pith. machine review for the scientific record. sign in

arxiv: 2604.26360 · v1 · submitted 2026-04-29 · 💻 cs.LG · cs.AI

Recognition: unknown

Uncertainty-Aware Reward Discounting for Mitigating Reward Hacking

Disha Singha
Authors on Pith no claims yet

Pith reviewed 2026-05-07 13:40 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords reinforcement learningreward hackinguncertainty estimationepistemic uncertaintypreference uncertaintyreward modelingreliability filteralignment
0
0 comments X

The pith

A dual-source uncertainty framework using ensemble disagreement and preference variability reduces reward hacking by 93.7 percent in RL.

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

The paper sets out to show that reward hacking in reinforcement learning stems from treating uncertain rewards as precise scalars, and that explicitly modeling two kinds of uncertainty can fix it. Epistemic uncertainty comes from disagreement among an ensemble of value predictors, while preference uncertainty comes from variation across human reward annotations. These signals feed a Reliability Filter that lowers the effective reward for high-uncertainty actions, tilting the agent toward caution instead of exploitation. Tests on grid worlds of increasing size and on standard continuous-control benchmarks show steadier learning curves and far less trapping behavior even when 30 percent of the supervisory signals are noisy. A reader should care because most real objectives, especially those learned from people, carry exactly this kind of ambiguity.

Core claim

We introduce a dual-source uncertainty-aware reward framework that explicitly models both epistemic uncertainty in value estimation and uncertainty in human preferences. Model uncertainty is captured via ensemble disagreement over value predictions, while preference uncertainty is derived from variability in reward annotations. We combine these signals through a confidence-adjusted Reliability Filter that adaptively modulates action selection, encouraging a balance between exploitation and caution. Empirical results across multiple discrete grid configurations and high-dimensional continuous control environments demonstrate that our approach yields more stable training dynamics and reduces

What carries the argument

The confidence-adjusted Reliability Filter, which fuses epistemic uncertainty (ensemble disagreement on values) with preference uncertainty (annotation variability) to scale down rewards for uncertain actions.

If this is right

  • Training becomes more stable under reward ambiguity in both discrete grids and continuous control tasks.
  • Exploitative behaviors drop sharply, with a measured 93.7 percent reduction in trap visitation.
  • Performance remains robust when up to 30 percent of reward annotations contain noise.
  • A modest reduction in peak reward occurs relative to unconstrained baselines.
  • Improvements reach statistical significance across the tested configurations.

Where Pith is reading between the lines

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

  • The same filter could be inserted into preference-tuning pipelines for language models where human feedback is known to be noisy.
  • Reward models might usefully output distributional or interval estimates rather than single scalars so that downstream RL can use the filter without extra ensembles.
  • The observed trade-off between safety and peak performance suggests a tunable knob that future work could set automatically from environment risk level.
  • Extending the approach to partially observable settings would test whether the same uncertainty sources still suffice when state uncertainty is also present.

Load-bearing premise

That ensemble disagreement reliably signals the epistemic uncertainty that matters for reward hacking and that annotation variability faithfully represents genuine preference uncertainty.

What would settle it

In the same 10x10 grid or Hopper environment, disable only the Reliability Filter while still computing the two uncertainty estimates; if trap visitation frequency stays as low as with the filter active, the claim that the filter itself drives the reduction is false.

Figures

Figures reproduced from arXiv: 2604.26360 by Disha Singha.

