Regret-Aware Policy Optimization: Environment-Level Memory for Replay Suppression under Delayed Harm

Prakul Sunil Hiremath

arxiv: 2604.07428 · v1 · submitted 2026-04-08 · 💻 cs.LG · cs.AI

Regret-Aware Policy Optimization: Environment-Level Memory for Replay Suppression under Delayed Harm

Prakul Sunil Hiremath This is my paper

Pith reviewed 2026-05-10 18:08 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords reinforcement learning safetyreplay suppressiondelayed harmenvironment augmentationpolicy optimizationgraph diffusionregret-aware optimization

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The pith

Augmenting RL environments with harm traces and scar fields suppresses replay of delayed harm.

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

The paper examines how standard RL safety methods fail under delayed harm because stationary observable dynamics allow harmful sequences to replay after a washout period. It defines a Replay Suppression Diagnostic to isolate this issue and introduces Regret-Aware Policy Optimization, which adds persistent harm-trace and scar fields to the environment along with bounded mass-preserving transition reweighting. This reduces the reachability of historically harmful regions. Experiments on graph diffusion tasks with 50 to 1000 nodes show that the method lowers re-amplification gain from 0.98 to 0.33 on 250-node graphs while retaining 82 percent of task return.

Core claim

By augmenting the environment with persistent harm-trace and scar fields and applying bounded mass-preserving transition reweighting, Regret-Aware Policy Optimization reduces reachability to historically harmful regions, thereby suppressing replay under delayed harm while preserving most task performance; disabling the reweighting during replay restores the original re-amplification gain.

What carries the argument

Persistent harm-trace and scar fields with bounded mass-preserving transition reweighting that deforms the environment to limit access to past harmful states without altering observable kernels.

Load-bearing premise

That adding harm-trace and scar fields plus bounded transition reweighting preserves stationarity of observable transition kernels and avoids unintended shifts in action distributions.

What would settle it

An experiment in which enabling the harm-trace and scar fields plus reweighting produces no reduction in re-amplification gain under the replay protocol would falsify the suppression claim.

Figures

Figures reproduced from arXiv: 2604.07428 by Prakul Sunil Hiremath.

**Figure 1.** Figure 1: Replay-phase odds contraction. Stepwise odds ratio during Replay (mean ± 1 s.d.). Under stationary transitions (PM-ST and other stationary baselines), contraction remains near 1. RAPO maintains persistent contraction; turning deformation off only during Replay restores odds ratio near 1, supporting a causal role for transition deformation. R4: Slow-decay scars maintain suppression. The slow-decay scar vari… view at source ↗

**Figure 2.** Figure 2: Scar persistence across phases. Total scar mass rises during Exposure due to delayed-harm injection and persists through Decay into Replay, enabling replay-time transition deformation and odds contraction. 6.4 Utility–Safety Trade-off We evaluate whether RAPO suppresses replay by trivial shutdown [PITH_FULL_IMAGE:figures/full_fig_p013_2.png] view at source ↗

**Figure 3.** Figure 3: Utility–safety trade-off. Replay return (normalized) vs. re-amplification gain (RAG). RAPO traces a Pareto-like curve as deformation strength varies, improving replay suppression while retaining substantial utility, in contrast to stationary-transition baselines and hard shielding. suppression requires either a persistent replay-time action shift or a change in the observable transition law (Theorem 1, Cor… view at source ↗

read the original abstract

Safety in reinforcement learning (RL) is typically enforced through objective shaping while keeping environment dynamics stationary with respect to observable state-action pairs. Under delayed harm, this can lead to replay: after a washout period, reintroducing the same stimulus under matched observable conditions reproduces a similar harmful cascade. We introduce the Replay Suppression Diagnostic (RSD), a controlled exposure-decay-replay protocol that isolates this failure mode under frozen-policy evaluation. We show that, under stationary observable transition kernels, replay cannot be structurally suppressed without inducing a persistent shift in replay-time action distributions. Motivated by platform-mediated systems, we propose Regret-Aware Policy Optimization (RAPO), which augments the environment with persistent harm-trace and scar fields and applies a bounded, mass-preserving transition reweighting to reduce reachability of historically harmful regions. On graph diffusion tasks (50-1000 nodes), RAPO suppresses replay, reducing re-amplification gain (RAG) from 0.98 to 0.33 on 250-node graphs while retaining 82\% of task return. Disabling transition deformation only during replay restores re-amplification (RAG 0.91), isolating environment-level deformation as the causal mechanism.

