Distributional Soft Actor-Critic with Diffusion Policy

Bin Shuai; Jingliang Duan; Liangfa Chen; Likun Wang; Shengbo Eben Li; Tong Liu; Wenjun Zou; Xujie Song; Yinuo Wang

REVIEW 4 major objections 5 minor 1 cited by

Distributional Soft Actor-Critic with Diffusion Policy

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read A dual-diffusion actor-critic algorithm claims to learn multimodal value distributions and policies while converging to an optimal policy.

desk verdict Interesting dual-diffusion combination undermined by an undefined policy update and an overclaimed SOTA result. read the letter →

arxiv 2507.01381 v3 pith:OPVOSQF7 submitted 2025-07-02 cs.LG cs.AI

Tong Liu , Yinuo Wang , Xujie Song , Wenjun Zou , Liangfa Chen , Likun Wang , Bin Shuai , Jingliang Duan

show 1 more author

Shengbo Eben Li

This is my paper

classification cs.LGcs.AI

keywords DistributionalreinforcementlearningDiffusionpolicyvaluenetworkSoftactor-criticMultimodaldistributionEntropyestimationbiasContinuouscontrol

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 tries to establish that reinforcement learning agents can represent both value functions and policies as multimodal distributions and still converge to an optimal policy. The authors propose DSAC-D, which models the value distribution with a diffusion value network and the policy with a diffusion policy network, alternating between distributional policy evaluation and improvement steps they call Multimodal Distributional Policy Iteration. They claim that the multimodal Q-value strictly increases with each iteration, and that the resulting algorithm suppresses value-estimation bias and achieves state-of-the-art returns on all nine MuJoCo tasks tested, with real-vehicle experiments showing multimodal driving trajectories. The practical stakes are that distributional RL need not be limited to unimodal value representations, and that diffusion models can supply the needed flexibility in both value and policy networks.

What carries the argument

The central object is the distributional Bellman equation with entropy regularisation, Eq. (9), which the paper calls the multimodal distributional policy evaluation step. Because diffusion policies lack an analytical density, the entropy $\hat H$ driving the adaptive temperature $\alpha$ is estimated by fitting a Gaussian mixture model to $N$ sampled actions per state via EM; the policy improvement step then uses this estimated entropy. The diffusion value network generates return samples through reverse denoising, and the combination forms the MDPI loop the proof of monotone Q-improvement relies on.

What would settle it

Compare the GMM-entropy estimate $\hat H$ against a large-sample Monte Carlo entropy of the diffusion policy on the same states; if the two diverge substantially, Eq. (11) is not an exact policy improvement and the MDPI convergence theorem does not apply. Alternatively, check the published Table I: DSAC-D does not achieve the maximum return in every task, since DAC's HalfCheetah-v3 score (17177) exceeds DSAC-D's (16409), so the 'SOTA in all 9 tasks' claim is contradicted by the paper's own table.

Watch

Extended reading notes

Core claim

The central claim is that a distributional Bellman self-consistency condition with an entropy term, $Z^\pi(s,a) \overset{D}{=} r + \gamma[Z(s',a') - \alpha\log\pi(a'|s')]$, together with a greedy policy improvement step, yields a Multimodal Distributional Policy Iteration (MDPI) in which the multimodal Q-value $Q^{\pi_k}(s,a)$ strictly monotonically increases with iteration $k$. The paper further claims that implementing the value distribution with a diffusion network (generating return samples by reverse denoising) and the policy with a diffusion policy network yields DSAC-D, an algorithm that learns multimodal policies, suppresses value overestimation bias, and outperforms baselines on all nine MuJoCo control tasks, with real-vehicle tests producing multimodal obstacle-avoidance trajectories.

Load-bearing premise

The algorithm's convergence rests on the assumption that the entropy of the diffusion policy is accurately captured by a Gaussian mixture fit to a small number of sampled actions; if that estimate is biased, the policy update is not a true soft policy improvement and the claimed monotone convergence can fail.

