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REVIEW 3 major objections 7 minor 1 cited by

Advancing CMA-ES with Learning-Based Cooperative Coevolution for Scalable Optimization

T0 review · 3 major / 7 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read A PPO-trained policy can pick the right variable decomposition for CMA-ES.

desk verdict A genuinely new RL-based decomposition scheduler for CC-CMAES with real zero-shot transfer results, but the headline optimization-quality claim is budget-dependent and needs stronger large-budget evidence and code before I'd fully trust it. read the letter →

arxiv 2504.17578 v1 pith:FUY4762B submitted 2025-04-24 cs.LG cs.NE

Hongshu Guo , Wenjie Qiu , Zeyuan Ma , Xinglin Zhang , Jun Zhang , Yue-Jiao Gong This is my paper · ORCID
classification cs.LGcs.NE
keywords cooperativecoevolutionCMA-ESlarge-scaleglobaloptimizationreinforcementlearningdecompositionstrategyselectionmeta-black-boxtransferabilityPPO
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

The paper sets out to show that the most expertise-heavy step in cooperative coevolution for large-scale optimization—deciding how to split variables into subgroups—can be automated by learning. It trains a Proximal Policy Optimization agent to choose, at every epoch, among three existing decomposition strategies (random, min-variance, and max-variance splitting) for CMA-ES, using a 58-dimensional state built from statistics of the covariance, subgroup populations, and action history. On the CEC 2013 LSGO benchmark the resulting LCC-CMAES significantly beats the expert-designed CC-CMAES in 11 of 15 problems, uses no extra function evaluations for decomposition, and keeps an edge on overlapping and non-separable problems. The authors also report zero-shot transfer to the BNS suite and to Mujoco neuroevolution tasks. If these results hold, cooperative coevolution becomes usable without expert decomposition knowledge and with a smaller evaluation budget.

What carries the argument

The load-bearing object is the learned policy $\pi_\theta$: a three-layer MLP with structure $58 \times 64 \times 64 \times 3$ that maps the decision vector $\mathrm{DV} = s^{GO} \oplus s^{SD} \oplus s^{AH} \in \mathbb{R}^{58}$ to a softmax distribution over the three decomposition strategies. MiVD, RD, and MaVD are covariance-based partitions of the variables into $m=10$ subgroups, ranging from low-diversity (exploitative) to high-diversity (exploratory) grouping; after each subgroup run, the subgroup covariance and mean are merged back into the global CMA-ES distribution. The reward $r_t = (f^*_{t-1} - f^*_t)/(f^*_0 - f^*)$ normalizes per-step fitness improvement and is the training signal for PPO. This mechanism is what lets the framework drop both the expert selection table of CC-CMAES and the extra function-evaluation cost of interaction-detection decomposition methods.

What would settle it

Evaluate the trained LCC-CMAES policy on a suite built from entirely new base functions with known, time-varying interaction graphs; if a fixed strategy such as always-MiVD or a cheap random switch matches its final fitness, then the state features are not capturing the scheduling-relevant information.

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Extended reading notes

Core claim

On the paper's own terms, the discovery is that a learned strategy scheduler can replace the expert-designed selection rule inside CC-CMAES and improve both final fitness and resource use. The policy observes global optimization statistics (12 features), per-subgroup statistics (40 features), and action-history statistics (6 features), and outputs a probability distribution over MiVD, RD, and MaVD; PPO trains it with a reward equal to the normalized best-fitness decrease per step. The evidence is a 25-run comparison on CEC 2013 LSGO in which LCC-CMAES outperforms CC-CMAES on 11 of 15 problems, outperforms most non-CC large-scale optimizers, and wins clearly on the overlapping functions F12-F14 and the fully non-separable F15. Additional experiments show the zero-shot policy retains advantages on the BNS benchmark and on four Mujoco neuroevolution tasks at dimensions up to 2312.

Load-bearing premise

The 58 hand-picked statistics of the current search state carry enough information to decide which of the three decompositions is best at every step, even on problems whose variable interactions were never seen in training.

