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REVIEW 3 major objections 6 minor 14 references

A Study of Value-Aware Eigenoptions

T0 review · 3 major / 6 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read Pre-specified eigenoptions speed up reinforcement learning through credit assignment, not just exploration, while online discovery can bias the agent's experience and hinder learning.

desk verdict A careful tabular study showing pre-specified eigenoptions can help credit assignment, but the 'strictly due to credit' claim in Fig. 2 is stronger than the evidence supports. read the letter →

arxiv 2507.09127 v1 pith:GO7NCJII submitted 2025-07-12 cs.LG stat.ML

Harshil Kotamreddy , Marlos C. Machado This is my paper · ORCID
classification cs.LGstat.ML
keywords eigenoptionscreditassignmentreinforcementlearningsuccessorrepresentationoptionsexplorationhierarchicalintra-optionQ-learning
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

This paper asks whether eigenoptions—options built from the eigenvectors of the successor representation, a matrix that tracks how information diffuses through an environment—can help a model-free reinforcement learning agent assign credit to the right decisions, not just explore. In tabular gridworld experiments, the authors report that when eigenoptions are pre-computed and the agent also learns their option-values, the agent reaches the goal faster than when the same options are used only for exploration. A second experimental phase, in which options are never executed during training yet their values are updated from primitive-action transitions, isolates a credit-assignment effect: the eigenoptions still speed up later time-to-goal evaluation. When options are instead discovered online while being used for credit assignment, the authors find the added influence can bias the agent's experience and slow learning in a subset of runs, and in deep pixel-based settings gains are smaller and termination conditions become the key fragility.

What carries the argument

The load-bearing object is the eigenoption: an option whose policy maximizes an intrinsic reward defined by an eigenvector of the successor representation, $\Psi^{\pi} = (I - \gamma P^{\pi})^{-1}$, which encodes expected discounted visitation between states. The mechanism that carries the credit-assignment argument is intra-option Q-learning: at each primitive transition $(s,a,r,s')$, the agent updates the value of every option that would have taken action $a$ in state $s$, using the update $Q(s,o) \leftarrow Q(s,o) + \alpha [r + \gamma U(s',o) - Q(s,o)]$ with $U(s,o) = (1-\beta_o(s))Q(s,o) + \beta_o(s)\max_{o'} Q(s,o')$. Because these updates do not require the option to be executed, they allow the evaluation-phase experiment that separates credit assignment from exploration. In the deep setting, the machinery is a hierarchical DQN with one network per option-value function plus a termination rule; the paper finds the termination rule is fragile under function approximation and uses a fixed ten-step horizon.

What would settle it

Run the Figure 2 protocol but replace eigenoption values with zero or random values before each training episode while keeping the same primitive-action updates; if time-to-goal still improves in the evaluation phase, the improvement is not caused by credit assignment to eigenoptions.

Watch

Extended reading notes

Core claim

On its own terms, the paper's central claim is that pre-specified eigenoptions have a dual role: beyond their known exploration benefit, they accelerate credit assignment in model-free reinforcement learning. The evidence is that value-aware eigenoptions learn faster than eigenoptions used solely for exploration and faster than bottleneck options in most four-rooms and nine-rooms configurations, and that a protocol restricting training to primitive actions while still updating option-values via intra-option Q-learning produces a time-to-goal improvement attributed to credit assignment. The paper also claims that when eigenoptions are discovered online and their values are learned, inaccurate early option-values can be selected too often, distorting state visitation and sometimes delaying goal discovery; the median run still improves. For deep reinforcement learning, the paper claims that option-values can be learned with non-linear function approximation through a hierarchical DQN with separate option-value networks, but the gains over exploration-only eigenoptions are modest, and termination conditions that fail to stop an option in bad states cause loops and walls.

Load-bearing premise

The credit-assignment conclusion rests on the assumption that updating an option's value from primitive-action transitions, without ever executing the option, yields accurate enough estimates that the observed time-to-goal improvement is genuinely due to credit assignment rather than to lucky initialization or to updates from actions the option never took.

