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arxiv: 2605.14897 · v1 · pith:MIGVCYVCnew · submitted 2026-05-14 · 💻 cs.LG · cs.AI

Critic-Driven Voronoi-Quantization for Distilling Deep RL Policies to Explainable Models

Senne Deproost , Denis Steckelmacher , Ann Now\'e This is my paper

Pith reviewed 2026-06-30 21:12 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords reinforcement learningpolicy distillationexplainable AIVoronoi partitioningcritic-drivenlinear subpoliciesstate space partitioningdeep RL
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The pith

Critic-driven Voronoi partitioning distills deep RL policies into a small set of linear functions.

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

The paper introduces a distillation method that breaks a deep RL policy into regions of the state space, each governed by its own linear function. It uses the critic network's value estimates to decide where to add a new linear piece, adding them only in regions where current performance falls short. This produces an explainable surrogate that assigns each state to a linear subpolicy via nearest-neighbor lookup in a Voronoi diagram. The goal is to reach performance close to the original black-box policy while keeping the number of linear pieces modest. A reader would care because it offers one concrete route to making high-performing RL agents more transparent without relying solely on matching observed actions.

Core claim

The paper claims that Critic-Driven Voronoi State Partitioning can turn a black-box deep RL policy into a collection of linear subpolicies. The method iteratively places new linear functions in state-space regions where the critic reports insufficient value, then uses a Voronoi quantizer with nearest-neighbor assignment to map every state to its nearest linear piece. Gradient descent optimizes each linear function inside its cell. On standard benchmarks the resulting model approximates the original policy's behavior with a reasonable number of such pieces.

What carries the argument

Critic-Driven Voronoi State Partitioning: a Voronoi quantizer that assigns linear functions to state-space regions via nearest-neighbor lookup, with the critic value network used to iteratively introduce new subpolicies where value is insufficient.

If this is right

  • A modest number of linear functions suffices to approach the original policy's returns.
  • The method incorporates critic value information rather than minimizing only behavioral distance.
  • The resulting cell diagram assigns every state to exactly one linear subpolicy through nearest-neighbor lookup.
  • Gradient descent can optimize the parameters of each linear function inside its assigned region.
  • The approach applies to multiple standard RL benchmark environments.

Where Pith is reading between the lines

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

  • The cell diagram might allow direct inspection of which linear piece is active in any given region, aiding manual verification.
  • The same critic-guided placement rule could be tested with other simple surrogate classes such as shallow trees.
  • If the number of pieces stays small across more domains, the method could reduce memory needed to store or transmit the policy.

Load-bearing premise

The critic value network supplies a reliable, non-circular signal for where additional linear subpolicies are needed to reduce overall policy complexity.

What would settle it

On the same benchmarks, the method either requires dozens of linear functions to reach the reported performance level or the distilled policy's returns fall substantially below the original policy's returns.

Figures

Figures reproduced from arXiv: 2605.14897 by Ann Now\'e, Denis Steckelmacher, Senne Deproost.

Figure 1
Figure 1. Figure 1: An example of a Voronoi diagram using 8 codeword points. [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: The used validation environments. From left to right: SimpleGoal, Moun [PITH_FULL_IMAGE:figures/full_fig_p011_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Performance of both the VSP-critic algorithm (green) and the random [PITH_FULL_IMAGE:figures/full_fig_p012_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Number of linear subpolicies found by the VSP algorithm (green) and the [PITH_FULL_IMAGE:figures/full_fig_p013_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: Control policies for the SimpleGoal environment using quiver plots. [PITH_FULL_IMAGE:figures/full_fig_p014_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Partitioning of both LunarLander (on its x and y position) and Bipedal [PITH_FULL_IMAGE:figures/full_fig_p015_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: A set of 3 linear functions for MountainCarContinuous using [PITH_FULL_IMAGE:figures/full_fig_p015_7.png] view at source ↗
read the original abstract

Despite many successful attempts at explaining Deep Reinforcement Learning policies using distillation, it remains difficult to balance the performance-interpretability trade-off and select a fitting surrogate model. In addition to this, traditional distillation only minimizes the distance between the behavior of the original and the surrogate policy while other RL-specific components such as action value are disregarded. To solve this, we introduce a new model-agnostic method called Critic-Driven Voronoi State Partitioning, which partitions a black box control policy into regions where a simple class of model can be optimized using gradient descent. By exploiting the critic value network of the original policy, we iteratively introduce new subpolicies in regions with insufficient value, standing in for a measure of policy complexity. The partitioning, a Voronoi quantizer, uses nearest neighbor lookups to assign a linear function to each point in the state space resulting in a cell-like diagram. We validate our approach on several well known benchmarks and proof that this distillation approaches the original policy using a reasonable sized set of linear functions.

