arxiv: 2605.06764 · v1 · submitted 2026-05-07 · 💻 cs.LG · cs.AI

Recognition: no theorem link

Revisiting Adam for Streaming Reinforcement Learning

Florin Gogianu , Adrian Catalin Lutu , Razvan Pascanu

Authors on Pith no claims yet

Pith reviewed 2026-05-11 01:05 UTC · model grok-4.3

classification 💻 cs.LG cs.AI

keywords streaming reinforcement learningonline learningAdam optimizereligibility tracesAtari gamesDQNC51variance-adjusted updates

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The pith

C51 matches StreamQ in streaming Atari RL without replay when the objective derivative is bounded and updates are variance-adjusted.

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

The paper examines standard deep RL updates like those in DQN and C51 inside a fully online streaming setting with no replay buffer or parallel sampling. It identifies two properties that make these updates robust: the loss derivative must remain bounded, and the optimizer must adjust weight updates for variance. C51 satisfies both conditions and performs on par with the recent StreamQ algorithm across 55 Atari games. From the same analysis the authors construct Adaptive Q(λ), an eligibility-trace method with explicit variance adjustment that reaches nearly twice the human baseline and improves on all reported metrics.

Core claim

In the online streaming reinforcement learning setting without replay, established algorithms such as DQN and C51 achieve robust performance when the derivative of the objective is bounded and the weight updates are variance-adjusted. C51 exhibits both properties and is competitive with StreamQ across 55 Atari games. Building on these insights, a variance-adjusted eligibility trace algorithm called Adaptive Q(λ) is derived, which approaches double the human baseline and surpasses prior methods on all performance metrics.

What carries the argument

The interaction of Adam with RL loss functions, requiring a bounded objective derivative together with variance-adjusted weight updates to stabilize learning in the absence of replay.

If this is right

C51 is competitive with StreamQ across the 55 Atari games in the streaming setting.
Adaptive Q(λ) approaches double the human baseline on the same games.
Adaptive Q(λ) surpasses existing methods by all reported performance metrics.
DQN-style updates succeed in streaming RL when they satisfy the two identified properties.

Where Pith is reading between the lines

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

The same two properties may explain why many other RL algorithms degrade when replay is removed.
Adaptive Q(λ) could be combined with other trace-based or distributional methods to further improve streaming agents.
Testing the bounded-derivative and variance-adjustment conditions on continuous-control or partially observable tasks would clarify their generality.
Simplifying agents by removing replay buffers may become practical if these optimizer conditions can be enforced reliably.

Load-bearing premise

The two properties of bounded objective derivatives and variance-adjusted weight updates are the essential and sufficient conditions for robust performance of DQN and C51 in the online streaming setting without replay.

What would settle it

An experiment in which C51 fails to match StreamQ on the 55-game Atari subset despite retaining bounded derivatives and variance-adjusted updates, or in which Adaptive Q(λ) does not exceed all baselines on every metric.

Figures

Figures reproduced from arXiv: 2605.06764 by Adrian Catalin Lutu, Florin Gogianu, Razvan Pascanu.

**Figure 2.** Figure 2: Aggregated normalised score on five MINATAR environments. Classical RL objectives using ADAM are strong performers. Fig.2 illustrates the final results on the five MINATAR environments. Surprisingly, DQN and C51 both outperform STREAMQ. Significant is the performance of DQN when compared to DQN1 from Elsayed et al. (2024) which always underperforms STREAMQ, given that they share the optimiser and the obje… view at source ↗

**Figure 3.** Figure 3: On aggregate, DQN performs better with larger [PITH_FULL_IMAGE:figures/full_fig_p008_3.png] view at source ↗

**Figure 4.** Figure 4: Performance increases with higher values of [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗

**Figure 5.** Figure 5: Large values for ADAM’s ε allow for stable learning on problems which are noisy or sparse. The y-axis component receives a stable gradient signal in both cases, whereas on the x-axis the gradient can either change sign randomly (left) or be zero 95% of the time (right). We hypothesise ADAM manifests a seldom-discussed implicit mechanism for scaling the updates differently across gradient components with va… view at source ↗

**Figure 6.** Figure 6: MINATAR results separated by game. The solid lines represent the mean evaluation return averaged over 9 independent runs 1e-7 1e-6 1e-5 1e-4 1e-3 1e-2 1e-1 0.3 0.4 0.5 0.6 QR aggregate performance on MinAtar for combinations of Adam(η,ε) ε value IQM score η value 1e-05 2.2e-05 4.6e-05 6.8e-05 0.0001 [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗

**Figure 7.** Figure 7: Performance increases with higher values of [PITH_FULL_IMAGE:figures/full_fig_p012_7.png] view at source ↗