Editorial extensions

If this is right

If MDPI converges as claimed, distributional RL can represent multimodal value functions without losing soft policy improvement guarantees.
DSAC-D's dual-diffusion design gives a concrete recipe for applying diffusion models inside actor-critic algorithms without an analytical policy density.
The claimed >10% average return improvement and bias suppression would make DSAC-D a strong candidate for high-dimensional continuous control and autonomous driving.
Real-vehicle demonstrations imply the same machinery can produce multimodal driving trajectories reflecting distinct driving styles.
The GMM entropy estimator (Eq. 18) becomes a reusable component for entropy-regularised diffusion policies.

Reading between the lines

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

A testable extension would be to replace the GMM entropy estimate with a learned density or a Monte Carlo estimator; if convergence behavior changes materially, the entropy estimate is the active ingredient.
The same MDPI framework could be applied to risk-sensitive objectives (e.g., CVaR) by changing the distributional criterion, since the framework is distributional rather than expectation-only.
The diffusion value network could be reused as an uncertainty estimator for out-of-distribution detection, since it returns a full return distribution rather than a scalar.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Desk Editor's Note

read the letter

Nothing wrong with the kernel here. The idea of putting a diffusion model on both the value distribution and the policy, with a GMM entropy estimate to keep the SAC-style objective computable, is a legitimate new combination. The real-vehicle experiments showing multi-modal trajectories are a useful addition; that sort of hardware demonstration is rare in RL papers and hard to fake. I also appreciate that the authors are explicit that the diffusion policy has no closed-form density, which is why they fit a GMM.

That said, the central theoretical claim is not supported. Equation (11) is the policy improvement step, but as written the maximand contains only pi_old—the expectation is over Z^pi_old and the log term is log pi_old. The argmax over pi is undefined. If they intended log pi inside, the paper never provides a tractable log-density for the diffusion policy; the GMM entropy H_s estimates the per-state entropy, not log pi(a|s). So the monotone convergence claim for MDPI has a missing premise. Algorithm 1 references a policy-gradient objective J_pi(omega) that is never defined. These aren't cosmetic issues; the guarantee the paper advertises is not derived.

The empirical side is also oversold. Table I shows HalfCheetah-v3 where DSAC-D (16409) is below both DAC (17177) and DSAC-T (17025), and Reacher is a three-way tie. That directly contradicts the abstract's 'SOTA in all 9 control tasks' and the text's 'outperforms all baselines in all tasks.' The bias-suppression claim in Table II is also mixed: on HalfCheetah and Swimmer, DSAC-D's bias is worse than SAC's. The paper's own numbers undo the headline.

Reproducibility is a problem too: the GMM component count K, the action sample count N, and the diffusion hyperparameters are not stated, so the entropy estimate that drives alpha and the policy update cannot be replicated.

Who benefits? Someone working on diffusion RL might take the idea and fix the theory. But as it stands the paper is not reliable enough to cite for its claims. I'd send it out for review only if I expected the referees to enforce a major rewrite; otherwise a desk reject with an invitation to resubmit a corrected version would be appropriate. My verdict is reject in current form.

Referee Report

4 major / 5 minor

Summary. This paper proposes DSAC-D, an actor-critic algorithm that uses a diffusion model for the value distribution and a diffusion policy, with a claimed Multimodal Distributional Policy Iteration (MDPI) convergence guarantee, state-of-the-art performance on nine MuJoCo tasks, reduced value-estimation bias, and multimodal trajectory behavior in real-vehicle tests. Section III-A introduces the distributional soft Bellman relation and the policy improvement step, Section III-B describes a diffusion value network, Section III-C uses a GMM entropy estimate for adaptive entropy tuning, and Section IV reports MuJoCo and vehicle experiments.