Editorial extensions

If this is right

  • Pre-computed eigenoptions should be included in the action space and have their option-values learned, not merely used to guide exploration, in tabular model-free reinforcement learning.
  • The evaluation-phase protocol—updating option-values while only executing primitive actions—gives a way to measure credit-assignment contributions separately from exploration contributions in tabular settings.
  • When options are discovered online, treating them as ordinary actions can be harmful because a single overvalued option can dominate the policy for many steps; exploration and credit assignment must be balanced.
  • In pixel-based settings, the credit-assignment gain is smaller than in tables, and termination conditions are the main source of failure; improving them may be necessary before deep gains appear.
  • Eigenoptions operating at multiple diffusion timescales can be competitive with bottleneck options for credit assignment even though, in these domains, any solution must pass through a bottleneck state.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • The evaluation-phase protocol could be applied to other option-discovery methods, not just eigenoptions; if the credit-assignment effect is a property of temporally extended actions generally, then any option set whose policies respect environment geometry should show a similar time-to-goal improvement.
  • If eigenoptions encode information diffusion at multiple timescales, their value estimates may act as a temporal-resolution curriculum; in larger or sparser environments than the nine-rooms gridworld, the credit-assignment advantage could be larger than observed here.
  • The online-discovery failure mode suggests a design principle: options added to the action space during learning should have conservative or bounded influence—through interruption mechanisms, optimistic initialization, or option-specific exploration schedules—until their values are trustworthy.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. This paper studies whether eigenoptions, options derived from the successor representation, can accelerate credit assignment in model-free RL, not just exploration. In tabular gridworlds, the authors introduce V AEO, which learns option-values for precomputed eigenoptions via intra-option Q-learning, and report that it outperforms both Q-learning with eigenoptions used only for exploration and intra-option Q-learning with bottleneck options (Fig. 1). A second protocol (Fig. 2) trains with primitive actions only while applying intra-option updates, then evaluates with options added to the action space; the authors interpret the resulting improvement as 'strictly due to credit being assigned to the eigenoptions.' The paper then introduces V ACE for online option discovery and DV AEO for deep RL, reporting that online discovery can bias experience too strongly and that deep results show only modest gains. The conclusion emphasizes challenges with termination conditions and the interaction between exploration and credit assignment.

Significance. If the Fig. 2 attribution were established, this would be a notable result: eigenoptions, originally designed for exploration, would have a demonstrated dual role in credit assignment. The tabular experiments are carefully run, with 100 independent runs, 99% confidence intervals, and hyperparameter sweeps documented in Appendix C, and the Fig. 2 protocol is a thoughtful attempt to separate exploration from value learning. The paper also gives credit where due by candidly discussing failure modes of online discovery and deep function approximation. However, the load-bearing attribution issue in Section 3.2 and the statistically weak deep results mean the paper currently supports a more modest claim than the abstract states: pre-specified eigenoptions show promise for credit assignment in tabular settings, with important caveats about protocol and approximation.