**Figure 8.** Figure 8: ATARI results separated by game. The solid lines represent the mean evaluation return averaged over 7 independent runs 12 [PITH_FULL_IMAGE:figures/full_fig_p013_8.png] view at source ↗

read the original abstract

Learning from a sequence of interactions, as soon as observations are perceived and acted upon, without explicitly storing them, holds the promise of simpler, more efficient and adaptive algorithms. For over a decade, however, deep reinforcement learning walked the contrary path, augmenting agents with replay buffers or parallel sampling routines, in an effort to tame learning instability. Recently, this topic has been revisited by Elsayed et al. (2024), focusing on update computation through eligibility traces and modifications to the optimisation routine, resulting in the StreamQ algorithm. In this work we take a step back, investigating the efficacy of established updates, such as those implemented by DQN and C51 within this online setting. Not only do we find that they perform well, but through analysing how the optimisation algorithm generally, and Adam in particular, interacts with these updates, we contend that two properties are essential for robust performance: i) the derivative of the objective is to be bounded and ii) weight updates are variance-adjusted. Rigorous and exhaustive experimentation demonstrates that C51, which exhibits both characteristics, is competitive with StreamQ across a subset of 55 Atari games. Using these insights, we derive a variance-adjusted algorithm based on eligibility traces, termed Adaptive Q$(\lambda)$, which approaches double the human baseline on the same subset, surpassing existing methods by all performance metrics.

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

C51 holds up in streaming RL without replay and Adaptive Q(λ) improves on it, but the paper's explanation for the two key properties rests on correlation rather than isolation tests.

read the letter

The main point is that standard updates like C51 can run stably in a pure online setting on Atari without any replay buffer, and the authors turn that observation into a new algorithm called Adaptive Q(λ) that gets stronger scores on their 55-game subset. They also give a clear account of how Adam's variance adjustment interacts with bounded-gradient losses to avoid the usual blow-ups. That analysis is the useful piece: it takes existing ideas from DQN, C51, and eligibility traces, then shows why they might transfer to the no-replay case and uses the insight to modify the update rule. The experiments compare directly to StreamQ and human baselines, and the results look competitive or better across the metrics they report. Credit to them for running the tests at scale and for grounding the new method in properties of the optimizer rather than ad-hoc fixes. The soft spot is the causal claim. They identify bounded derivatives and variance-adjusted steps as the essential conditions because C51 has both and works while other methods do not. But the paper does not run the obvious controls, such as swapping the loss for an unbounded variant or replacing Adam inside the same framework to see what actually breaks. Without those, it is hard to rule out that distributional RL structure or trace implementation details are carrying more of the load. The 55-game subset also leaves open the usual selection questions, even if the authors describe the evaluation as exhaustive. This is worth a serious referee for anyone working on memory-constrained or real-time RL. The empirical results are concrete enough to check, the derivation is reproducible from the stated assumptions, and the new algorithm could be a practical option if the claims survive closer scrutiny. I would send it to review rather than desk reject.

Referee Report

3 major / 2 minor

Summary. The paper examines the performance of established deep RL updates (DQN, C51) in the online streaming setting without replay buffers or parallel sampling. It argues that two properties—bounded derivatives of the objective and variance-adjusted weight updates (via Adam)—are essential for robustness, shows that C51 exhibits both and is competitive with StreamQ on a 55-game Atari subset, and derives Adaptive Q(λ) (a variance-adjusted eligibility-trace method) that approaches double the human baseline and outperforms prior methods on the same subset.

Significance. If the central claims hold, the work would be significant for demonstrating that simpler online methods can achieve strong Atari performance without replay, for providing an explanatory account of why certain updates succeed in the streaming regime, and for introducing Adaptive Q(λ) as a new high-performing algorithm. The emphasis on optimization properties rather than architectural changes could influence future streaming RL designs.

major comments (3)

[Analysis and derivation sections] The attribution of C51’s success (and the justification for deriving Adaptive Q(λ)) to the two properties is load-bearing but rests on correlational evidence rather than controlled interventions. The manuscript shows that C51 (which has bounded objective derivatives and uses Adam) is competitive while other methods are not, yet does not isolate each property (e.g., by replacing C51’s loss with an unbounded-gradient variant or swapping Adam for SGD inside the same update). Without such ablations, alternative explanations (distributional RL structure, eligibility-trace implementation details) cannot be ruled out. (Analysis section preceding the derivation of Adaptive Q(λ); experimental comparisons in §4.)
[§4] All performance claims (C51 competitiveness with StreamQ, Adaptive Q(λ) approaching 2× human baseline and surpassing existing methods) are reported only on a post-hoc subset of 55 Atari games. No justification for the subset selection, no results on the full 57-game suite, and no statistical significance tests or confidence intervals are mentioned, raising the risk that the subset was chosen to favor the narrative. (Abstract; §4 experimental results and tables.)
[Property identification paragraphs] The manuscript states that the two properties are “essential for robust performance” of established updates, yet provides no direct test that removing either property degrades streaming performance while holding other factors fixed. This weakens both the explanatory claim and the motivation for Adaptive Q(λ). (Paragraphs deriving the properties from Adam–update interactions.)

minor comments (2)

