic knowledge.

What carries the argument

H-PPO-Product and H-PPO-SymLoss, the two ways of integrating transferred partial logical policy specifications to bias sampling or regularize the PPO loss.

If this is right

Faster learning curves appear on OfficeWorld, WaterWorld, and DoorKey relative to plain PPO.
Higher returns at convergence are achieved compared to both PPO and reward-machine baselines.
Performance gains hold when the provided symbolic knowledge is imperfect rather than exact.
The transfer mechanism applies to domains that combine multiple sub-goals with infrequent rewards.

Where Pith is reading between the lines

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

The same partial-specification transfer could be tested with other policy-gradient algorithms beyond PPO.
Logical abstractions obtained in simulation might reduce real-world trials needed for robotic control tasks.
If the symbolic component can be learned online rather than pre-supplied, the approach might extend to fully end-to-end settings.

Load-bearing premise

Partial logical policy specifications learned or provided from easier task instances can be transferred to meaningfully guide and improve learning in more challenging settings with long horizons and sparse rewards.

What would settle it

An experiment on a new long-horizon sparse-reward task where the neuro-symbolic PPO variants show no improvement in convergence speed or final returns over standard PPO despite using the transferred partial specifications.

Figures

Figures reproduced from arXiv: 2604.25534 by Celeste Veronese, Daniele Meli, Simone Murari.

**Figure 1.** Figure 1: Benchmark domains 5. Experiments We evaluate our methodologies on three benchmarks2 ( view at source ↗

**Figure 2.** Figure 2: DoorKey results same policy in RedGreenAndBlueCyan and RedGreenAndBlueCyanAndMagentaYellow. In the charts, learning curves include H-PPO-Product with εr = 0.4 and εf = 0 (blue), H-PPO-SymLoss with linearly decaying Θ = Θt = max(Θi − t · Θr, Θf ), where Θr = 0.4 and Θf = 0 (pink), PPO (yellow) and PPO RM (green). For the RM baseline, we exclude the additional shaping reward from the plotted return for a fai… view at source ↗

**Figure 3.** Figure 3: OfficeWorld results 5.2. OfficeWorld Results view at source ↗

**Figure 4.** Figure 4: WaterWorld results In the RedGreen task (where PPO hyperparameters were tuned), all methods easily learn the optimal behavior. However, as the tasks become more complex, the differences in performance become clear. In RedGreenAndBlueCyan, H-PPO-Product emerges as the most robust approach, actively driving the exploration toward trajectories that follow the required ordering and reaching the highest return … view at source ↗

**Figure 5.** Figure 5: Ablation charts for Θ in DoorKey 17 view at source ↗

**Figure 6.** Figure 6: Ablation charts for Θ in OfficeWorld (a) RedGreen (b) RedGreenAndBlueCyan (c) RedGreenAndBlueCyan AndMagentaYellow view at source ↗

**Figure 7.** Figure 7: Ablation charts for Θ in WaterWorld 18 view at source ↗

**Figure 8.** Figure 8: Ablation charts for εf in DoorKey 19 view at source ↗

**Figure 9.** Figure 9: Ablation charts for εf in OfficeWorld (a) RedGreen (b) RedGreenAndBlueCyan (c) RedGreenAndBlueCyan AndMagentaYellow view at source ↗

**Figure 10.** Figure 10: Ablation charts for εf in WaterWorld 20 view at source ↗

read the original abstract

Deep Reinforcement Learning (DRL) algorithms often require a large amount of data and struggle in sparse-reward domains with long planning horizons and multiple sub-goals. In this paper, we propose a neuro-symbolic extension of Proximal Policy Optimization (PPO) that transfers partial logical policy specifications learned in easier instances to guide learning in more challenging settings. We introduce two integrations of symbolic guidance: (i) H-PPO-Product, which biases the action distribution at sampling time, and (ii) H-PPO-SymLoss, which augments the PPO loss with a symbolic regularization term. We evaluate our methods on three benchmarks (OfficeWorld, WaterWorld, and DoorKey), showing consistently faster learning and higher return at convergence than PPO and a Reward Machine baseline, also under imperfect symbolic knowledge.

