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arxiv: 2605.18508 · v1 · pith:W7XYTDFAnew · submitted 2026-05-18 · 💻 cs.LG · cs.AI

DiPRL: Learning Discrete Programmatic Policies via Architecture Entropy Regularization

Chengpeng Hu , Yingqian Zhang , Hendrik Baier This is my paper

Pith reviewed 2026-05-20 12:02 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords programmatic reinforcement learningdiscrete policiesentropy regularizationinterpretable RLpolicy optimization
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The pith

DiPRL uses architecture entropy regularization so that programmatic policies become discrete by the end of training.

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

The paper aims to solve the issue in programmatic reinforcement learning where converting continuous program relaxations to discrete forms causes performance to drop. It does this by adding regularization that makes the program architecture nearly discrete while still allowing gradient-based updates. This eliminates the need for a separate discretization step followed by fine-tuning. If the method works as described, it would let users train readable, editable policies that perform well right after optimization across various tasks.

Core claim

DiPRL shows that programmatic architecture entropy regularization can be used during training to encourage policies to converge to discrete programs, thereby avoiding the performance collapse that occurs when optimized branches and parameters are discarded in post-hoc discretization.

What carries the argument

Programmatic architecture entropy regularization that adds an entropy penalty to architecture choices to promote discreteness while keeping training differentiable.

If this is right

  • Programmatic policies reach strong performance levels on discrete and continuous control tasks.
  • Training stays efficient using gradients without losing expressivity from discretization.
  • Interpretable policies become more usable since no recovery fine-tuning is needed after training.

Where Pith is reading between the lines

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

  • Similar regularization techniques could help in other domains requiring discrete decisions during optimization, such as program synthesis.
  • Future work might test if this leads to more stable training dynamics in larger program spaces.

Load-bearing premise

The regularization term successfully pushes the architecture to a discrete state without discarding useful optimized components or requiring recovery steps.

What would settle it

A direct comparison where DiPRL policies are evaluated immediately after training and show no significant performance difference from the continuous relaxation without any fine-tuning applied.

Figures

Figures reproduced from arXiv: 2605.18508 by Chengpeng Hu, Hendrik Baier, Yingqian Zhang.

Figure 1
Figure 1. Figure 1: A programmatic policy discovered by DiPRL for CartPole-v1. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Domain-specific language (DSL) for programmatic policies. A denotes a terminal ac￾tion. ϕw(s) is a parameterized predicate, specifi￾cally a linear function of state features. Domain-specific language. Following prior work [9], we represent programmatic policies using the context-free domain-specific language (DSL) shown in [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Motivating example of the performance drop [PITH_FULL_IMAGE:figures/full_fig_p003_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Workflow of DiPRL. E denotes a program node. A denotes an action node, marked in yellow. B denotes a condition in an incomplete program if B then A else E. The maximal depth Dm is set to 2 in the figure. A programmatic policy is relaxed into a continuous derivation program tree by fully expanding and assigning expansion probabilities to program branches. During the training, the program architecture entrop… view at source ↗
Figure 5
Figure 5. Figure 5: Architecture entropy curves in discrete tasks. The architecture entropy of [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Normalized architecture entropy before discretization on discrete tasks. Lower values indi￾cate architectures closer to discrete programs. The most closely related method to DiPRL is π-PRL, which also optimizes a continuous re￾laxation of a programmatic policy. However, the post-hoc discretization stage required by π￾PRL can destabilize the final discrete policy by discarding useful learned branches. This … view at source ↗
Figure 7
Figure 7. Figure 7: Goal distance curves in continuous tasks in a comparison with [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Ablation on regularizer α selected from set {0, 0.001, 0.01, 0.1, 0.5} and automatic tuning. Automatic tuning (marked as rhombus ⋄) is overall stable. 7 Conclusion In this work, we first demonstrate a performance drop that can occur when extracting discrete pro￾grams post-hoc from a continuous program derivation tree in state-of-the-art PRL approaches. Even with further fine-tuning, it might be unrecoverab… view at source ↗
Figure 9
Figure 9. Figure 9: Ablation on target entropy selected from [PITH_FULL_IMAGE:figures/full_fig_p017_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Training curves on discrete tasks. The left column reports reward, where higher is better, [PITH_FULL_IMAGE:figures/full_fig_p020_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Training curves on continuous tasks. Each row reports reward, goal distance, and [PITH_FULL_IMAGE:figures/full_fig_p021_11.png] view at source ↗
read the original abstract