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

RAPO gives concrete empirical suppression of delayed-harm replay on graphs via persistent environment fields, but those fields likely make observable transitions history-dependent and undercut the stationarity premise.

read the letter

The main thing to know is that this paper shows a practical environment augmentation that cuts replay of harmful cascades after a delay, with clear numbers on graph diffusion tasks and an ablation that ties the gain to the deformation step. It also defines a controlled RSD protocol to measure the problem under frozen policies. On 250-node graphs it drops re-amplification gain from 0.98 to 0.33 while keeping 82% task return, and disabling the reweighting only at replay time restores most of the gain. That ablation is useful because it tests the mechanism instead of just showing an overall win. The work is aimed at RL safety settings where harm arrives late, such as recommendation platforms or long-horizon control, and the specific RAG metric plus the exposure-decay-replay structure makes the claims falsifiable. A reader who wants to see environment-level memory tried on a concrete failure mode will find something to work with here. The soft spot is the stationarity tension. The motivation rests on the claim that stationary observable kernels force any replay suppression to come through persistent action-distribution shifts. Yet the harm-trace and scar fields accumulate across trajectories, so the reweighting factor for a given observable state-action pair can change with history. That makes the observable next-state distribution depend on prior path, which means the kernel is no longer stationary. The ablation does not check this directly; it only shows deformation is needed for the reported drop. Without error bars, sensitivity on the reweighting bound, or a fuller derivation of the action-shift claim, it is hard to tell how much of the retained return comes from clean suppression versus the introduced non-stationarity. The protocol choices also look post-hoc and could affect how general the result is. Still, the empirical piece is sharp enough that a serious referee should see it. The numbers are specific, the ablation isolates a causal piece, and the problem it targets is real for deployed systems. I would send it to review and ask the authors to clarify the stationarity status of the augmented kernel and add variance estimates.

Referee Report

2 major / 2 minor

Summary. The paper claims that under stationary observable transition kernels, replay under delayed harm in RL cannot be structurally suppressed without inducing persistent shifts in replay-time action distributions. It introduces the Replay Suppression Diagnostic (RSD), a controlled exposure-decay-replay protocol, and proposes Regret-Aware Policy Optimization (RAPO), which augments the environment with persistent harm-trace and scar fields and applies bounded mass-preserving transition reweighting to reduce reachability of harmful regions. On graph diffusion tasks (50-1000 nodes), RAPO reduces re-amplification gain (RAG) from 0.98 to 0.33 on 250-node graphs while retaining 82% of task return; an ablation disabling deformation only during replay restores RAG to 0.91.

Significance. If the results hold, the work provides a concrete environment-level mechanism for suppressing replay in delayed-harm settings while preserving substantial task performance, with quantitative support on graph tasks of varying scale. The RSD protocol and ablation isolating transition deformation as the causal factor are strengths, as is the explicit framing around observable stationarity. The approach could inform safety mechanisms in platform-mediated or history-dependent systems if the stationarity implications are resolved.

major comments (2)

[Abstract / theoretical statement] Abstract and theoretical statement on action distribution shifts: the claim that replay cannot be suppressed under stationary observable kernels without persistent shifts is load-bearing for motivating RAPO, yet the derivation is not detailed. This makes it hard to evaluate whether the proposed augmentation is consistent with the premise or circumvents it in a controlled way.
[Abstract / RAPO construction] Abstract and § on RAPO construction: augmenting with persistent harm-trace and scar fields (which accumulate over trajectories) plus history-dependent reweighting renders the observable transition kernel non-stationary, since the reweighting factor for a fixed (s, a) can vary with prior history. This directly contradicts the stationarity premise used to derive the necessity of action-distribution shifts. The ablation (disabling deformation only during replay) tests necessity of deformation but does not address whether retained return (82%) arises from unintended non-stationarity rather than clean suppression.

minor comments (2)

[Abstract / empirical results] Results summary lacks error bars or variance measures across the graph-task experiments (50-1000 nodes).
[RSD protocol] The exposure-decay-replay protocol choices appear post-hoc; clarify whether they were fixed a priori or tuned, and discuss implications for generalizability beyond the reported graph sizes.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments on our manuscript. We address each major comment in turn, clarifying the theoretical premise and the role of the RAPO augmentation while noting where revisions will strengthen the presentation.

read point-by-point responses

Referee: [Abstract / theoretical statement] Abstract and theoretical statement on action distribution shifts: the claim that replay cannot be suppressed under stationary observable kernels without persistent shifts is load-bearing for motivating RAPO, yet the derivation is not detailed. This makes it hard to evaluate whether the proposed augmentation is consistent with the premise or circumvents it in a controlled way.

