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arxiv: 2509.25438 · v2 · submitted 2025-09-29 · 💻 cs.LG · cs.AI

Beyond Noisy-TVs: Noise-Robust Exploration Via Learning Progress Monitoring

Zhibo Hou , Zhiyu An , Wan Du This is my paper

Pith reviewed 2026-05-18 11:47 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords intrinsic motivationexplorationnoisy environmentsreinforcement learninglearning progressdynamics modelinformation gainAtari
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The pith

Intrinsic rewards based on learning progress let agents explore past unlearnable noise sources instead of getting stuck on them.

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

This paper introduces Learning Progress Monitoring (LPM) to solve the problem of agents trapping themselves on unlearnable randomness in environments. Traditional methods that reward prediction error or novelty treat noise as worth exploring and waste effort there. LPM instead gives reward for actual reductions in the agent's prediction error by using an auxiliary error model to estimate what the error should have been in the prior step. The authors prove this reward signal is zero-equivariant and rises monotonically with information gain, provided the error model is present. Experiments in noisy MNIST, a large maze with image inputs, and Atari games show faster reward convergence, broader state coverage, and higher task rewards than prior baselines.

Core claim

LPM defines the intrinsic reward as the difference between the current iteration's dynamics-model error and the error that an auxiliary error model predicts for the previous iteration. The resulting signal is shown to be zero-equivariant and a monotone indicator of information gain; the error model is required to preserve this monotonic correspondence. Consequently the agent is directed toward learnable transitions while ignoring unlearnable noisy ones, producing more efficient exploration in stochastic settings.

What carries the argument

Dual-network architecture in which an error model predicts the dynamics model's prior error so that their difference supplies the intrinsic reward signal.

If this is right

  • Intrinsic reward converges faster than uncertainty or novelty baselines.
  • Agents visit more distinct states in image-based maze environments.
  • Higher extrinsic task reward is obtained in noisy Atari settings.
  • Exploration succeeds without explicit handling of each noise source.

Where Pith is reading between the lines

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

  • The same progress signal could be applied to partially observable or real-robot tasks that contain sensor noise.
  • Replacing absolute-error rewards with difference rewards may reduce the sample complexity of curiosity-driven training at scale.
  • The necessity of the auxiliary model suggests that any future progress-based method will need a comparable tracking network.

Load-bearing premise

The auxiliary error model can reliably forecast the dynamics model's expected prediction error from the previous iteration.

What would settle it

A controlled test in which the LPM reward fails to increase monotonically with independently measured information gain on learnable versus noisy transitions would disprove the claimed correspondence.

Figures

Figures reproduced from arXiv: 2509.25438 by Wan Du, Zhibo Hou, Zhiyu An.

Figure 1
Figure 1. Figure 1: Rendering of the experiment environments. [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: Exploration performance across noise conditions, averaged over 10 random seeds. State coverage during training in 3D maze environment. Left: Deterministic setting (best: EDT state coverage 1276.1). Center: State noise condition (best: LPM state coverage 1434.0). Right: Action noise setting (best: LPM state coverage 1340.0). two representative baselines: AMA, a noise-robust curiosity-driven method, and Epis… view at source ↗
Figure 2
Figure 2. Figure 2: Noisy MNIST with deterministic and stochastic transitions over 5 runs [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 4
Figure 4. Figure 4: Average and standard deviation extrinsic rewards achieved by each method across deter [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
read the original abstract

When there exists an unlearnable source of randomness (noisy-TV) in the environment, a naively intrinsic reward driven exploring agent gets stuck at that source of randomness and fails at exploration. Intrinsic reward based on uncertainty estimation or distribution similarity, while eventually escapes noisy-TVs as time unfolds, suffers from poor sample efficiency and high computational cost. Inspired by recent findings from neuroscience that humans monitor their improvements during exploration, we propose a novel method for intrinsically-motivated exploration, named Learning Progress Monitoring (LPM). During exploration, LPM rewards model improvements instead of prediction error or novelty, effectively rewards the agent for observing learnable transitions rather than the unlearnable transitions. We introduce a dual-network design that uses an error model to predict the expected prediction error of the dynamics model in its previous iteration, and use the difference between the model errors of the current iteration and previous iteration to guide exploration. We theoretically show that the intrinsic reward of LPM is zero-equivariant and a monotone indicator of Information Gain (IG), and that the error model is necessary to achieve monotonicity correspondence with IG. We empirically compared LPM against state-of-the-art baselines in noisy environments based on MNIST, 3D maze with 160x120 RGB inputs, and Atari. Results show that LPM's intrinsic reward converges faster, explores more states in the maze experiment, and achieves higher extrinsic reward in Atari. This conceptually simple approach marks a shift-of-paradigm of noise-robust exploration. For code to reproduce our experiments, see https://github.com/Akuna23Matata/LPM_exploration

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 a new intrinsic motivation method called Learning Progress Monitoring (LPM) to enable robust exploration in environments with unlearnable noise sources (noisy-TVs). LPM uses a dual-network architecture where an error model predicts the dynamics model's previous prediction error, and the difference between current and previous errors serves as the intrinsic reward, focusing on learnable transitions. The authors claim to theoretically demonstrate that this reward is zero-equivariant and monotonically corresponds to Information Gain (IG), with the error model being essential for this property. Empirically, LPM is shown to outperform baselines in noisy MNIST, a 3D maze with RGB inputs, and Atari games by achieving faster reward convergence, more state exploration, and higher extrinsic rewards.