Editorial extensions

If this is right

  • Cooperative coevolution loses its main knowledge barrier: the same trained policy can decide decomposition on a new large-scale problem without an expert tuning the grouping rule.
  • Because LCC-CMAES spends no function evaluations on detecting variable interactions, its whole budget goes to optimization, giving it a concrete resource advantage over CSG, ERDG, MDG, and FII.
  • The scheduling policy transfers zero-shot: trained on a subset of CEC 2013 LSGO, it still improves over CC-CMAES on the BNS suite and on Mujoco tasks with up to 2312 dimensions.
  • Dynamic scheduling is most valuable exactly where static CC methods fail—overlapping and fully non-separable problems—so the approach targets the hardest cases rather than only separable ones.
  • The agent's choices are informed by recent strategy effectiveness through the action-history features, meaning the same policy can behave exploitatively at one stage and exploratively at another within a single run.

Reading between the lines

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

  • A direct extension is to enlarge the action set beyond the three covariance-based splits, for example the number of subgroups or the offspring size; the MDP formalism in the paper would carry over unchanged.
  • Part of the reported transfer may come from shared base functions: the paper's training subset contains Elliptic and Rastrigin variants, so hold-out tests built from entirely new base-function families would separate landscape familiarity from learned grouping ability.
  • The current reward charges no cost for switching strategies or for time; if the strategy pool ever includes decomposition methods that consume function evaluations, the reward would need a budget term, which is a modification the paper does not address.
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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 / 7 minor

Summary. The paper proposes LCC-CMAES, a cooperative coevolution (CC) framework in which a PPO-trained neural network selects, at each epoch, one of three CMA-ES decomposition strategies (MiVD, RD, MaVD) based on 58 hand-crafted features comprising global optimization statistics, per-subgroup statistics, and action history. The policy is trained on a subset of the CEC 2013 LSGO benchmark with a budget of 2E5 function evaluations and evaluated on the remaining CEC 2013 functions, the BNS suite, and four Mujoco neuroevolution tasks, with additional ablations on state features and reward designs. The central claims are that LCC-CMAES improves optimization effectiveness and resource consumption relative to CC and non-CC baselines and that the learned strategy selector transfers to unseen problems without additional decomposition FEs.

Significance. The core idea—replacing expert-designed decomposition selection with a learned, dynamic strategy scheduler—is timely and potentially useful for low-budget, high-dimensional regimes. Strengths include 25-run comparisons with Wilcoxon tests, a dedicated ablation of state features and reward formulations, and zero-shot transfer experiments to BNS and Mujoco tasks; these make the main positive results concrete. The paper is also honest about the extended-budget behavior in Figure 4, which is important because that evidence substantially qualifies the headline 'excels in optimization results' claim. If the authors quantify the 3E6-FE comparison, address the privileged f* in the reward, and soften the transferability claims to match the reported tables, the contribution would be a solid addition to the MetaBBO and CC literature.

major comments (3)
  1. [§5.2.2, Fig. 4, Tables 2, 4, and 5] The headline claim that LCC-CMAES "excels ... in optimization results" is supported only at 2E5 FEs, which is 15x smaller than the standard 3E6 budget for CEC 2013 LSGO. In §5.2.2 the authors state that at 3E6 FEs the advantage "gradually diminishes and may even be surpassed" and that non-CC algorithms show "more prominent optimization performance" on most problems, but no final means, standard deviations, or Wilcoxon statistics are given for the 3E6 budget. Because the conclusion is unqualified and the low budget is motivated by resource consumption rather than by the optimization-quality claim, the authors should report full significance-tested comparisons at 3E6 and either show the advantage persists or explicitly restrict the claim to limited-budget settings.
  2. [§4.2.3, Eq. (4)] The reward in Eq. (4) divides by f*0 - f*, where f* is the true optimal fitness. This quantity is unknown in real-world applications and in the BNS/Mujoco transfer experiments, and the paper does not state that f* is used only in training or analyze what happens when f* is inaccurate. Since the learned policy is trained exclusively against this reward, the dependence on a privileged benchmark quantity should be acknowledged and the robustness of the policy to mis-specified f* should be tested, for instance by training with a biased estimate of f* and re-running the transfer evaluations.
  3. [§5.3, Table 4, and Conclusion] The transferability conclusion is stronger than the evidence in Table 4: on the BNS suite, LCC-CMAES is significantly worse than CMA-ES, Sep-CMAES, LM-MA-ES, and LM-CMA on several problems (e.g., problems 1, 9, and 12), and the summary row shows LCC-CMAES winning only five of ten pairwise comparisons against each of several non-CC baselines. The conclusion that LCC-CMAES holds "a distinct advantage" on BNS is therefore not supported; the authors should report the loss counts as prominently as the wins and phrase the transferability claim in terms of "competitive transfer" or "advantages on CC-type baselines" rather than blanket superiority.
minor comments (7)
  1. [§5.2.1] There is a typo in the bullet list: "LCC-CAMES" should be "LCC-CMAES".
  2. [Table 2] The entries for problems 3 and 6 contain stray "+" and "\" symbols that make the table hard to read; these formatting artifacts should be removed.
  3. [§5.4] The sentence "we zero-shot the pre-trained LCC-CMAES agent in Section 5.2" should refer to the training setup in Section 5.1.2, since Section 5.2 is the main comparison rather than the training description.
  4. [§5.3] The BNS experiment omits MetaES and L-BFGS from Table 4 without explanation, although both are listed as comparison algorithms in Section 5.1.1; a sentence explaining the omission would be helpful.
  5. [§5.5.2] The formula for reward1 should include parentheses to be mathematically unambiguous: r_t = (f*0 - f*t) / f*0.
  6. [Table 1] The state features require the full global covariance matrix C_t at each step, which costs O(D^2) memory and computation; since the paper targets scalable optimization, a brief comment on the practical dimension limit and the cost of computing Corrcoef(C_t) for D > 10^4 would be useful.
  7. [§5.1.2] The sentence "F13 and F14 in CEC2013LSGO is 905" should read "are 905" for grammatical agreement.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the transfer results are genuine zero-shot evaluations, not fitted predictions.