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 introduces Critic-Driven Voronoi State Partitioning, a model-agnostic distillation technique that partitions the state space of a black-box deep RL policy into Voronoi cells, each assigned an optimized linear subpolicy. It iteratively adds new subpolicies in regions flagged by the original policy's critic value network as having insufficient value (serving as a proxy for complexity), with nearest-neighbor assignment yielding the final surrogate. The central claim is that this produces an explainable linear model that approaches the original policy's performance using a reasonable number of components, validated on standard RL benchmarks.

Significance. If the empirical results hold and the critic-based partitioning is shown to be reliable, the method would provide a concrete advance in explainable RL by moving beyond pure behavior cloning to incorporate value information, potentially yielding more compact and interpretable surrogates than existing distillation approaches.

major comments (2)
  1. [Abstract / iterative introduction of subpolicies] Abstract and method description of the iterative procedure: the fixed critic value network is used to identify regions needing additional linear subpolicies, yet no mechanism is described for re-evaluating or correcting the critic under the evolving surrogate's state distribution; this directly risks misalignment and must be addressed to support the claim that the approach 'approaches the original policy'.
  2. [Validation / benchmarks] Validation section (benchmarks and results): the manuscript asserts that the distillation 'approaches the original policy using a reasonable sized set of linear functions' but provides no quantitative details on performance gaps, number of cells used, baselines, or statistical significance in the visible description, leaving the central empirical claim unsupported.
minor comments (2)
  1. [Abstract] Abstract uses 'proof' for what appears to be empirical validation; rephrase to 'demonstrate' or 'show empirically'.
  2. The Voronoi quantizer and linear function assignment lack explicit equations or pseudocode in the high-level description; adding these would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the detailed and constructive report. We address each major comment below, indicating planned revisions where appropriate.

read point-by-point responses

  1. Referee: [Abstract / iterative introduction of subpolicies] Abstract and method description of the iterative procedure: the fixed critic value network is used to identify regions needing additional linear subpolicies, yet no mechanism is described for re-evaluating or correcting the critic under the evolving surrogate's state distribution; this directly risks misalignment and must be addressed to support the claim that the approach 'approaches the original policy'.

    Authors: We acknowledge that the manuscript describes the critic as fixed from the original policy and does not detail any re-evaluation step under the surrogate's state distribution. This is a valid concern regarding potential misalignment. In revision we will expand the method section with an explicit discussion of this design choice (the critic serves as a static proxy for the target policy's value landscape) together with a short analysis of the resulting distribution shift; if the analysis indicates material risk we will also add an optional re-evaluation procedure. revision: yes

  2. Referee: [Validation / benchmarks] Validation section (benchmarks and results): the manuscript asserts that the distillation 'approaches the original policy using a reasonable sized set of linear functions' but provides no quantitative details on performance gaps, number of cells used, baselines, or statistical significance in the visible description, leaving the central empirical claim unsupported.

    Authors: The full manuscript contains benchmark results and figures, yet we agree that the quantitative support for the central claim is not presented with sufficient clarity or detail. We will revise the validation section to include a summary table reporting performance gaps to the original policy, the number of Voronoi cells, comparisons against behavior-cloning baselines, and statistical significance (means and standard errors over multiple random seeds). revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation uses external critic signal

full rationale

The paper's core construction iteratively adds linear subpolicies in regions flagged by the original policy's fixed critic value network. This critic is an input taken from the pretrained deep RL agent and is not defined in terms of, fitted to, or updated from the surrogate Voronoi-quantized model. No equations or steps reduce a claimed prediction to a fitted parameter by construction, and the provided text invokes no self-citations, uniqueness theorems, or ansatzes from prior author work. The method therefore remains self-contained against an independent external benchmark (the original policy's critic) rather than tautological.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the unstated premise that the critic network's value estimates can be used directly as a complexity signal without additional validation; no free parameters or invented entities are explicitly introduced in the abstract.

axioms (1)
  • domain assumption The critic value network accurately indicates regions where the current linear approximation is insufficient.
    Invoked when the method iteratively introduces new subpolicies based on value.

pith-pipeline@v0.9.1-grok · 5713 in / 1110 out tokens · 20011 ms · 2026-06-30T21:12:49.501121+00:00 · methodology

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