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 gives two workable ways to inject transferred logical policies into PPO and reports solid empirical gains on three benchmarks, but the sampling bias in one variant likely breaks the standard PPO surrogate without correction.

read the letter

The main thing to know is that this work transfers partial logical policy specs from easier task instances to harder ones and folds them into PPO via two routes: H-PPO-Product, which biases the action distribution when sampling trajectories, and H-PPO-SymLoss, which adds a symbolic regularization term to the loss. On OfficeWorld, WaterWorld, and DoorKey it shows faster learning and higher final returns than plain PPO and a Reward Machine baseline, and the gains hold up even with imperfect symbolic knowledge. That combination of transfer plus the two explicit integrations is the concrete new piece, and the experiments give a practical demonstration that the idea can help in sparse-reward, long-horizon settings. The paper does a reasonable job of keeping the claims tied to those three domains and noting robustness to noisy symbols. The clearest soft spot is in H-PPO-Product. Biasing the sampling distribution changes the behavior policy that generates the data, yet the abstract gives no sign that the importance ratio or clipping in the PPO surrogate is adjusted accordingly. If the ratio still uses the unmodified policy probabilities, the estimator becomes off-policy without the usual correction, which would undermine the proximal guarantee and could explain part of the performance difference through distribution shift rather than the symbolic guidance itself. The empirical results look consistent across the benchmarks, but the summary lacks error bars, full ablation tables, or details on how the ratio is computed, so it is hard to judge how robust the gains really are. The citation pattern is standard for neuro-symbolic RL and does not raise red flags. This is for people working on hybrid symbolic-deep RL for robotics or planning who need better sample efficiency. A reader focused on that intersection would get usable techniques and a clear transfer idea from it. It deserves a serious referee because the problem is real, the approach is grounded, and the experiments provide enough evidence to make detailed review worthwhile, even if the PPO validity question needs fixing.

Referee Report

2 major / 2 minor

Summary. The manuscript presents a neuro-symbolic extension of Proximal Policy Optimization (PPO) for improving sample efficiency in sparse-reward, long-horizon RL tasks. It introduces two integrations of partial logical policy specifications transferred from easier instances: H-PPO-Product, which biases the action distribution during sampling, and H-PPO-SymLoss, which augments the PPO loss with a symbolic regularization term. Empirical results on OfficeWorld, WaterWorld, and DoorKey benchmarks claim consistently faster learning and higher returns at convergence compared to standard PPO and a Reward Machine baseline, including under imperfect symbolic knowledge.

Significance. If the integrations are shown to preserve PPO's theoretical properties while delivering the reported gains, the work could provide a practical bridge between symbolic guidance and neural policy optimization, addressing key limitations in data efficiency for complex planning domains. The multi-benchmark evaluation offers initial support for the transfer approach, though its broader impact depends on resolving the validity concerns.

major comments (2)

[Methods (H-PPO-Product integration)] In the methods section describing H-PPO-Product, the action distribution is explicitly biased at sampling time, but it is not stated whether the importance sampling ratio in the clipped PPO surrogate objective is recomputed with respect to the modified (biased) policy or retained from the original policy. If the ratio is unmodified, the estimator becomes off-policy without correction, violating the proximal guarantee and potentially attributing performance differences to uncontrolled distribution shift rather than symbolic guidance. This is load-bearing for the claim that both methods are valid extensions of PPO.
[Experiments and evaluation setup] The central claim rests on transferring partial logical policy specifications learned from easier task instances to guide harder settings, yet the manuscript provides insufficient detail on the extraction process, completeness criteria, or sensitivity to specification quality. Without ablations isolating this transfer mechanism (e.g., comparing learned vs. provided specs or varying imperfection levels), it is difficult to verify that gains stem from the neuro-symbolic integration rather than other factors.

minor comments (2)

[Abstract] The abstract refers to 'imperfect symbolic knowledge' without a concise definition; adding one sentence would improve accessibility for readers unfamiliar with the specific benchmarks.
[Results] Tables or figures reporting returns should include standard deviations or confidence intervals across runs to allow assessment of consistency beyond mean values.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Methods (H-PPO-Product integration)] In the methods section describing H-PPO-Product, the action distribution is explicitly biased at sampling time, but it is not stated whether the importance sampling ratio in the clipped PPO surrogate objective is recomputed with respect to the modified (biased) policy or retained from the original policy. If the ratio is unmodified, the estimator becomes off-policy without correction, violating the proximal guarantee and potentially attributing performance differences to uncontrolled distribution shift rather than symbolic guidance. This is load-bearing for the claim that both methods are valid extensions of PPO.