Significance. The paper targets a real gap: standard unimodal value distributions can be biased, and diffusion policies can represent multimodal action distributions. The combination is timely, and the real-vehicle demonstration of multimodal trajectories is a useful qualitative result. However, the manuscript's two headline claims—the MDPI monotone-convergence guarantee and SOTA on all nine tasks—are not supported. The policy improvement step in Eq. (11) is mathematically undefined as written, the convergence proof is only announced, the algorithm pseudo-code references objectives that are never defined, and Table I contradicts the SOTA claim. These are load-bearing issues, so the paper cannot be accepted in its present form.

major comments (4)

[Section III-A, Eq. (11)] The proposed multimodal distributional policy improvement step is not a valid argmax: the expression E[E_{Z^π_old}[Z^π_old(s,a)] − α log π_old(a|s)] is independent of the optimization variable π, so π_new is undefined. If the intended expression replaces log π_old by log π, the update still cannot be computed because the diffusion policy is not given a closed-form log-density anywhere in the paper. The statement immediately after Eq. (11) that 'we can prove' Q^{π_k} strictly monotonically increases is therefore unsupported; no theorem statement or proof appears.
[Algorithm 1 / Sections III-B and III-C] The pseudo-code calls for updates θ ← θ − β_z ∇_θ J_z(θ) and ω ← ω + β_π ∇_ω J_π(ω), but neither objective is defined in the text. Eq. (15) gives a simplified diffusion loss for the value network, but no J_z; no policy-gradient objective J_π is given at all. Without these definitions, the algorithm as presented is not reproducible and the claimed connection to the MDPI framework cannot be checked.
[Section IV-B, Tables I and II] The text claims DSAC-D 'outperforms all baselines in all tasks,' but Table I shows DSAC-D's HalfCheetah-v3 return (16409 ± 477) is below DAC (17177 ± 176) and DSAC-T (17025 ± 157), and Reacher-v2 is a tie across several algorithms. Table II also fails to show consistent bias suppression: on HalfCheetah-v3 DSAC-D's relative bias is 21.45, worse than SAC's −4.82, and on Reacher-v2 DDPG's −0.28 beats DSAC-D's −3.85. The SOTA and bias-suppression claims are therefore contradicted by the paper's own data.
[Section III-C, Eqs. (16)-(19)] The GMM entropy estimate Ĥ depends on unstated hyperparameters K and N and on EM initialization, and no validation is provided against the true (unknown) policy entropy. Since α is adapted from Ĥ and α enters Eq. (10) and the policy update, the correctness of the policy-improvement step is contingent on an unvalidated estimator. The paper should state K, N, and any safeguards, and provide evidence that Ĥ is unbiased or conservatively bounded.

minor comments (5)

[Section IV-A] The text says 'we run 20 parallel environment interactions per iteration' and later 'conduct 9 independent tests for each algorithm,' while Table I reports 'standard deviation over five runs.' These numbers should be reconciled.
[Section II] The notation in Eqs. (8)-(9) mixes r_i and r, and the definition of Z^π(s,a) at state-action pair (s,a) is inconsistent with the inner expectation notation; please clean up the indices.
[Section IV-B] Figure 4 measures PPO and TRPO by number of network updates while other algorithms are measured by environment interactions; this makes the comparison non-uniform and should be justified.
[Algorithm 1] The added exploration noise term a = a + λ_α * N(0,I) introduces a hyperparameter λ_α that is never defined or reported.
[Abstract and Section V] The claimed 'total average return improvement of over 10%' is not derived or tabulated anywhere; please report the aggregate calculation or remove the claim.

Circularity Check

1 steps flagged · score 6.0 of 10

The central MDPI convergence claim reduces by construction: Eq. (11) defines the policy improvement step as maximizing an objective that is independent of the new policy, so the asserted strict monotonic increase is a tautology rather than a derivation.

self definitional [Section III-A, Eq. (11) and the subsequent claim of strict monotonic increase of Q^{π_k}]
"The corresponding multimodal distributional policy improvement step is: πnew = arg max π E [ E Zπold(s,a)∼Zπold(·|s,a) [Zπold(s, a)] − α log πold(a|s)]. We call this process the multimodal distributional policy improvement step."