[Abstract] Notation for Adaptive Q(λ) uses inconsistent LaTeX rendering in the abstract; ensure consistent math mode throughout.
[Abstract and §4] The claim of “rigorous and exhaustive experimentation” should be tempered given the 55-game subset; consider adding a sentence clarifying the scope.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their constructive and detailed feedback. We address each major comment point by point below, providing the strongest honest defense of the manuscript while acknowledging where revisions improve clarity or rigor.

read point-by-point responses

Referee: [Analysis and derivation sections] The attribution of C51’s success (and the justification for deriving Adaptive Q(λ)) to the two properties is load-bearing but rests on correlational evidence rather than controlled interventions. The manuscript shows that C51 (which has bounded objective derivatives and uses Adam) is competitive while other methods are not, yet does not isolate each property (e.g., by replacing C51’s loss with an unbounded-gradient variant or swapping Adam for SGD inside the same update). Without such ablations, alternative explanations (distributional RL structure, eligibility-trace implementation details) cannot be ruled out. (Analysis section preceding the derivation of Adaptive Q(λ); experimental comparisons in §4.)

Authors: We agree that the support for the two properties is correlational rather than based on isolated interventions within a fixed algorithm. The manuscript compares established updates (DQN vs. C51) that differ in multiple respects and derives the properties analytically from Adam's interaction with the objectives. This analysis motivates Adaptive Q(λ) but does not claim to have ruled out all alternatives via ablation. We have revised the analysis section to explicitly note the correlational nature of the empirical evidence and to frame the properties as a useful explanatory lens and derivation guide rather than a fully causal isolation. We maintain that the comparative results and theoretical derivation still provide a coherent account for why C51 succeeds in streaming RL. revision: partial
Referee: [§4] All performance claims (C51 competitiveness with StreamQ, Adaptive Q(λ) approaching 2× human baseline and surpassing existing methods) are reported only on a post-hoc subset of 55 Atari games. No justification for the subset selection, no results on the full 57-game suite, and no statistical significance tests or confidence intervals are mentioned, raising the risk that the subset was chosen to favor the narrative. (Abstract; §4 experimental results and tables.)

Authors: The 55-game subset was selected to match the evaluation protocol of Elsayed et al. (2024) and thereby enable direct comparison with StreamQ; this choice was made prior to running our experiments. We have added an explicit justification for the subset in the revised manuscript, along with statistical significance tests and confidence intervals for all reported metrics in §4. We did not run the full 57-game suite because of the high computational cost of streaming RL training; the 55-game subset remains diverse and representative for the purpose of comparing online methods. We disagree that the subset was chosen post-hoc to favor the narrative. revision: yes
Referee: [Property identification paragraphs] The manuscript states that the two properties are “essential for robust performance” of established updates, yet provides no direct test that removing either property degrades streaming performance while holding other factors fixed. This weakens both the explanatory claim and the motivation for Adaptive Q(λ). (Paragraphs deriving the properties from Adam–update interactions.)

Authors: The properties were identified by analyzing the mathematical interaction between common RL objectives and Adam's variance-adjusted updates. While we do not perform direct ablations that hold all other factors fixed (e.g., C51 with SGD or an unbounded-gradient loss), the performance gap between DQN and C51 under identical streaming conditions is consistent with the presence of both properties in C51. We have revised the relevant paragraphs to replace the stronger phrasing “essential” with “important for robust performance” and to clarify that the properties provide analytical motivation for Adaptive Q(λ) rather than a claim of exhaustive causal proof. revision: partial

Circularity Check

0 steps flagged

No circularity: derivation applies observed properties to construct new algorithm without reduction to inputs or self-citation chains

full rationale

The paper analyzes how Adam interacts with standard RL updates (DQN, C51) in the streaming no-replay regime, identifies two properties (bounded objective derivative and variance-adjusted updates) as correlated with robust performance, verifies C51 exhibits both and matches StreamQ on 55 Atari games, then constructs Adaptive Q(λ) by incorporating variance-adjusted updates into an eligibility-trace framework. This construction follows directly from the stated properties rather than fitting parameters to target performance numbers or renaming prior results. All comparisons use independently published baselines (StreamQ, human scores) with no load-bearing self-citations or uniqueness theorems invoked. No equations reduce by construction to the inputs, and the central claim remains independent of the new algorithm's measured outcomes.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The central claim rests on the assumption that bounded gradients and variance adjustment are the key missing ingredients for streaming stability; no new entities or free parameters are introduced in the abstract.

axioms (2)

domain assumption The derivative of the RL objective must be bounded for stable Adam updates in streaming settings.
Invoked to explain why C51 succeeds and to motivate Adaptive Q(λ).
domain assumption Weight updates must be variance-adjusted for robust online performance.
Second essential property identified from analysis of Adam with DQN/C51 updates.

pith-pipeline@v0.9.0 · 5538 in / 1351 out tokens · 23800 ms · 2026-05-11T01:05:57.061842+00:00 · methodology

discussion (0)

Reference graph

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