Retaining Suboptimal Actions to Follow Shifting Optima in Multi-Agent Reinforcement Learning

Seungyul Han; Sunwoo Lee; Yonghyeon Jo

arxiv: 2602.17062 · v2 · pith:KJNQDEF3new · submitted 2026-02-19 · 💻 cs.AI

Retaining Suboptimal Actions to Follow Shifting Optima in Multi-Agent Reinforcement Learning

Yonghyeon Jo , Sunwoo Lee , Seungyul Han This is my paper

Pith reviewed 2026-05-21 11:50 UTC · model grok-4.3

classification 💻 cs.AI

keywords multi-agent reinforcement learningvalue decompositionsub-value Q-learningpersistent explorationadaptability to shifting optimacooperative MARLQ-learning

0 comments

The pith

S2Q learns multiple sub-value functions to retain alternative high-value actions and adapt to shifting optima in MARL.

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

Existing value decomposition methods in cooperative multi-agent reinforcement learning rely on a single optimal action and struggle when the value function shifts during training. The paper introduces Successive Sub-value Q-learning (S2Q) that learns multiple sub-value functions to keep alternative high-value actions available. These functions are combined with a Softmax-based behavior policy to promote persistent exploration. This setup allows the total Q-function to adjust rapidly to new optima. Experiments on challenging benchmarks show S2Q outperforming other MARL algorithms in adaptability and performance.

Core claim

The central discovery is that by learning multiple sub-value functions instead of a single optimal action, S2Q can retain suboptimal but potentially useful actions. When incorporated into a Softmax behavior policy, this enables faster adaptation of Q^tot to changing optima during training, leading to improved performance in cooperative MARL tasks.

What carries the argument

Successive Sub-value Q-learning (S2Q), a method that learns multiple sub-value functions to retain alternative high-value actions and integrates them into a Softmax-based behavior policy for exploration.

If this is right

Q^tot can adjust quickly when the underlying optima change during the training process.
Persistent exploration is encouraged without converging prematurely to suboptimal policies.
Overall performance improves consistently across various MARL benchmarks.
The approach addresses the limitation of single-action reliance in value decomposition methods.

Where Pith is reading between the lines

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

This could allow MARL agents to handle more dynamic environments where rewards or dynamics shift over time.
Similar ideas might apply to single-agent settings with non-stationary rewards to prevent early convergence.
Future work could explore combining S2Q with other advanced exploration strategies for even better results.

Load-bearing premise

That learning and maintaining multiple sub-value functions combined with a Softmax-based behavior policy will produce persistent exploration and faster adaptation without introducing new instabilities or excessive computational cost.

What would settle it

A direct comparison showing that S2Q does not outperform baseline MARL methods on benchmarks with frequently shifting optima, or exhibits higher computational overhead that negates performance gains.

read the original abstract

Value decomposition is a core approach for cooperative multi-agent reinforcement learning (MARL). However, existing methods still rely on a single optimal action and struggle to adapt when the underlying value function shifts during training, often converging to suboptimal policies. To address this limitation, we propose Successive Sub-value Q-learning (S2Q), which learns multiple sub-value functions to retain alternative high-value actions. Incorporating these sub-value functions into a Softmax-based behavior policy, S2Q encourages persistent exploration and enables $Q^{\text{tot}}$ to adjust quickly to the changing optima. Experiments on challenging MARL benchmarks confirm that S2Q consistently outperforms various MARL algorithms, demonstrating improved adaptability and overall performance. Our code is available at https://github.com/hyeon1996/S2Q.

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

S2Q keeps multiple sub-value functions to hold alternative actions so the joint Q can track shifting optima in cooperative MARL, but the absence of any diversity mechanism makes collapse a live risk.

read the letter

The main thing to know is that this paper introduces S2Q to learn successive sub-value functions that retain suboptimal high-value actions, then feeds them into a softmax behavior policy so the total Q can adapt faster when the optimum moves during training. That directly targets a practical weakness in standard value-decomposition MARL, where single-action focus often leads to premature convergence in changing environments like multi-robot coordination. The abstract claims consistent gains over existing algorithms on challenging benchmarks, which is the kind of incremental improvement that could matter for applications with non-stationary optima. If the full results back that up with solid ablations, the mechanism has real utility. The paper does a clean job of framing the problem and positioning the new structure against prior value-decomposition work. The code release is also a plus for anyone who wants to test the idea themselves. The soft spot is exactly the one the stress-test note raises. Nothing described prevents the sub-value functions from collapsing to the same estimates under the shared decomposition loss, and there is no mention of orthogonality constraints, diversity penalties, or separate target networks that would keep the alternatives distinct. Without that, the extra parameters risk adding cost without delivering persistent exploration or faster adaptation. The abstract also gives no details on statistical tests, variance across seeds, or ablation studies, so it is hard to tell how much of the reported outperformance comes from the new retention mechanism versus other implementation choices. This is for researchers working on cooperative MARL and value decomposition who care about adaptability in dynamic settings. A reader looking for practical tweaks to exploration and tracking shifting rewards would get something out of it. It deserves a serious referee because the core problem is well-motivated and the proposed fix is straightforward enough to evaluate properly. I would send it to peer review, with the expectation that the authors strengthen the diversity argument and add the missing experimental controls.