The maximand inside the argmax contains only π_old: the expected return is taken over Z^{π_old}, and the entropy penalty is log π_old(a|s). No term depends on the candidate π being optimized. Therefore every policy, including π_old itself, attains the maximum; the 'new' policy is not determined by the update. The paper then claims that by alternating evaluation and improvement 'we can prove that ... the multimodal Q-value Q^{π_k}(s,a) corresponding to the policy π_k strictly monotonically increases with the number of iterations k.' That monotonicity is not a consequence of a policy-improvement operation; it is a tautology of leaving the policy unchanged.

full rationale

The one exhibitable circularity is the policy-improvement step: Eq. (11) defines π_new as the argmax of an expression that is independent of π, so the claimed strict monotonic improvement of Q^{π_k} reduces by construction to a no-op on the current policy. This is the load-bearing theoretical claim of the paper, so I rate it as partial circularity (6). I do not count the GMM entropy estimate of Eqs. (16)-(18) as circular: it is an unvalidated approximation of the diffusion policy entropy, not a fitted quantity renamed as a prediction, though it leaves the adaptive-α convergence claim unsupported. The DACER references [11,12] are used as baselines and are not load-bearing for the MDPI derivation, so they do not raise the score. The MuJoCo experiments are external benchmarks and are not circular, although the abstract's 'state-of-the-art (SOTA) performance in all 9 control tasks' is contradicted by Table I on HalfCheetah-v3 (DSAC-D 16409±477 vs DAC 17177±176 and DSAC-T 17025±157); that is an empirical inconsistency, not a circularity. Algorithm 1 also refers to a policy-gradient objective J_π(ω) that is never defined, which is a missing derivation rather than a circular reduction.

Assumptions & free parameters 6 free parameters · 6 assumptions · 0 invented entities

Most of the strong mathematical content is pulled from prior work or asserted without proof: the MDPI convergence theorem is unproven, the DDPM representation power is assumed, and the GMM entropy estimator comes from the authors' earlier DACER papers. The only fitted quantities in the reported experiments are the adaptive entropy temperature, the unreported GMM/diffusion hyperparameters, and the 10,000-step policy update cadence. The paper therefore adds an engineering combination on top of a large uncounted set of prior assumptions.

free parameters (6)

Adaptive entropy coefficient alpha = online, target H = -dim(A), not reported
Updated online via Eq. (19) toward target H = -dim(A); the paper does not specify initial alpha, learning rate beta_alpha, or schedules, and the resulting entropy trade-off is fitted to this target.
GMM component count K = not reported
The number of Gaussian components for entropy estimation is chosen by hand and never stated; no sensitivity analysis is given, yet Eq. (18) entropy depends on it.
Action samples N per state for entropy estimation = not reported
N actions are sampled from the diffusion policy to fit the GMM; N is never given, but the entropy estimate quality depends on it.
Diffusion timesteps T and noise schedule beta_t = not reported
Both diffusion networks use a DDPM with total steps T and variance schedule; neither is reported, and Eq. (13)-(15) depend on both.
Policy update interval of 10,000 iterations = 10000
Algorithm 1 updates the diffusion policy only when the iteration step number is divisible by 10,000; no theoretical or empirical justification is given, and it determines how often the actor adapts.
Network learning rates and soft update rate = not reported
Algorithm 1 references beta_z, beta_pi, beta_alpha, and tau, but none are specified, and the central results depend on them.

assumptions (6)

domain assumption The Markov Decision Process and Bellman equations in Section II-A define the objective and update rules.
Standard RL modeling assumption; the paper invokes it without discussion.
domain assumption The reverse diffusion process in Eq. (12)-(13) can represent the true multimodal distribution of the return Z(s,a).
The paper assumes the DDPM can approximate the return distribution accurately, but provides no representation or consistency proof.
domain assumption A Gaussian mixture model with K components fit by EM to N action samples approximates the diffusion policy's distribution and entropy.
Stated in Section III-C without validation; the entropy estimate drives alpha adaptation and policy improvement.
ad hoc to paper The Multimodal Distributional Policy Iteration fixed point exists and Q^{pi_k} strictly increases in k.
Section III-A states 'we can prove' but no proof appears; the convergence claim is assumed for the algorithm's correctness.
domain assumption The discounted accumulated sampled rewards used in Table II are a valid proxy for the true Q-value.
The table text defines true Q this way; it is not a ground-truth value and can bias the reported bias measurements.
domain assumption The adaptive entropy update Eq. (19) converges and drives the estimated entropy to the target H bar.
The paper assumes that the online update of alpha behaves like SAC's temperature update, but no convergence analysis is provided.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Distributional Soft Actor-Critic with Diffusion Policy." pith.science (2026). https://pith.science/paper/OPVOSQF7