major comments (3)
  1. [Section 3.2, Eq. (3), Fig. 2] The statement that the Fig. 2 result is 'strictly due to credit being assigned to the eigenoptions' is not supported. Because options are never executed during training, Q(s,o) is updated only in states where the selected primitive action coincides with pi_o(s), and Q(s,o) remains at its initial value in all other states. The bootstrap target in Eq. (3) includes a max over options, so stale initial values can propagate through learning. At evaluation, greedy selection over the augmented action space can therefore choose an option in a state where its value was never learned, and the option's pre-specified temporally extended policy may itself reduce time-to-goal even if no credit was assigned to that option. The paper provides no bias or convergence analysis for this training/evaluation asymmetry and no control condition in which options are added to the action space with unlearned or randomly initialized option-values. I recommend adding such a control or rephrasing the claim to 'consistent with credit assignment' before the central claim is accepted.
  2. [Section 5.1, Fig. 4, Appendix C] The deep RL experiments do not support the general claim that value-aware eigenoptions help under function approximation. In the four rooms domain the curves overlap, and in the nine rooms domain the advantage is described as 'slightly better' with overlapping 99% confidence intervals and no significance tests. Moreover, Appendix C states that the number of eigenoptions was not swept in the deep setting, so the comparison is not as well-controlled as the tabular experiments. Please either add statistical comparisons or explicitly restrict the abstract and conclusion claims to the tabular setting and describe the deep results as preliminary.
  3. [Section 5.2, Appendix C] The conclusion of Section 5.2 attributes the lack of improvement to 'suboptimal termination conditions,' and the fixed termination horizon T=10 is a key free parameter in that argument. The text says this value came from a hyperparameter sweep, but Appendix C does not report the sweep range, the values considered, or the selection criterion for T. Given that the negative result in these experiments is explained by termination, this undocumented choice is load-bearing. Please document the sweep or soften the attribution to termination conditions.
minor comments (6)
  1. [Eq. (7)] In the definition of U(s', o; ...), the termination probability is written as beta_o(s) rather than beta_o(s'); since the target is evaluated at the next state, the termination function should be evaluated at s'.
  2. [Appendix B] The word 'hierachical' in the caption of Fig. 7 should be 'hierarchical.'
  3. [Section 3.2 and Fig. 2] The paper never states how episodes in which the goal is not reached are treated when computing time-to-goal; please specify whether such episodes are truncated at the episode length.
  4. [Appendix A, Figs. 5 and 6] The V ACE comparison relies on mean curves plus a median curve, but no paired or significance test is reported; given the paper's own observation that V ACE has a few very bad runs, a per-seed comparison or a rank-based test would strengthen the 'median outperformance' claim.
  5. [Conclusion] The conclusion is appropriately cautious, but the abstract's wording 'pre-specified eigenoptions aid not only exploration but also credit assignment' is stronger than the evidence presented; consider aligning the abstract with the conclusion's 'potential for credit assignment' framing.
  6. [General] No code availability statement is provided; including one would help reproducibility, especially for the deep experiments.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the paper's central claims are empirical comparisons against external baselines, not derivations that reduce to their inputs.

full rationale

This paper is an empirical study, not a derivation. The central claims compare value-aware eigenoptions against external baselines such as Q-learning, bottleneck options, covering eigenoptions, and DDQN. Eigenoptions are precomputed from the successor representation of the environment, independent of the task reward, and the reported learning curves are measured outcomes rather than quantities fitted by construction. The Section 3.2 evaluation protocol, in which options are never executed during training and intra-option updates are made from primitive-action experience, is an experimental attribution design; the paper does not derive the observed time-to-goal improvement from the fitted option-values by equation, so it is not a fitted-input-called-prediction circularity. Hyperparameter sweeps over the number of eigenoptions and termination length reduce external validity but do not make the conclusions definitionally equivalent to the inputs. Self-citations to prior eigenoption work support background premises (e.g., eigenoptions aid exploration) but are not load-bearing for the new credit-assignment claim, which is evaluated against non-self baselines. No circular step can be exhibited from the paper's own equations or citations.

Assumptions & free parameters 3 free parameters · 4 assumptions · 0 invented entities

The central claim rests on standard RL theory (Q-learning, SR, intra-option updates) and on several choices: the number of eigenoptions, the online discovery interval, and the deep termination horizon were tuned on the evaluation environments. The eigenoption premise itself comes from prior work by the same group. No new conceptual entities are introduced.

free parameters (3)
  • Number of eigenoptions Noptions = 6 in four rooms, 24 in nine rooms
    Selected via sweep over {2,4,6,8,16,24,32} in both tabular domains (App. C) and reused in deep experiments; the reported benefits depend on this choice.
  • Option discovery interval Nsteps (V ACE) = 1000 timesteps
    Swept over {100,500,1000,10000} in both domains (App. C); results are reported only for 1000.
  • Deep termination horizon T = 10 steps
    Chosen by hyperparameter sweep over both environments (Sec. 5.2); the deep negative results are conditioned on this termination rule.
assumptions (4)
  • domain assumption The top eigenvectors of the successor representation, Ψ=(I-γP)^-1, define useful options (eigenoptions) for exploration and, here, for credit assignment.
    Borrowed from Machado et al. (2017, 2023); the paper does not justify it beyond citing prior work (Sec. 2.3).
  • domain assumption Intra-option Q-learning (Eq. 3) converges to the correct option-values in the tabular setting, and its function-approximation version (Eq. 7) is a valid learning rule in deep RL.
    Relied on throughout Secs. 3 and 5 without new proof; standard in the options literature.
  • domain assumption A random exploration policy provides sufficient coverage to learn the SR, its eigenvectors, and the eigenoption policies used as pre-specified options.
    The option policies are trained from random starts (Sec. 3.1); the paper does not measure coverage.
  • ad hoc to paper Fixed-horizon termination (10 steps) is an adequate substitute for the option's true termination function in the deep experiments.
    Introduced in Sec. 5.2 after constant-beta termination performed poorly; the analysis of termination brittleness is conditioned on this choice.