Programmatic reinforcement learning (PRL) offers an interpretable alternative to deep reinforcement learning by representing policies as human-readable and -editable programs. While gradient-based methods have been developed to optimize continuous relaxations of programs, they face a significant performance drop when converting the continuous relaxations back into discrete programs. Post-hoc discretization can discard optimized branches and parameters in a program, which results in a collapse of policy expressivity and lowered task performance, leading in turn to a need for additional fine-tuning. To overcome these limitations, we propose Differentiable Discrete Programmatic Reinforcement Learning (DiPRL), a method that learns programmatic policies that become nearly discrete during training, avoiding a separate post-hoc fine-tuning stage. We first analyze the inherent risks of performance drop introduced by post-hoc discretization of gradient-based methods. Then, we introduce programmatic architecture entropy regularization, which enables smooth, differentiable training that encourages convergence toward a discrete program. DiPRL maintains the efficiency of gradient-based optimization while mitigating the risks of post-hoc discretization. Our experiments across multiple discrete and continuous RL tasks demonstrate that DiPRL can achieve strong performance via interpretable programmatic policies.

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 / 1 minor

Summary. The paper proposes DiPRL, a gradient-based method for programmatic reinforcement learning that incorporates architecture entropy regularization to produce nearly discrete policies during training. It first analyzes risks of post-hoc discretization (performance drops from discarded branches/parameters and resulting expressivity collapse requiring fine-tuning), then adds the regularizer to encourage convergence to discrete programs while retaining optimization efficiency. Experiments on discrete and continuous RL tasks are claimed to show strong performance with interpretable programmatic policies.

Significance. If the central claims hold, DiPRL would offer a practical advance for interpretable RL by integrating discreteness into differentiable training, eliminating separate post-hoc stages and their associated risks. The post-hoc risk analysis provides useful diagnostic insight, and the regularization approach could generalize to other structured policy representations.

major comments (2)
  1. [Abstract] Abstract: the claim that 'experiments across multiple discrete and continuous RL tasks demonstrate that DiPRL can achieve strong performance' is unsupported by any quantitative results, baselines, error bars, or implementation details on how the regularization was applied or how near-discreteness was measured; this directly undermines assessment of the central performance claim.
  2. [Section 3] Section 3 (programmatic architecture entropy regularization): no derivation or analysis is provided showing that the entropy term preserves gradient flow on retained branches or prevents premature pruning of parameters that were optimized under the continuous relaxation; without this, the claim that the method avoids the same information loss seen in post-hoc discretization remains ungrounded.
minor comments (1)
  1. [Abstract] The phrase 'nearly discrete' is used repeatedly but never given a precise operational definition (e.g., a threshold on architecture probabilities or entropy value).

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback on our manuscript. We address each major comment point by point below, indicating the revisions we plan to make.

read point-by-point responses

  1. Referee: [Abstract] Abstract: the claim that 'experiments across multiple discrete and continuous RL tasks demonstrate that DiPRL can achieve strong performance' is unsupported by any quantitative results, baselines, error bars, or implementation details on how the regularization was applied or how near-discreteness was measured; this directly undermines assessment of the central performance claim.

    Authors: We agree that the abstract would be strengthened by including quantitative support for the performance claims. In the revised manuscript, we will update the abstract to report key results such as average returns with standard errors across tasks, comparisons against relevant baselines, and brief details on regularization hyperparameters and the metric used to quantify near-discreteness (e.g., average architecture entropy or post-training discretization fidelity). revision: yes

  2. Referee: [Section 3] Section 3 (programmatic architecture entropy regularization): no derivation or analysis is provided showing that the entropy term preserves gradient flow on retained branches or prevents premature pruning of parameters that were optimized under the continuous relaxation; without this, the claim that the method avoids the same information loss seen in post-hoc discretization remains ungrounded.

    Authors: This observation is fair. The current draft motivates the regularization but does not supply a formal derivation of its effect on gradients. We will add a new subsection to Section 3 that derives the gradient of the combined objective and shows that the entropy term maintains non-zero flow through retained branches while discouraging premature collapse of optimized parameters. This analysis will directly support the claim that DiPRL mitigates the expressivity loss observed in post-hoc discretization. revision: yes

Circularity Check

0 steps flagged

No circularity; derivation adds independent regularization term

full rationale

The paper describes first analyzing post-hoc discretization risks in gradient-based PRL, then proposing programmatic architecture entropy regularization to drive near-discrete convergence during training. No equations, self-citations, or steps are shown that reduce the central claim to a fitted input, self-definition, or prior author result by construction. The method is presented as an additive regularizer on existing optimization, keeping the derivation self-contained.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

The abstract does not enumerate free parameters, background axioms, or newly postulated entities. The approach appears to rest on standard gradient-based optimization plus an entropy term whose precise definition and weighting are not supplied.

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