@misc{pith2026250701381,
  author       = {Pith},
  title        = {Pith review of: Distributional Soft Actor-Critic with Diffusion Policy},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/OPVOSQF7}},
  note         = {Machine review of arXiv:2507.01381}
}

read the original abstract

Reinforcement learning has been proven to be highly effective in handling complex control tasks. Traditional methods typically use unimodal distributions, such as Gaussian distributions, to model the output of value distributions. However, unimodal distribution often and easily causes bias in value function estimation, leading to poor algorithm performance. This paper proposes a distributional reinforcement learning algorithm called DSAC-D (Distributed Soft Actor Critic with Diffusion Policy) to address the challenges of estimating bias in value functions and obtaining multimodal policy representations. A multimodal distributional policy iteration framework that can converge to the optimal policy was established by introducing policy entropy and value distribution function. A diffusion value network that can accurately characterize the distribution of multi peaks was constructed by generating a set of reward samples through reverse sampling using a diffusion model. Based on this, a distributional reinforcement learning algorithm with dual diffusion of the value network and the policy network was derived. MuJoCo testing tasks demonstrate that the proposed algorithm not only learns multimodal policy, but also achieves state-of-the-art (SOTA) performance in all 9 control tasks, with significant suppression of estimation bias and total average return improvement of over 10% compared to existing mainstream algorithms. The results of real vehicle testing show that DSAC-D can accurately characterize the multimodal distribution of different driving styles, and the diffusion policy network can characterize multimodal trajectories.

Figures

Figures reproduced from arXiv: 2507.01381 by the authors.

**Figure 2.** DSAC-D Algorithm Framework learning algorithm can be derived, and its complete pseudocode is shown in Algorithm 1. The algorithm flowchart can be seen in the [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗

**Figure 3.** Vehicle Meeting: We designed a vehicle trajectory tracking and obstacle avoidance environment with three-degreeof-freedom and perimeter vehicle constraints. In this intersection vehicle-meeting scenario, the surrounding vehicles’ driving styles (aggressive, normal, conservative) are randomly selected at the start, resulting in different accelerations near the meeting point. The environment’s reward function pena… view at source ↗

Figures from the paper (6 more)

**Figure 4.** Figure 4: Training curves on benchmarks. The solid lines represent the mean, while the shaded regions indicate the 95% confidence interval over five runs. The iteration of PPO and TRPO is measured by the number of network updates. algorithms use a three-layer MLP with GeLU [19] …

**Figure 5.** Figure 5: Different decision-making action modes on MuJoCo tasks [PITH_FULL_IMAGE:figures/full_fig_p006_5.png]

**Figure 6.** Figure 6: Schematic diagram of vehicle meeting environment [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]

**Figure 7.** Figure 7: Training curve and multimodal trajectories in scenario 1 [PITH_FULL_IMAGE:figures/full_fig_p007_7.png]

**Figure 8.** Figure 8: Multimodal trajectories with different driving styles in scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p008_8.png]

**Figure 9.** Figure 9: Experimental photos of different driving styles in scenario 2 [PITH_FULL_IMAGE:figures/full_fig_p008_9.png]

Discussion (0). Sign in to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Learning When to Stop: Prefix-Optimal Dynamic Diffusion Policies for Continuous Control
cs.LG 2026-08 conditional novelty 6.0 of 10

POGP trains a prefix value function over the diffusion denoising chain, giving a learned early-stopping rule that cuts average denoising steps about 2.7x with 98-99% of full-chain return and a small gain in final task...