Figure 1
Figure 1. Figure 1: Architecture of the UARD Framework. The Reliability Filter integrates the dual-source view at source ↗
Figure 2
Figure 2. Figure 2: Comparative analysis showing that the UARD Reciprocal Filter avoids the Zero-Reward view at source ↗
Figure 3
Figure 3. Figure 3: Comparative Analysis of Reward Hacking Resilience. The UARD framework (blue) view at source ↗
Figure 4
Figure 4. Figure 4: Comparative analysis of True Return across 500 training episodes. The view at source ↗
Figure 5
Figure 5. Figure 5: Frequency of trap visits per episode. While baseline models (Blue, Orange) increas view at source ↗
Figure 6
Figure 6. Figure 6: Empirical demonstration of the Alignment Gap in the baseline agent. While the observed proxy reward (Blue) increases, the true performance (Orange) remains stagnant. To evaluate the alignment between the agent’s internal value estimates and the true objective, 14 view at source ↗
Figure 7
Figure 7. Figure 7: Evolution of Dual-Source Uncertainty. The model uncertainty ( view at source ↗
Figure 8
Figure 8. Figure 8: Performance comparison in Hopper-v4. While baseline PPO and SAC agents exhibit gradual ”optimization drift” away from the true aligned objective (red dotted line), UARD remains more consistent, filtering out the subtle rewards associated with simulator inaccuracies. 16 view at source ↗
Figure 9
Figure 9. Figure 9: Performance comparison in Walker2d-v4. Baseline agents exhibit large reward spikes, view at source ↗
Figure 10
Figure 10. Figure 10: Robustness comparison under adversarial reward distortion. view at source ↗
Figure 11
Figure 11. Figure 11: Robustness comparison against SUNRISE under adversarial reward distortion. view at source ↗
Figure 12
Figure 12. Figure 12: Response to OOD perturbation. The baseline agent exhibits instability following the view at source ↗
Figure 13
Figure 13. Figure 13: Robustness under increasing supervisory noise. Mean safety violations (lower is better) are plotted across noise levels σ ∈ {0%, 10%, 20%, 30%} applied to human feedback annotations. Baseline PPO/SAC (gray dashed line) exhibits linear degradation, with violations increasing from 6.2 ± 7.1 at 0% noise to 23.4 ± 8.3 at 30% noise. In contrast, UARD (blue solid line) remains stable across all noise levels, wi… view at source ↗
Figure 14
Figure 14. Figure 14: Robustness to adversarial reward regions. view at source ↗
Figure 15
Figure 15. Figure 15: Sign-Preservation Analysis under reward perturbations. The UARD framework (blue) view at source ↗
Figure 16
Figure 16. Figure 16: Activation profile of Feature #42 over time. The shaded region (Steps 60–80) indicates view at source ↗
Figure 17
Figure 17. Figure 17: Interventional analysis using activation steering. Left: Necessity test—clamping Feature view at source ↗
Figure 18
Figure 18. Figure 18: Abstention behavior under rising uncertainty. The purple curve represents the risk view at source ↗
read the original abstract

Reinforcement learning (RL) systems typically optimize scalar reward functions that assume precise and reliable evaluation of outcomes. However, real-world objectives--especially those derived from human preferences--are often uncertain, context-dependent, and internally inconsistent. This mismatch can lead to alignment failures such as reward hacking, over-optimization, and overconfident behavior. We introduce a dual-source uncertainty-aware reward framework that explicitly models both epistemic uncertainty in value estimation and uncertainty in human preferences. Model uncertainty is captured via ensemble disagreement over value predictions, while preference uncertainty is derived from variability in reward annotations. We combine these signals through a confidence-adjusted Reliability Filter that adaptively modulates action selection, encouraging a balance between exploitation and caution. Empirical results across multiple discrete grid configurations (6x6, 8x8, 10x10) and high-dimensional continuous control environments (Hopper-v4, Walker2d-v4) demonstrate that our approach yields more stable training dynamics and reduces exploitative behaviors under reward ambiguity, achieving a 93.7% reduction in reward-hacking behavior as measured by trap visitation frequency. We demonstrate statistical significance of these improvements and robustness under up to 30% supervisory noise, albeit with a trade-off in peak observed reward compared to unconstrained baselines. By treating uncertainty as a first-class component of the reward signal, this work offers a principled approach toward more reliable and aligned reinforcement learning systems.

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

3 major / 2 minor

Summary. The manuscript proposes a dual-source uncertainty-aware reward framework for RL that models epistemic uncertainty through ensemble disagreement on value predictions and preference uncertainty through variability in reward annotations. These signals are integrated via a confidence-adjusted Reliability Filter to adaptively modulate action selection, aiming to balance exploitation and caution while mitigating reward hacking. Empirical evaluations are reported across discrete grid worlds (6x6, 8x8, 10x10) and continuous control environments (Hopper-v4, Walker2d-v4), claiming a 93.7% reduction in reward-hacking behavior (measured by trap visitation frequency), more stable training dynamics, statistical significance, and robustness to up to 30% supervisory noise, albeit with a trade-off in peak reward.

Significance. If the central empirical claims hold after providing missing methodological details, the work could offer a practical contribution to preference-based RL and alignment by explicitly incorporating uncertainty to reduce exploitative behaviors. The dual-uncertainty approach and reported quantitative gains across both discrete and high-dimensional continuous domains represent a potentially useful extension of standard ensemble and annotation techniques, though the absence of ablations and exact formulations limits immediate assessment of novelty and generalizability.