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Cite this review

Pith. "Pith review of A Study of Value-Aware Eigenoptions." pith.science (2026). https://pith.science/paper/GO7NCJII

@misc{pith2026250709127,
  author       = {Pith},
  title        = {Pith review of: A Study of Value-Aware Eigenoptions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/GO7NCJII}},
  note         = {Machine review of arXiv:2507.09127}
}
read the original abstract

Options, which impose an inductive bias toward temporal and hierarchical structure, offer a powerful framework for reinforcement learning (RL). While effective in sequential decision-making, they are often handcrafted rather than learned. Among approaches for discovering options, eigenoptions have shown strong performance in exploration, but their role in credit assignment remains underexplored. In this paper, we investigate whether eigenoptions can accelerate credit assignment in model-free RL, evaluating them in tabular and pixel-based gridworlds. We find that pre-specified eigenoptions aid not only exploration but also credit assignment, whereas online discovery can bias the agent's experience too strongly and hinder learning. In the context of deep RL, we also propose a method for learning option-values under non-linear function approximation, highlighting the impact of termination conditions on performance. Our findings reveal both the promise and complexity of using eigenoptions, and options more broadly, to simultaneously support credit assignment and exploration in reinforcement learning.

Figures

Figures reproduced from arXiv: 2507.09127 by the authors.

Figure 1
Figure 1. Performance of value-aware eigenoptions (VAEO) compared to baselines. VAEO out [PITH_FULL_IMAGE:figures/full_fig_p004_1.png] view at source ↗
Figure 2
Figure 2. Credit assignment through an evaluation phase. We evaluate both algorithms for 100 seeds [PITH_FULL_IMAGE:figures/full_fig_p005_2.png] view at source ↗
Figure 3
Figure 3. Value propagation in a) a typical run of CEO, b) a typical run of VACE and c) a bad run of [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Performance of DVAEO and baselines with pixel observations. Environment configura [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Performance of VACE and baselines when discovering options online every 1000 time [PITH_FULL_IMAGE:figures/full_fig_p014_5.png]
Figure 6
Figure 6. Figure 6: Median over 100 independent runs for VACE and baselines in the nine rooms environment. [PITH_FULL_IMAGE:figures/full_fig_p014_6.png]
Figure 7
Figure 7. Figure 7: Hierarchical DQN architecture. We include a separate network to predict the value of each [PITH_FULL_IMAGE:figures/full_fig_p015_7.png]
Figure 8
Figure 8. Figure 8: Performance of DVAEO (with approximated option policies) and baselines with pixel [PITH_FULL_IMAGE:figures/full_fig_p015_8.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

14 extracted references · 9 canonical work pages

  1. [1]

    For the algorithms in Figure 1, we use ϵ = 0 .05, γ, γo = 0 .99, and α, αo = 0 .1 where γo and αo correspond to the discount factor and step size in the intra-option updates. We conducted a hyperparameter sweep on the number of eigenoptions in each environment, leading to the choice of six eigenoptions in the four rooms domain and 24 eigenoptions in the n...

    work page 2025

  2. [3]

    For all algorithms, we use γ = 0.9, an update interval of 1 step, a target update interval of 2000 steps, a replay buffer of size 20,000, and the Adam optimizer (Kingma & Ba,

    work page 2000

  3. [6]

    The Eigenoption-Critic Framework

    Miao Liu, Marlos C. Machado, Gerald Tesauro, and Murray Campbell. The eigenoption-critic framework. CoRR, abs/1712.04065,

    work page Pith review arXiv

  4. [8]

