Title: Actor-Free Continuous Control via Structurally Maximizable Q-Functions
Venue: NeurIPS 2025
Accepted: yes
Keywords: Reinforcement Learning

Q-learning
Abstract: Value-based algorithms are a cornerstone of off-policy reinforcement learning due to their simplicity and training stability. However, their use has traditionally been restricted to discrete action spaces, as they rely on estimating Q-values for individual state-action pairs. In continuous action spaces, evaluating the Q-value over the entire action space becomes computationally infeasible. To address this, actor-critic methods are typically employed, where a critic is trained on off-policy data to estimate Q-values, and an actor is trained to maximize the critic's output. Despite their popularity, these methods often suffer from instability during training. In this work, we propose a purely value-based framework for continuous control that revisits structural maximization of Q-functions, introducing a set of key architectural and algorithmic choices to enable efficient and stable learning. We evaluate the proposed actor-free Q-learning approach on a range of standard simulation tasks, demonstrating performance and sample-efficiency on par with state-of-the-art baselines, without the cost of learning a separate actor. Particularly, in environments with constrained action spaces, where the value functions are typically non-smooth, our method with structural maximization outperforms traditional actor-critic methods with gradient-based maximization.


Peer reviews:
{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis manuscript introduces Q3C, which is an actor-free RL algorithm designed for continuous control tasks. The key idea is to approximate the Q-function with a set of learned control points via a wire-fitting interpolator, so that the maximum Q-value for any state is achieved at one of these actions. By turning the maximization problem into a comparison over a finite set of candidate actions, Q3C sidesteps the need for a separately trained actor to navigate the continuous action space. To make this idea suitable with deep RL, several architectural and algorithmic enhancements are proposed on top of the TD3 algorithm to stabilize training and improve performance. These enhancements include action-conditioned Q-value generation, relevance-based control-point filtering, a diversity loss to encourage control points to cover the action space, and control point scaling. Empirical evaluations across standard Gymnasium environments demonstrate that Q3C achieves performance comparable to TD3 on most tasks. However, in tasks with constrained action spaces where the valid actions are limited to certain region and therefore Q-functions tends to be highly non-convex, Q3C significantly outperforms TD3.\n\nSTRENGTHS AND WEAKNESSES:\n* Strengths\n\n1. The manuscript presents a simple yet effective solution via control-points-based wire-fitting interpolators to the long-standing “max-Q” problem in continuous action spaces. This is an interesting solution that departs from conventional actor-critic methods.\n2. Empirical results demonstrate that Q3C matches the performance of the TD3 algorithm on most Gym environments, and significantly outperforms it in challenging settings with constrained action ranges. The fact that Q3C can find better policies where gradient-based actors get stuck in local optima demonstrates a clear advantage of the proposed method.  Additionally, the manuscript includes comprehensive ablations to pinpoint the contribution of each component in the design of Q3C. \n3. The proposed method is also well-motivated theoretically since the wire-fitting formulation can approximate any continuous $Q(s,.)$ arbitrarily well based on proposition 3.\n\n* Weaknesses\n1. Given that the performance of Q3C is largely on par with TD3, the main benefit of is in the method being actor-free, which potentially means smaller memory footprint and faster training. However, there are no discussion on the computational complexity or experiments to evaluate the computational speed ups.\n\n2. Q3C introduces new hyperparameters such as the number of control points and $\\gamma$, in addition to the control point generator. It is not clear how different choices for these hyperparameters impact the performance of Q3C, and the manuscript does not explore how sensitive the results are to these settings\n\n3. The evaluation could be more complete if other baselines are included such as SAC. Also, while the benchmark suite is diverse, the manuscript does not explore real-world tasks where control-point scalability could be more challenging.\n\nQUESTIONS:\n1. Could the authors provide runtime comparisons or memory usage statistics relative to TD3 and NAF?\n2. There are some notational inconsistencies throughout the manuscript. For instance, equation 4 is quite understandable but it is not clear how action-conditioned Q-value generation fits within equation 4. Do authors mean to say $Q_i(s) = h_\\psi(s, a_i(s))$? \n3. What is the typical number of control points that is needed? Does it have to be the same for all state-action pairs? Does it grow with action dimensionality or task complexity? Please discuss the trade-offs involved with the choice of the number of control points.\n4. How robust is Q3C to the choice of the number of control points and other new hyperparameters (top-$k$, $\\gamma$, etc.)? The method introduces several knobs – it would help to know if these were fixed across all experiments or tuned per environment.  \n5. The manuscript mentions that future work could extend Q3C to stochastic settings. Could the authors elaborate on the challenges and potential approaches for modelling soft-Q functions with control points?\n\nLIMITATIONS:\nyes", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 3, "IMPACT": 3, "ORIGINALITY": 3, "DATE": "2025-06-28"}

comments: SUMMARY:
The authors in this submission proposed a value-based framework for reinforcement learning with continuous actions. In contrast to the actor-critic methods, they first constructed the control points and subsequently learned policies with respect to Q-functions over those points. In order to overcome the issues reported in previous work, they proposed a few techniques to address them. The experiments showed that the proposed method is on par with TD3 in standard domains, and achieves better performance on constricted environments.