major comments (3)
  1. [§3] §3 (Method), Reliability Filter subsection: The abstract and methods description provide no exact equations for how ensemble disagreement and annotation variability are combined into the confidence-adjusted modulation of action selection or reward discounting. This is load-bearing for the central claim, as the reported 93.7% reduction in trap visitation depends on the filter's specific implementation; without the formulation (e.g., the functional form of the confidence adjustment), the results cannot be reproduced or verified.
  2. [§4] §4 (Experiments), grid and MuJoCo results: The 93.7% reduction claim and statistical significance are stated without details on trap visitation measurement protocol, exact baseline algorithms, data exclusion criteria, or ablation studies isolating the contribution of epistemic vs. preference uncertainty. This undermines verification of the weakest assumption that ensemble disagreement and annotation variability faithfully proxy hacking-relevant uncertainties.
  3. [Abstract, §4.3] Abstract and §4.3 (Robustness): The claim of robustness to 30% supervisory noise lacks specification of noise type (e.g., label flips vs. additive), how it affects annotations, and whether ablations confirm that the Reliability Filter still correctly balances caution without discarding useful actions under such noise.
minor comments (2)
  1. [Abstract] The abstract refers to 'reward discounting' in the title but describes modulation of action selection; clarify if discounting is applied to the reward signal itself or only to selection probabilities.
  2. [§4] Figure captions and tables (if present in §4) should explicitly state the number of random seeds and error bars used for the reported improvements to support the statistical significance claims.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. We address each major comment below and will revise the manuscript accordingly to enhance clarity, reproducibility, and completeness.

read point-by-point responses

  1. Referee: [§3] §3 (Method), Reliability Filter subsection: The abstract and methods description provide no exact equations for how ensemble disagreement and annotation variability are combined into the confidence-adjusted modulation of action selection or reward discounting. This is load-bearing for the central claim, as the reported 93.7% reduction in trap visitation depends on the filter's specific implementation; without the formulation (e.g., the functional form of the confidence adjustment), the results cannot be reproduced or verified.

    Authors: We agree that the exact equations are essential for reproducibility. The initial submission described the dual-uncertainty integration conceptually but omitted the closed-form expressions for the confidence-adjusted Reliability Filter. In the revision we will insert the full mathematical specification in §3, including the functional form that combines ensemble disagreement (epistemic) and annotation variability (preference) to modulate the effective reward and action probabilities. revision: yes

  2. Referee: [§4] §4 (Experiments), grid and MuJoCo results: The 93.7% reduction claim and statistical significance are stated without details on trap visitation measurement protocol, exact baseline algorithms, data exclusion criteria, or ablation studies isolating the contribution of epistemic vs. preference uncertainty. This undermines verification of the weakest assumption that ensemble disagreement and annotation variability faithfully proxy hacking-relevant uncertainties.

    Authors: We will expand §4 with the requested details. Trap visitation is quantified as the normalized count of entries into predefined suboptimal loops or states; baselines are standard PPO and vanilla preference RL; no data were excluded; and new ablations will isolate each uncertainty source. These additions will directly test the proxy assumption and confirm the contribution of both components to the observed 93.7% reduction. revision: yes

  3. Referee: [Abstract, §4.3] Abstract and §4.3 (Robustness): The claim of robustness to 30% supervisory noise lacks specification of noise type (e.g., label flips vs. additive), how it affects annotations, and whether ablations confirm that the Reliability Filter still correctly balances caution without discarding useful actions under such noise.

    Authors: We will specify that the noise consists of random label flips applied to 30% of the preference annotations. Revised §4.3 will include the exact noise-generation procedure and additional ablation results demonstrating that the Reliability Filter continues to balance caution and exploitation without systematically discarding high-value actions at this noise level. revision: yes

Circularity Check

0 steps flagged

No circularity: empirical claims rest on standard RL components without self-referential reductions

full rationale

The paper presents a dual-source uncertainty framework (ensemble disagreement for epistemic uncertainty plus annotation variability for preference uncertainty) combined via a confidence-adjusted Reliability Filter. All reported outcomes are empirical measurements (93.7% trap-visitation reduction, robustness to 30% noise) across grid and MuJoCo environments. No equations appear that define the filter output or the reduction metric as a direct algebraic rearrangement of fitted parameters; no load-bearing self-citations invoke prior uniqueness theorems or ansatzes from the same authors; the derivation relies on established ensemble methods and RL baselines rather than renaming or re-deriving its own inputs. The central result therefore remains an independent empirical observation rather than a tautology.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 1 invented entities

Abstract-only view limits visibility; the framework appears to rest on standard RL assumptions plus the new Reliability Filter, with no free parameters, axioms, or invented entities explicitly quantified in the provided text.

invented entities (1)
  • Reliability Filter no independent evidence
    purpose: Adaptively modulates action selection using combined uncertainty signals
    Introduced as the central mechanism to balance exploitation and caution; no independent evidence supplied beyond the reported empirical gains.

pith-pipeline@v0.9.0 · 5543 in / 1318 out tokens · 45050 ms · 2026-05-07T13:40:17.797121+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

16 extracted references · 4 canonical work pages · 2 internal anchors

  1. [1]

    Concrete Problems in AI Safety

    Dario Amodei, Chris Olah, Jacob Steinhardt, Paul Christiano, John Schulman, and Dan Man´ e. Concrete problems in ai safety.arXiv preprint arXiv:1606.06565, 2016

    work page internal anchor Pith review arXiv 2016

  2. [2]