    Hon Tik Tse, Siddarth Chandrasekar, and Marlos C. Machado. Reward-aware proto-representations in reinforcement learning. CoRR, abs/2505.16217,

    arXiv

  5. [10]

    Append option to Ω, append column of zeros to Q. Inductive Biases in Reinforcement Learning Workshop at RLC 2025 Algorithm 2 Update Option Values Input: o ▷ Option Do ▷ Sequence of samples collected while taking the option snext ▷ State the agent is in after taking option o return ← 0 for (s, a, r, s′) in reverse(Do) do return ← r + γ · return Q(s, o) ← Q...

    work page 2025

  6. [11]

    The original Minigrid environment included actions to rotate the agent and move the agent

    using Gym (Brockman et al., 2016). The original Minigrid environment included actions to rotate the agent and move the agent. We use a simplified action set where the agent can move up, down, right and left. For clarity, we outline the differences among algorithms introduced in each section in Table

    work page 2016

  7. [1000]

    To learn eigenoption policies, we store all samples in a dataset and sweep over the dataset Nsweeps = 100 times using Q-learning with γ = 0.9 and α = 0.1

    We ran a hyperparameter sweep over Nsteps = {100, 500, 1000, 10000} in both the four rooms and nine rooms domains. To learn eigenoption policies, we store all samples in a dataset and sweep over the dataset Nsweeps = 100 times using Q-learning with γ = 0.9 and α = 0.1. For the algorithms in Figures 4 and 8, we use modified implementations from PFRL (Fujit...

    work page 2021

  8. [2016]

    Minigrid & Miniworld: Modular & customizable reinforcement learning environments for goal-oriented tasks

    Maxime Chevalier-Boisvert, Bolun Dai, Mark Towers, Rodrigo de Lazcano, Lucas Willems, Salem Lahlou, Suman Pal, Pablo Samuel Castro, and Jordan Terry. Minigrid & Miniworld: Modular & customizable reinforcement learning environments for goal-oriented tasks. CoRR, abs/2306.13831,

    arXiv

Show all 14 references
  1. [2017]

    Czarnecki, Michaël Mathieu, Andrew Dudzik, Juny- oung Chung, David H

    Inductive Biases in Reinforcement Learning Workshop at RLC 2025 Oriol Vinyals, Igor Babuschkin, Wojciech M. Czarnecki, Michaël Mathieu, Andrew Dudzik, Juny- oung Chung, David H. Choi, Richard Powell, Timo Ewalds, Petko Georgiev, Junhyuk Oh, Dan Horgan, Manuel Kroiss, Ivo Danih...

    2025

  2. [2019]

    OpenAI Gym

    Greg Brockman, Vicki Cheung, Ludwig Pettersson, Jonas Schneider, John Schulman, Jie Tang, and Wojciech Zaremba. OpenAI Gym. CoRR, abs/1606.01540,

    arXiv

  3. [2020]

    Christopher Berner, Greg Brockman, Brooke Chan, Vicki Cheung, Przemysław D˛ ebiak, Christy Dennison, David Farhi, Quirin Fischer, Shariq Hashme, Chris Hesse, Rafal Józefowicz, Scott Gray, Catherine Olsson, Jakub Pachocki, Michael Petrov, Henrique P. d. O. Pinto, Jonathan Raima...

    1912 arXiv

  4. [2023]

    Martin Klissarov, Akhil Bagaria, Ziyan Luo, George Dimitri Konidaris, Doina Precup, and Mar- los C. Machado. Discovering temporal structure: An overview of hierarchical reinforcement learning. CoRR, abs/2506.14045,

    arXiv

  5. [2024]

    When waiting is not an option: Learning options with a deliberation cost

    Inductive Biases in Reinforcement Learning Workshop at RLC 2025 Jean Harb, Pierre-Luc Bacon, Martin Klissarov, and Doina Precup. When waiting is not an option: Learning options with a deliberation cost. In AAAI Conference on Artificial Intelligence,

    2025

  6. [2025]

    Machado and Michael Bowling

    Marlos C. Machado and Michael Bowling. Learning purposeful behaviour in the absence of rewards. CoRR, abs/1605.07700,

    arXiv

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Reviewed August 6, 2026 · model on record in the stance chip above.