Reference graph

Works this paper leans on

21 extracted references · 13 canonical work pages · cited by 1 Pith paper

[1]

& Faheem, M

Kakolu, S. & Faheem, M. Autonomous Robotics in Field Operations: A Data-Driven Approach to Optimize Performance and Safety.Iconic Research And Engineering Journals.7, 565-578 (2023)

work page 2023
[2]

& Westerlund, T

Xianjia, Y ., Qingqing, L., Queralta, J., Heikkonen, J. & Westerlund, T. Applications of UWB networks and positioning to autonomous robots and industrial systems.2021 10th Mediterranean Conference On Embedded Computing (MECO). pp. 1-6 (2021)

work page 2021
[3]

Hua, M., Shuai, B., Zhou, Q., Wang, J., He, Y . & Xu, H. Recent progress in energy management of connected hybrid electric vehi- cles using reinforcement learning.ArXiv Preprint ArXiv:2308.14602. (2023)

work page Pith review arXiv 2023
[4]

& Munos, R

Bellemare, M., Dabney, W. & Munos, R. A distributional perspective on reinforcement learning.International Conference On Machine Learning. pp. 449-458 (2017)

work page 2017
[5]

& Munos, R

Dabney, W., Ostrovski, G., Silver, D. & Munos, R. Implicit quan- tile networks for distributional reinforcement learning.International Conference On Machine Learning. pp. 1096-1105 (2018)

work page 2018
[6]

& Liu, T

Yang, D., Zhao, L., Lin, Z., Qin, T., Bian, J. & Liu, T. Fully pa- rameterized quantile function for distributional reinforcement learning. Advances In Neural Information Processing Systems.32(2019)

work page 2019
[7]

& Abbeel, P

Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. Advances In Neural Information Processing Systems.33pp. 6840- 6851 (2020)

work page 2020
[8]

& Others Deepmind control suite.ArXiv Preprint ArXiv:1801.00690

Tassa, Y ., Doron, Y ., Muldal, A., Erez, T., Li, Y ., Casas, D., Budden, D., Abdolmaleki, A., Merel, J., Lefrancq, A. & Others Deepmind control suite.ArXiv Preprint ArXiv:1801.00690. (2018)

arXiv 2018

Show all 21 references

[9]

& Others GOPS: A general optimal control problem solver for autonomous driving and industrial control appli- cations.Communications In Transportation Research.3pp

Wang, W., Zhang, Y ., Gao, J., Jiang, Y ., Yang, Y ., Zheng, Z., Zou, W., Li, J., Zhang, C., Cao, W. & Others GOPS: A general optimal control problem solver for autonomous driving and industrial control appli- cations.Communications In Transportation Research.3pp. 100096 (2023)

2023
[10]

Jiang, Y ., Zhan, G., Lan, Z., Liu, C., Cheng, B. & Li, S. A reinforce- ment learning benchmark for autonomous driving in general urban scenarios.IEEE Transactions On Intelligent Transportation Systems. 25, 4335-4345 (2023)

2023
[11]

& Others Diffusion actor-critic with entropy regulator.Advances In Neural Information Processing Systems.37pp

Wang, Y ., Wang, L., Jiang, Y ., Zou, W., Liu, T., Song, X., Wang, W., Xiao, L., Wu, J., Duan, J. & Others Diffusion actor-critic with entropy regulator.Advances In Neural Information Processing Systems.37pp. 54183-54204 (2024)

2024
[12]

& Others Enhanced DACER Algorithm with High Diffusion Efficiency.ArXiv Preprint ArXiv:2505.23426

Wang, Y ., Tan, M., Zou, W., Lin, H., Song, X., Wang, W., Liu, T., Wang, L., Zhan, G., Zhu, T. & Others Enhanced DACER Algorithm with High Diffusion Efficiency.ArXiv Preprint ArXiv:2505.23426. (2025)

2025
[13]

& Wierstra, D

Lillicrap, T., Hunt, J., Pritzel, A., Heess, N., Erez, T., Tassa, Y ., Silver, D. & Wierstra, D. Continuous control with deep reinforcement learning.ArXiv Preprint ArXiv:1509.02971. (2015)

2015 arXiv
[14]

& Meger, D

Fujimoto, S., Hoof, H. & Meger, D. Addressing function approx- imation error in actor-critic methods.International Conference On Machine Learning. pp. 1587-1596 (2018)

2018
[15]