STRENGTHS AND WEAKNESSES:
Strength:
The revisit of the Q-function approximation using the control-points is an interesting direction. The authors also showed that the proposed method, when combined with neural networks, works reasonablly well in some standard domains

Weakness:
Given the additional complexity involving the control points, the performance of the proposed Q3C algorithm is mostly similar to that of TD3. Note that TD3 is far behind some other policy gradient methods, e.g., SAC. Subsequently, its significance is a bit limited.

Some steps in the proposed method need justification and the presentation can be improved. A few of them are listed as follows. 
* In L175-L179, the authors proposed to keep top k from N candidates, so why not just generate k control-points?
* In Eq. (6), should there be $N (N - 1) / 2$ pairs only?

QUESTIONS:
* Could you comment on the complexity for Q3C, when compared against relevant value or policy based methods, given the additional steps w.r.t. control points?
* Why is the variance for Q3C in Table 2 on InvertedPendulum 0?

LIMITATIONS:
Yes
TITLE: Official Review
CLARITY: 2
IMPACT: 2
ORIGINALITY: 2
DATE: 2025-07-02

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper proposes Q-learning for Continuous Control with Control-points (Q3C), a value-based method for control in domains with continuous action spaces. This approach structures the Q-function approximator such that it covers the entire continuous space, but the maximizing action can still be determined efficiently. The authors prove that this method retains the universal approximator property of the underlying neural network models and that it compares favorably to some other value-based methods in several continuous control domains.\n\nSTRENGTHS AND WEAKNESSES:\n# Strengths\n\nThe paper is well-written and easy to follow.\n\nThe problem of value-based continuous control is an important one that I believe is relevant and of interest to the community.\n\nQ3C's control point diversity and control point ranking components appear novel and useful additions to the algorithm.\n\nQ3C performs well compared to the baselines the authors use and the experiments thoroughly cover a large number of interesting domains, though key baselines are missing (see Weaknesses).\n\n\n# Weaknesses\n\nQ3C is very similar to RBF-DQN [1], but it the latter is neither mentioned in either the text nor used as a baseline for the experiments. RBF-DQN uses the same kind of structure to generate candidate actions (centroids there) and values as functions of the state. These are then interpolated, but using radial basis functions explicitly. Equation 4 for Q3C is essentially the same as Equation 5 in the RBF-DQN paper, but uses something like an inverse quadratic RBF where RBF-DQN uses negative exponential RBF. RBF-DQN similarly retains the universal approximator property and the approximator is maximized (with bounded error) by selecting the maximizing centroid.\n\nQ3C is not compared to policy-based methods (policy gradient or actor-critic) in the experiments.\n\n# References\n[1]  Deep Radial-Basis Value Functions for Continuous Control, Asadi et al., AAAI 2021\n\nQUESTIONS:\nHow would you present Q3C in a context including RBF-DQN?\n\nWhat would you say are the signfiicant differences between Q3C and RBF-DQN and how do you think they improve on RBF-DQN?\n\nCan you add RBF-DQN as a baseline?\n\nIs there a principled (or inspired-by-principle) way of selecting the number of control points used for a problem?\n\nLIMITATIONS:\nI would like to see more discussion about how to select the number of control points to use. While the theory contribution shows that there exists an N such that any arbitrary maximum error can be guaranteed, such an N could be quite large for domains with complex value functions.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 5, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 2, "DATE": "2025-07-03"}