Significance. This work could be significant for the field of intrinsically motivated reinforcement learning if the theoretical results hold, as it offers a noise-robust alternative to uncertainty or novelty-based methods with potentially better sample efficiency. The empirical results in complex domains like Atari support its practical value. Explicitly providing code for reproduction strengthens the contribution by enabling verification.

major comments (2)
  1. [Abstract] The theoretical result that the LPM intrinsic reward is zero-equivariant and a monotone indicator of IG, along with the necessity of the error model for monotonicity, is stated without any proof details, equations, or lemmas. This is a load-bearing claim for the paper's central contribution and requires detailed derivation to allow verification.
  2. [Abstract] The empirical claims of faster convergence, more states explored in the maze, and higher extrinsic reward in Atari lack specific quantitative metrics, tables, or ablation results, making it difficult to assess the magnitude and reliability of the improvements over state-of-the-art baselines.
minor comments (1)
  1. The abstract contains a minor grammatical issue with 'shift-of-paradigm' which should be 'paradigm shift'.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive feedback and positive assessment of the work's significance. We address the major comments point by point below, with plans to revise the manuscript for improved clarity and verifiability.

read point-by-point responses

  1. Referee: [Abstract] The theoretical result that the LPM intrinsic reward is zero-equivariant and a monotone indicator of IG, along with the necessity of the error model for monotonicity, is stated without any proof details, equations, or lemmas. This is a load-bearing claim for the paper's central contribution and requires detailed derivation to allow verification.

    Authors: We agree that the abstract summarizes the theoretical claims at a high level without derivations. The full manuscript contains a dedicated theoretical analysis section deriving the zero-equivariance property of the LPM reward and its monotonic correspondence to Information Gain, including a formal proof that the error model is required for monotonicity (via a counterexample showing non-monotonicity without it). To address the concern, we will revise the manuscript to include a concise proof sketch with key equations and lemmas in the main text (e.g., in a new subsection or highlighted box), while retaining full details in the appendix. This ensures the central contribution is more readily verifiable. revision: yes

  2. Referee: [Abstract] The empirical claims of faster convergence, more states explored in the maze, and higher extrinsic reward in Atari lack specific quantitative metrics, tables, or ablation results, making it difficult to assess the magnitude and reliability of the improvements over state-of-the-art baselines.

    Authors: The abstract offers a qualitative overview of the results. The complete manuscript includes detailed experimental sections with tables providing quantitative metrics (means and standard deviations over multiple seeds), such as specific improvements in convergence speed, number of unique states visited in the maze, and extrinsic rewards in Atari, along with ablation studies comparing variants. We will revise the abstract to incorporate representative quantitative highlights (e.g., percentage gains or key values) and ensure these metrics are prominently referenced in the introduction and results summary for easier assessment of magnitude and reliability. revision: yes

Circularity Check

0 steps flagged

No circularity detected; derivation chain not inspectable from abstract

full rationale

Only the abstract is available, which states that the authors 'theoretically show that the intrinsic reward of LPM is zero-equivariant and a monotone indicator of Information Gain (IG), and that the error model is necessary to achieve monotonicity correspondence with IG.' No equations, derivation steps, or self-citations are provided in the given text. Without access to the specific mathematical reductions or load-bearing premises, no instance can be quoted where a claimed prediction or result reduces by construction to its inputs, a fitted quantity, or an unverified self-citation. The paper therefore presents as self-contained on the basis of the visible material, warranting a score of 0.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

Abstract-only view limits visibility into exact hyperparameters or background lemmas; the central addition is the auxiliary error model and the assumption that its output difference tracks information gain.

axioms (1)
  • domain assumption The difference between current and previous-iteration model errors is a monotone indicator of information gain.
    Core theoretical claim stated in the abstract.
invented entities (1)
  • Error model no independent evidence
    purpose: Predicts the expected prediction error of the dynamics model from the previous iteration
    New component introduced to compute the learning-progress signal.

pith-pipeline@v0.9.0 · 5796 in / 1155 out tokens · 47051 ms · 2026-05-18T11:47:18.170425+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

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

  • IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    We theoretically show that the intrinsic reward of LPM is zero-equivariant and a monotone indicator of Information Gain (IG), and that the error model is necessary to achieve monotonicity correspondence with IG.

  • IndisputableMonolith/Cost.lean Jcost_pos_of_ne_one echoes
    ?
    echoes

    ECHOES: this paper passage has the same mathematical shape or conceptual pattern as the Recognition theorem, but is not a direct formal dependency.

    r_i_t = E_D[ε^{(τ-1)}_t(o_{t+1})] - ε^{(τ)}_t(o_{t+1})

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
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Reference graph

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13 extracted references · 13 canonical work pages · 3 internal anchors

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    Consequently, the expectation in the first term ofri is necessary to guarantee a deterministic mono- tone relationship between intrinsic reward and information gain

    There existθfor whichr i,point <0whileIG>0. Consequently, the expectation in the first term ofri is necessary to guarantee a deterministic mono- tone relationship between intrinsic reward and information gain. Proof.Express each reward in terms of the log-likelihood: log MSE(θ) =− 1 c (logp(D|θ)−const(D)), so that ri,point = 1 c logp(D|θ D)−logp(D|θ) , r ...

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