full rationale

The paper's central claim is that a PPO-trained policy can select among the existing MiVD/RD/MaVD decomposition strategies of CC-CMAES and thereby improve optimization performance and transfer to unseen problems. The derivation chain is empirical rather than analytical, and I could not find a step where a claimed output is equivalent to an input by construction. The policy is trained on the asterisk-marked subset of CEC 2013 LSGO, and the headline transfer claims rest on held-out CEC problems, the BNS suite, and Mujoco neuroevolution tasks in Table 4 and Table 5; none of these held-out results are back-fitted into the policy, so they are real predictions rather than renamed training data. The reward in Eq. (4) uses the known optimum f* as a normalizer, which is a benchmark-privileged training signal, but f* is not part of the inference-time state in Table 1 and the zero-shot transfer results do not require f* at decision time; this is an evaluation-design caveat rather than a circular reduction. The use of MiVD/RD/MaVD and the handcrafted state features is an ansatz inherited from CC-CMAES [33], not an output claimed to be derived, so the ansatz-smuggling pattern does not apply. Self-citations to prior MetaBBO work are contextual and are not load-bearing for the reported comparisons; no uniqueness theorem is invoked. Finally, the large-budget results in Figure 4 openly report that the advantage diminishes and can be surpassed, so the paper does not hide a forced conclusion. For these reasons, the appropriate circularity score is 0.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

The method's contribution is the trained policy and its feature/action design. The free parameters are the network weights and the hand-chosen hyperparameters. The axioms are the representational sufficiency of the state, the representativeness of the training problems, the adequacy of the three-strategy pool, and the availability of f* in the reward. No new entities are postulated.

free parameters (5)
  • PPO policy network parameters theta = not disclosed (trained network weights)
    The actor network mapping 58 state features to a distribution over the three decomposition strategies is fitted via PPO on the training subset of CEC 2013 LSGO. This is the central learned object of the paper.
  • number of subgroups m = 10
    Chosen by hand in Sec 5.1.2; affects state dimension (4*m) and the granularity of decomposition.
  • subgroup max FEs (SubMaxFEs) = 1E3
    Hand-set budget per subgroup optimization in Sec 5.1.2; a key hyperparameter for the CC loop.
  • action selection count ns = 20
    Number of MDP decisions in a run (Sec 5.1.2); determines total FEs = 2E5.
  • reward normalization using f* = true optimum of each problem
    Eq. 4 uses f* in the denominator; this is privileged information available on benchmarks but not in real-world problems.
assumptions (5)
  • ad hoc to paper The 58 hand-crafted state features (Table 1) contain sufficient information to select the optimal decomposition strategy at each step.
    Core representational assumption of the MDP (Sec 4.2.1). No proof or analysis of feature sufficiency is provided; the ablation study shows removing whole feature groups hurts performance.
  • domain assumption The training problem subset (F1/F4/F5/F8/F9/F12/F13 of CEC 2013 LSGO) is representative of unseen problems from the same suite, BNS, and neuroevolution tasks.
    Sec 5.1.2 partitions the benchmark; transfer claims rest on this representativeness.
  • domain assumption The strategy pool {MiVD, RD, MaVD} is sufficient for effective decomposition of all tested problems.
    Taken from CC-CMAES [33]; the agent can only choose among these three, so any problem requiring a different decomposition is outside the method's reach.
  • domain assumption CMA-ES is a suitable base optimizer when applied to the resulting subgroups.
    The whole framework is instantiated on CMA-ES; results may not generalize to other EAs.
  • domain assumption Reward computed with the known global optimum f* is an appropriate training signal and matches the deployment objective.
    Eq. 4 uses f*; this is a benchmark-specific assumption that does not hold for real black-box problems.