{"IS_META_REVIEW": false, "comments": "SUMMARY:\nThis paper introduces Q3C, a novel actor-free Q-learning approach for continuous control, aiming to overcome the stability issues associated with actor-critic methods. Traditional actor-critic methods suffer from instability during training due to the coupling of policy and value function updates. The authors propose a solution using a structurally maximizable Q-function, optimized by learning control points. By leveraging deep learning and a set of architectural and algorithmic improvements, Q3C is designed to be stable and sample-efficient.\n\nSTRENGTHS AND WEAKNESSES:\n**Strengths:**\n\n1. The method proposed is technically robust, with clear theoretical motivation and sound empirical validation.\nThe integration of control points for Q-function maximization is a novel approach, ensuring that the maximum value can be found efficiently in continuous action spaces, a known challenge in Q-learning.\n\n2. The variance reduction techniques, such as exponential moving averages (EMA), effectively address training instability, ensuring better convergence.\n\n3. Empirical results show Q3C is competitive with leading actor-critic methods such as TD3, SAC, and others, performing well across multiple environments, including complex and constrained settings.\n\n**Weaknesses:**\n\n1. While the concept of using control points is not entirely new, the combination of this approach with deep learning and the specific modifications introduced by the authors is what makes this work original.\nHowever, it would be useful to see a deeper comparison of how Q3C outperforms or offers advantages over other actor-free methods, such as Implicit Q-learning or Policy-conditioned Q-learning, which also aim to address similar problems in continuous control.\n\n2. The paper suggests that actor-critic methods are generally stable, but the proposed method also involves training two models: one for the policy and another for the value function. This dual-model structure could introduce potential instability, as the training of both models might become misaligned. Could the authors elaborate on how stability is maintained in their method despite the dual-model setup? What specific mechanisms or architectural choices help ensure training stability, and how does Q3C compare with traditional actor-critic methods in this regard?\n\n3. The paper compares Q3C primarily with value-based methods. To gain a better understanding of its performance and robustness, would the authors consider adding comparisons to stronger policy-gradient methods like PPO? How do the proposed method’s strengths and weaknesses compare with these baselines, particularly in terms of exploration, sample efficiency, and policy robustness?\nGeneralization to High-Dimensional Action Spaces:\nHow does Q3C scale to environments with high-dimensional action spaces? Are there any performance bottlenecks in optimizing the Q-function in such spaces? Additionally, how well does the method handle partial observability or environments where the action space is not fully observable?\n\n4. Given that Q3C does not use an explicit actor for exploration, how does the method ensure sufficient exploration during training? Would additional exploration mechanisms, such as Boltzmann over the control-point values, improve performance in environments that require more extensive exploration?\nReal-World Applicability and Sample Efficiency:\nWhile the paper provides strong empirical results in simulation environments, has there been any consideration of the method's applicability in real-world settings, especially for high-dimensional or physical tasks? Additionally, Q3C’s sample efficiency could be compared in greater detail with methods such as SAC or TD3, especially in tasks with sparse rewards or large state spaces.\n\nQUESTIONS:\n1. The paper suggests that actor-critic methods are generally stable, but the proposed method also involves training two models: one for the policy and another for the value function. This dual-model structure could introduce potential instability, as the training of both models might become misaligned. Could the authors elaborate on how stability is maintained in their method despite the dual-model setup? What specific mechanisms or architectural choices help ensure training stability, and how does Q3C compare with traditional actor-critic methods in this regard?\n\n2. The paper compares Q3C primarily with value-based methods. To gain a better understanding of its performance and robustness, would the authors consider adding comparisons to stronger policy-gradient methods like PPO? How do the proposed method’s strengths and weaknesses compare with these baselines, particularly in terms of exploration, sample efficiency, and policy robustness?\nGeneralization to High-Dimensional Action Spaces:\nHow does Q3C scale to environments with high-dimensional action spaces? Are there any performance bottlenecks in optimizing the Q-function in such spaces? Additionally, how well does the method handle partial observability or environments where the action space is not fully observable?\n\n3. Given that Q3C does not use an explicit actor for exploration, how does the method ensure sufficient exploration during training? Would additional exploration mechanisms, such as Boltzmann over the control-point values, improve performance in environments that require more extensive exploration?\nReal-World Applicability and Sample Efficiency:\nWhile the paper provides strong empirical results in simulation environments, has there been any consideration of the method's applicability in real-world settings, especially for high-dimensional or physical tasks? Additionally, Q3C’s sample efficiency could be compared in greater detail with methods such as SAC or TD3, especially in tasks with sparse rewards or large state spaces.\n\nLIMITATIONS:\nYes. The paper acknowledges that Q3C’s performance may suffer in certain high-dimensional or sparse-reward environments, and it notes that further exploration of the method’s sample efficiency and real-world scalability would be useful. However, a more detailed discussion of the computational limitations or potential scalability challenges in real-world applications would provide a more comprehensive understanding.", "TITLE": "Official Review", "RECOMMENDATION": 5, "REVIEWER_CONFIDENCE": 4, "CLARITY": 4, "IMPACT": 2, "ORIGINALITY": 3, "DATE": "2025-07-05"}