& Klimov, O

Schulman, J., Wolski, F., Dhariwal, P., Radford, A. & Klimov, O. Proximal policy optimization algorithms.ArXiv Preprint ArXiv:1707.06347. (2017)

2017 arXiv
[16]

& Others Soft actor-critic algorithms and applications.ArXiv Preprint ArXiv:1812.05905

Haarnoja, T., Zhou, A., Hartikainen, K., Tucker, G., Ha, S., Tan, J., Kumar, V ., Zhu, H., Gupta, A., Abbeel, P. & Others Soft actor-critic algorithms and applications.ArXiv Preprint ArXiv:1812.05905. (2018)

2018 arXiv
[17]

Duan, J., Wang, W., Xiao, L., Gao, J., Li, S., Liu, C., Zhang, Y ., Cheng, B. & Li, K. Distributional Soft Actor-Critic With Three Refinements. IEEE Transactions On Pattern Analysis And Machine Intelligence. (2025)

2025
[18]

& Moritz, P

Schulman, J., Levine, S., Abbeel, P., Jordan, M. & Moritz, P. Trust region policy optimization.International Conference On Machine Learning. pp. 1889-1897 (2015)

2015
[19]

& Gimpel, K

Hendrycks, D. & Gimpel, K. Gaussian error linear units (gelus).ArXiv Preprint ArXiv:1606.08415. (2016)

2016 arXiv
[20]

A Self Regularized Non-Monotonic Activation Function

Mish, M. A Self Regularized Non-Monotonic Activation Function. 2019.ArXiv Preprint ArXiv:1908.08681. (1908)

1908 arXiv
[21]

Adam: A method for stochastic optimization.ArXiv Preprint ArXiv:1412.6980

Kingma, D. Adam: A method for stochastic optimization.ArXiv Preprint ArXiv:1412.6980. (2014)

2014 arXiv

Pith tools

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

[1] [1]

& Faheem, M

Kakolu, S. & Faheem, M. Autonomous Robotics in Field Operations: A Data-Driven Approach to Optimize Performance and Safety.Iconic Research And Engineering Journals.7, 565-578 (2023)

work page 2023

[2] [2]

& Westerlund, T

Xianjia, Y ., Qingqing, L., Queralta, J., Heikkonen, J. & Westerlund, T. Applications of UWB networks and positioning to autonomous robots and industrial systems.2021 10th Mediterranean Conference On Embedded Computing (MECO). pp. 1-6 (2021)

work page 2021

[3] [3]

Hua, M., Shuai, B., Zhou, Q., Wang, J., He, Y . & Xu, H. Recent progress in energy management of connected hybrid electric vehi- cles using reinforcement learning.ArXiv Preprint ArXiv:2308.14602. (2023)

work page Pith review arXiv 2023

[4] [4]

& Munos, R

Bellemare, M., Dabney, W. & Munos, R. A distributional perspective on reinforcement learning.International Conference On Machine Learning. pp. 449-458 (2017)

work page 2017

[5] [5]

& Munos, R

Dabney, W., Ostrovski, G., Silver, D. & Munos, R. Implicit quan- tile networks for distributional reinforcement learning.International Conference On Machine Learning. pp. 1096-1105 (2018)

work page 2018

[6] [6]

& Liu, T

Yang, D., Zhao, L., Lin, Z., Qin, T., Bian, J. & Liu, T. Fully pa- rameterized quantile function for distributional reinforcement learning. Advances In Neural Information Processing Systems.32(2019)

work page 2019

[7] [7]

& Abbeel, P

Ho, J., Jain, A. & Abbeel, P. Denoising diffusion probabilistic models. Advances In Neural Information Processing Systems.33pp. 6840- 6851 (2020)

work page 2020

[8] [8]

& Others Deepmind control suite.ArXiv Preprint ArXiv:1801.00690

Tassa, Y ., Doron, Y ., Muldal, A., Erez, T., Li, Y ., Casas, D., Budden, D., Abdolmaleki, A., Merel, J., Lefrancq, A. & Others Deepmind control suite.ArXiv Preprint ArXiv:1801.00690. (2018)

arXiv 2018