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Cite this review

Pith. "Pith review of Advancing CMA-ES with Learning-Based Cooperative Coevolution for Scalable Optimization." pith.science (2026). https://pith.science/paper/FUY4762B

@misc{pith2026250417578,
  author       = {Pith},
  title        = {Pith review of: Advancing CMA-ES with Learning-Based Cooperative Coevolution for Scalable Optimization},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/FUY4762B}},
  note         = {Machine review of arXiv:2504.17578}
}
read the original abstract

Recent research in Cooperative Coevolution~(CC) have achieved promising progress in solving large-scale global optimization problems. However, existing CC paradigms have a primary limitation in that they require deep expertise for selecting or designing effective variable decomposition strategies. Inspired by advancements in Meta-Black-Box Optimization, this paper introduces LCC, a pioneering learning-based cooperative coevolution framework that dynamically schedules decomposition strategies during optimization processes. The decomposition strategy selector is parameterized through a neural network, which processes a meticulously crafted set of optimization status features to determine the optimal strategy for each optimization step. The network is trained via the Proximal Policy Optimization method in a reinforcement learning manner across a collection of representative problems, aiming to maximize the expected optimization performance. Extensive experimental results demonstrate that LCC not only offers certain advantages over state-of-the-art baselines in terms of optimization effectiveness and resource consumption, but it also exhibits promising transferability towards unseen problems.

Figures

Figures reproduced from arXiv: 2504.17578 by the authors.

Figure 1
Figure 1. The core idea of LCC-CMAES. researchers initially tried random decomposition and some decomposition strategies utilizing statis￾tical data but did not obtain satisfactory results [53, 74]. Later, they attempted to dynamically select strategies by calculating the probability of each using a table of historical statistical information, designed by expert-level knowledge, which yielded some positive effects (e.g., CC-C… view at source ↗
Figure 2
Figure 2. The overall structure of LCC. 3.2 Markov Decision Process A Markov Decision Process (MDP) is commonly characterized as M :=< S, A, T, 𝑅 >. At each time step 𝑡, given the current environment state 𝑠𝑡 ∈ S, an action 𝑎𝑡 ∈ A is performed according to a policy Π : S → A. Then the environment reaches at the next state 𝑠𝑡+1 according to the transition dynamics T (𝑠𝑡+1 | 𝑠𝑡 , 𝑎𝑡). The reward function 𝑅 : S × A → R indicates… view at source ↗
Figure 3
Figure 3. The Neural Network workflow for 𝜋𝜃 (Actor) and 𝑣𝜙 (Critic). 4.2.2 Action. We designed a strategy pool Λ in advance, containing various decomposition strate￾gies for selection. LCC selects a CC decomposition strategy from Λ based on the state to achieve dynamic decomposition. For the purpose of balancing exploration and exploitation, LCC-CMAES utilize three types of decomposition strategies [33]: MiVD, RD, and MaVD a… view at source ↗
Figures from the paper (2 more)
Figure 4
Figure 4. Figure 4: Comparison with a 3E6 budget in CEC2013LSGO. [PITH_FULL_IMAGE:figures/full_fig_p010_4.png]
Figure 5
Figure 5. Figure 5: The ablation study on state features and reward designs. [PITH_FULL_IMAGE:figures/full_fig_p013_5.png]

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Pith tools

Reviewed August 16, 2026 · model on record in the stance chip above.