Authors: We agree the derivation merits greater visibility. The manuscript contains a formal argument establishing that, for any fixed observable transition kernel that is stationary, replay of a harmful trajectory under matched observable conditions is inevitable unless the replay-time action distribution is persistently altered. This result is used only to motivate the need for an augmentation that relaxes pure observability-stationarity in a structured way. We will revise the main text to include the full derivation (currently in an appendix) and add an explicit forward reference from the abstract. revision: yes
Referee: [Abstract / RAPO construction] Abstract and § on RAPO construction: augmenting with persistent harm-trace and scar fields (which accumulate over trajectories) plus history-dependent reweighting renders the observable transition kernel non-stationary, since the reweighting factor for a fixed (s, a) can vary with prior history. This directly contradicts the stationarity premise used to derive the necessity of action-distribution shifts. The ablation (disabling deformation only during replay) tests necessity of deformation but does not address whether retained return (82%) arises from unintended non-stationarity rather than clean suppression.

Authors: The stationarity premise applies strictly to the unaugmented observable kernel; the claim is that suppression is impossible while remaining within that class. RAPO augments the state with persistent, bounded harm-trace and scar fields and applies mass-preserving reweighting precisely to exit that class in a controlled, history-dependent manner. The resulting non-stationarity is therefore the intended mechanism, not an unintended side-effect. The ablation isolates the contribution of the reweighting step itself: when deformation is disabled only at replay time, RAG returns to 0.91, showing that the performance retention (82 %) is achieved under the same augmented dynamics that produce suppression. We will add a dedicated paragraph in the RAPO section and discussion explicitly distinguishing the original stationary premise from the controlled non-stationarity introduced by augmentation. revision: partial

Circularity Check

0 steps flagged

No significant circularity; derivation and empirical claims remain independent

full rationale

The paper first states a theoretical necessity result under the assumption of stationary observable transition kernels, then defines RAPO via explicit augmentation with harm-trace/scar fields plus bounded reweighting, and reports direct experimental outcomes (RAG reduction, return retention, ablation) on graph diffusion tasks. These outcomes are measured quantities from policy rollouts, not quantities obtained by fitting parameters to the same data or by re-expressing the input assumptions. No self-citations, ansatzes, or uniqueness theorems are invoked as load-bearing steps in the provided chain. The ablation (disabling deformation during replay) tests a causal component without reducing the reported effect sizes to a definitional identity. The overall construction is therefore self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 1 invented entities

The approach rests on domain assumptions about stationary kernels and the feasibility of persistent non-observable fields; limited details available from abstract.

free parameters (1)

reweighting bound
The bounded mass-preserving transition reweighting parameter is introduced to control deformation but its specific value or selection method is not stated in the abstract.

axioms (1)

domain assumption Stationary observable transition kernels
Invoked to establish that replay cannot be structurally suppressed without action distribution shifts.

invented entities (1)

harm-trace and scar fields no independent evidence
purpose: Provide persistent environment-level memory of past harm to alter reachability
New fields added to the environment state to enable replay suppression; no independent evidence outside the proposed mechanism.

pith-pipeline@v0.9.0 · 5516 in / 1388 out tokens · 61964 ms · 2026-05-10T18:08:28.462418+00:00 · methodology

discussion (0)

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/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

RAPO augments the environment with persistent harm-trace and scar fields and applies a bounded, mass-preserving transition reweighting
IndisputableMonolith/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

?

unclear
Relation between the paper passage and the cited Recognition theorem.

under stationary observable transition kernels, replay cannot be suppressed without persistent shifts in replay-time action distributions

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: The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses: The paper appears to rely on the theorem as machinery.
contradicts: The paper's claim conflicts with a theorem or certificate in the canon.
unclear: Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

2 extracted references · 2 canonical work pages

[1]

A survey of deep reinforcement learning in non-stationary environments.arXiv preprint arXiv:2301.02804,

17 Robert Kirk, Amy Zhang, Edward Grefenstette, and Tim Rockt¨ aschel. A survey of deep reinforcement learning in non-stationary environments.arXiv preprint arXiv:2301.02804,

work page arXiv
[2]

TODO: verify authors/title/venue Wang

Often cited as 2018 online/early access; use journal year as final. TODO: verify authors/title/venue Wang. Adaptive control for warehouse operations with reinforcement learning. InTODO,

work page 2018

[1] [1]

A survey of deep reinforcement learning in non-stationary environments.arXiv preprint arXiv:2301.02804,

17 Robert Kirk, Amy Zhang, Edward Grefenstette, and Tim Rockt¨ aschel. A survey of deep reinforcement learning in non-stationary environments.arXiv preprint arXiv:2301.02804,

work page arXiv

[2] [2]

TODO: verify authors/title/venue Wang

Often cited as 2018 online/early access; use journal year as final. TODO: verify authors/title/venue Wang. Adaptive control for warehouse operations with reinforcement learning. InTODO,

work page 2018