Referee Report

2 major / 1 minor

Summary. The manuscript introduces Successive Sub-value Q-learning (S2Q) for cooperative multi-agent reinforcement learning. S2Q learns multiple sub-value functions to retain alternative high-value actions and incorporates them into a Softmax-based behavior policy to encourage persistent exploration, allowing Q^tot to adjust quickly to shifting optima. It claims consistent outperformance over various MARL algorithms on challenging benchmarks, with code released.

Significance. If the sub-value functions remain distinct without collapse and the adaptation mechanism delivers the claimed gains without offsetting instabilities or costs, S2Q could usefully extend value-decomposition approaches for non-stationary cooperative MARL. Releasing code aids reproducibility.

major comments (2)

§3 (method): The description of S2Q provides no diversity term, orthogonality constraint, or separate target networks to prevent the sub-value functions from converging to identical estimates under the shared value-decomposition loss. This risks reducing the retention benefit to standard Q-learning plus extra parameters, directly threatening the central claim that alternative high-value actions are retained for faster adaptation.
§5 (experiments): The reported outperformance lacks details on the number of independent runs, statistical significance tests, ablation studies varying the number of sub-value functions, or verification that the sub-functions actually remain distinct. This makes it impossible to fully assess whether the gains stem from the proposed mechanism.

minor comments (1)

Abstract: The phrase 'challenging MARL benchmarks' should name the specific environments (e.g., SMAC maps) for clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive and detailed feedback. The comments highlight important aspects for strengthening the presentation of S2Q, particularly regarding the distinctness of sub-value functions and the rigor of the experimental evaluation. We address each major comment below and outline the revisions we will make.

read point-by-point responses

Referee: §3 (method): The description of S2Q provides no diversity term, orthogonality constraint, or separate target networks to prevent the sub-value functions from converging to identical estimates under the shared value-decomposition loss. This risks reducing the retention benefit to standard Q-learning plus extra parameters, directly threatening the central claim that alternative high-value actions are retained for faster adaptation.

Authors: We appreciate this observation on the risk of sub-value function collapse. In the S2Q design, sub-value functions are learned successively such that each subsequent function is optimized to retain high-value actions alternative to those already captured by prior sub-values; this is reinforced by the Softmax behavior policy, which explicitly samples from the union of high-value actions across all sub-values to drive persistent exploration. This successive structure and policy integration provide an implicit mechanism for maintaining distinct estimates even under the shared value-decomposition loss. Nevertheless, to make this explicit and further safeguard against collapse, we will revise §3 to include a dedicated discussion of the successive learning process and introduce a lightweight orthogonality constraint on the sub-value heads. We will also report empirical checks (e.g., pairwise cosine similarities) confirming distinctness. revision: partial
Referee: §5 (experiments): The reported outperformance lacks details on the number of independent runs, statistical significance tests, ablation studies varying the number of sub-value functions, or verification that the sub-functions actually remain distinct. This makes it impossible to fully assess whether the gains stem from the proposed mechanism.

Authors: We agree that these details are essential for a complete assessment. In the revised manuscript we will report results over 5 independent random seeds with mean and standard deviation, include statistical significance tests (paired t-tests against baselines), add ablation studies varying the number of sub-value functions (k = 1, 2, 3, 4), and provide verification metrics such as average pairwise cosine similarity and action-selection entropy across sub-values to demonstrate that they remain distinct. These additions will appear in §5 and the appendix. revision: yes

Circularity Check

0 steps flagged

No circularity: new algorithmic structure with empirical claims

full rationale

The paper proposes S2Q as a novel method that learns multiple sub-value functions and incorporates them into a Softmax behavior policy to address adaptation in MARL. The central claims rest on the definition of this structure and its empirical outperformance on benchmarks rather than any derivation that reduces by construction to fitted parameters, self-citations, or renamed inputs. No load-bearing step equates the output to the input via the enumerated circular patterns; the approach introduces independent algorithmic content evaluated externally.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The central claim rests on standard cooperative MARL assumptions plus the new sub-value function construct.

axioms (1)

domain assumption Value decomposition is a valid and useful framework for cooperative multi-agent settings
The method is explicitly built on top of existing value decomposition approaches.

invented entities (1)

sub-value functions no independent evidence
purpose: To retain and utilize alternative high-value actions beyond the single optimal one
New construct introduced to address the limitation of single-action focus in shifting optima.

pith-pipeline@v0.9.0 · 5664 in / 1212 out tokens · 44072 ms · 2026-05-21T11:50:37.434032+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/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear

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

S2Q learns multiple sub-value functions to retain alternative high-value actions... Softmax-based behavior policy... Q^tot to adjust quickly to the changing optima
IndisputableMonolith/Foundation/AlphaCoordinateFixation.lean alpha_pin_under_high_calibration unclear

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

Theorem 4.1... successive suboptimal joint actions... suppression factor alpha sufficiently large

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