Authors: We agree this clarification is essential for establishing that H-PPO-Product remains a valid on-policy extension of PPO. The implementation recomputes the importance sampling ratio using the biased policy at each update step, ensuring the surrogate objective stays proximal and the estimator does not introduce uncontrolled off-policy bias. We will revise the methods section to explicitly state this recomputation, include the updated importance ratio formula, and add a short paragraph discussing how the proximal guarantee is preserved under symbolic biasing. revision: yes
Referee: [Experiments and evaluation setup] The central claim rests on transferring partial logical policy specifications learned from easier task instances to guide harder settings, yet the manuscript provides insufficient detail on the extraction process, completeness criteria, or sensitivity to specification quality. Without ablations isolating this transfer mechanism (e.g., comparing learned vs. provided specs or varying imperfection levels), it is difficult to verify that gains stem from the neuro-symbolic integration rather than other factors.

Authors: We acknowledge that the current manuscript lacks sufficient detail on the specification extraction pipeline and does not include targeted ablations on transfer quality. In the revised version we will expand the methods section with a precise description of the extraction algorithm, the completeness criteria applied to the learned logical policies, and the procedure for transferring them across task instances. We will also add new ablation experiments that (i) compare performance when using the automatically extracted specifications versus hand-provided ones and (ii) systematically vary the degree of imperfection in the symbolic knowledge while measuring learning curves and final returns. These additions will isolate the contribution of the neuro-symbolic transfer mechanism. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical method extensions rest on independent benchmarks

full rationale

The paper introduces two algorithmic modifications to PPO (H-PPO-Product biasing sampling and H-PPO-SymLoss adding a regularization term) and reports empirical results on OfficeWorld, WaterWorld, and DoorKey. No equations derive a prediction from a fitted parameter defined within the paper, no self-citations form load-bearing uniqueness claims, and no ansatz or renaming reduces the central performance claims to inputs by construction. The evaluation compares against PPO and Reward Machine baselines under imperfect knowledge, making the claims falsifiable on external benchmarks rather than self-referential.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the domain assumption that partial logical policies transfer usefully across difficulty levels and on standard RL assumptions such as the existence of a Markov decision process; no free parameters or new invented entities are introduced in the abstract.

axioms (1)

domain assumption Partial logical policy specifications learned on easier instances can be transferred to guide learning on harder instances
This transfer is the core mechanism described in the abstract.

pith-pipeline@v0.9.0 · 5428 in / 1266 out tokens · 83956 ms · 2026-05-07T16:32:12.096160+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

6 extracted references · 4 canonical work pages · 3 internal anchors

[1]

Chevalier-Boisvert, B

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work page arXiv
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work page internal anchor Pith review arXiv
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High-Dimensional Continuous Control Using Generalized Advantage Estimation

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work page internal anchor Pith review arXiv
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Sample-Efficient Neurosymbolic Deep Reinforcement Learning

URLhttps: //proceedings.mlr.press/v284/veronese25a.html. Celeste Veronese, Daniele Meli, and Alessandro Farinelli. Sample-efficient neurosymbolic deep reinforcement learning.arXiv preprint arXiv:2601.02850,

work page internal anchor Pith review Pith/arXiv arXiv
[6]

13 Murari Veronese Meli Appendix A. A.1. Domains A.1.1. DoorKey DoorKey is a partially observable grid navigation task (Figure 1(a)) where the agent (red arrow) must retrieve a key, unlock a door of the same color, and then reach the goal cell (green). The MDP observation covers a 7×7 area (light gray), with each cell encoded by object type, color and sta...

2023