    Uncertainty-based of- fline reinforcement learning with diversified Q-ensemble

    Gaon An, Seungyong Moon, Jang-Hyun Kim, and Hyun Oh Song. Uncertainty-based of- fline reinforcement learning with diversified Q-ensemble. InAdvances in Neural Information Processing Systems, volume 34, pages 751–763, 2021

    2021

  3. [3]

    Deep reinforcement learning from human preferences.Advances in neural information process- ing systems, 30, 2017

    Paul F Christiano, Jan Leike, Tom Brown, Miljan Martic, Shane Legg, and Dario Amodei. Deep reinforcement learning from human preferences.Advances in neural information process- ing systems, 30, 2017

    2017

  4. [4]

    Reward tampering problems and solutions in reinforcement learning: A survey.Synthese, 198:27–61, 2021

    Tom Everitt, Gary Lea, and Marcus Hutter. Reward tampering problems and solutions in reinforcement learning: A survey.Synthese, 198:27–61, 2021

    2021

  5. [5]

    Dropout as a bayesian approximation: Representing model uncertainty in deep learning

    Yarin Gal and Zoubin Ghahramani. Dropout as a bayesian approximation: Representing model uncertainty in deep learning. InInternational conference on machine learning, pages 1050–1059. PMLR, 2016

    2016

  6. [6]

    A comprehensive survey on safe reinforcement learning

    Javier Garc´ ıa and Fernando Fern´ andez. A comprehensive survey on safe reinforcement learning. Journal of Machine Learning Research, 16(1):1437–1480, 2015

    2015

  7. [7]

    Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor

    Tuomas Haarnoja, Aurick Zhou, Pieter Abbeel, and Sergey Levine. Soft actor-critic: Off- policy maximum entropy deep reinforcement learning with a stochastic actor. InInternational conference on machine learning, pages 1861–1870. PMLR, 2018

    2018

  8. [8]

    Inverse reward design.Advances in neural information processing systems, 30, 2017

    Dylan Hadfield-Menell, Smith Millington, Pieter Abbeel, Stuart Russell, and Anca Dragan. Inverse reward design.Advances in neural information processing systems, 30, 2017

    2017

  9. [9]

    Reward learning from human preferences and demonstrations in atari

    Borja Ibarz, Jan Leike, Tobias Pohlen, Geoffrey Irving, Miljan Shane, and Dario Amodei. Reward learning from human preferences and demonstrations in atari. InAdvances in Neural Information Processing Systems, 2018

    2018

  10. [10]

    Stabilizing off- policy Q-learning via bootstrapping error reduction

    Aviral Kumar, Justin Fu, Matthew Soh, George Tucker, and Sergey Levine. Stabilizing off- policy Q-learning via bootstrapping error reduction. InAdvances in Neural Information Pro- cessing Systems, volume 32, 2019

    2019

  11. [11]

    Conservative Q-learning for offline reinforcement learning

    Aviral Kumar, Aurick Zhou, George Tucker, and Sergey Levine. Conservative Q-learning for offline reinforcement learning. InAdvances in Neural Information Processing Systems, volume 33, pages 1179–1191, 2020

    2020

  12. [12]

    SUNRISE: A simple unified framework for ensemble learning in deep reinforcement learning

    Kimin Lee, Michael Laskin, Aravind Srinivas, and Pieter Abbeel. SUNRISE: A simple unified framework for ensemble learning in deep reinforcement learning. InInternational Conference on Machine Learning, pages 5714–5731. PMLR, 2021

    2021

  13. [13]

    Scalable agent alignment via reward modeling: a research direction

    Jan Leike, Miljan Martic, Nevena Lazic, Catherine Olsson, Tomer Kogabaev, Nicholas Schiefer, and Jared Kaplan. Scalable agent alignment via reward modeling: a research direction.arXiv preprint arXiv:1811.07871, 2018

    work page Pith review arXiv 2018

  14. [14]

    The effects of reward misspecification: Mapping and mitigating misaligned models

    Alexander Pan, Kush Bhatia, and Jacob Steinhardt. The effects of reward misspecification: Adversarial examples in reinforcement learning.arXiv preprint arXiv:2201.03544, 2022. 30

    work page arXiv 2022

  15. [15]

    Proximal Policy Optimization Algorithms

    John Schulman, Filip Wolski, Prafulla Dhariwal, Alec Radford, and Oleg Klimov. Proximal policy optimization algorithms.arXiv preprint arXiv:1707.06347, 2017

    work page internal anchor Pith review arXiv 2017

  16. [16]

    Defining and charac- terizing reward hacking.International Conference on Machine Learning, 2022

    Joar Skalse, Matthew Knott, Dominik Hintersdorf, and Pieter Abbeel. Defining and charac- terizing reward hacking.International Conference on Machine Learning, 2022. 31

    2022