Scaling reinforcement learning to tens of thousands of parallel environments requires overcoming the limited exploration capacity of a single policy. Ensemble-based policy gradient methods, which employ multiple policies to collect diverse samples, have recently been proposed to promote exploration. However, merely broadening the exploration space does not always enhance learning capability, since excessive exploration can reduce exploration quality or compromise training stability. In this work, we theoretically analyze the impact of inter-policy diversity on learning efficiency in policy ensembles, and propose Coupled Policy Optimization which regulates diversity through KL constraints between policies. The proposed method enables effective exploration and outperforms strong baselines such as SAPG, PBT, and PPO across multiple tasks, including challenging dexterous manipulation, in terms of both sample efficiency and final performance. Furthermore, analysis of policy diversity and effective sample size during training reveals that follower policies naturally distribute around the leader, demonstrating the emergence of structured and efficient exploratory behavior. Our results indicate that diverse exploration under appropriate regulation is key to achieving stable and sample-efficient learning in ensemble policy gradient methods. Project page at https://naoki04.github.io/paper-cpo/ .
Figures & tables
Figure 1: Appropriately controlled policy diversity improves the learning efficiency of ensemble RL in large-scale environments. (a) The leader-follower approach is an agent ensemble method that aggregates samples from multiple followers into a leader policy. (b) Misalignment between policies may causes a decline in sample efficiency and training stability. (c) Our method introduces KL divergence constraints to keep followers distributed around the leader, as well as adversarial reward to prevent policies overconcentration.
Task
PPO
PBT
SAPG
CPO (ours)
ShadowHand
10661 ± 1050
10294 ± 1728
12882 ± 343
13762 ± 414
AllegroHand
10439 ± 1282
13239 ± 239
11989 ± 817
14421 ± 885
Regrasping
0.76 ± 0.99
35.26 ± 2.82
37.20 ± 0.65
37.44 ± 1.21
Reorientation
1.04 ± 0.98
2.92 ± 4.27
38.79 ± 1.66
43.75 ± 0.65
Throw
15.69 ± 3.34
19.08 ± 1.02
22.51 ± 1.15
21.69 ± 2.44
Two-Arms Reorientation
1.41 ± 0.80
26.43 ± 11.12
5.11 ± 3.41
35.30 ± 2.77
Table 1: Performance on dexterous manipulation tasks after 2×1010 environment steps of training. Bold indicates the method with the highest average performance for each task, as well as those not significantly different from it, as determined by a t-test (p > 0.05).
Figure 2: Comparison of algorithm performance across ten robotic tasks. Learning curves across six dexterous manipulation, two gripper-based manipulation and two locomotion tasks comparing CPO to SAPG, PBT, and PPO. CPO consistently achieves higher sample efficiency and final performance, particularly in ShadowHand, AllegroHand, AllegroKukaReorientation, Two-Arms Reorientation, FrankaCubePush and Stack.
Figure 3: Training Curves from the ablation study with different λf .
Task
Method
Mean IS Ratio Deviation ( ↓ )
ESS Rate ( ↑ )
ShadowHand
SAPG
0.889
0.0223
CPO(0.5)
0.403
0.763
CPO(0.2)
0.297
0.871
CPO(0.1)
0.222
0.923
CPO(0.05)
0.187
0.941
AllegroKuka Reorientation
SAPG
0.608
0.110
Table 2: Mean IS Ratio Deviation and Overall ESS Rate at 5×109 environment steps. The reported values are computed by averaging over a window of eleven iterations.
Figure 4: Comparison of the transition of KL divergence between agents with different algorithms. Each heatmap shows the KL divergence between the leader and follower policies during training. Row i , column j indicates the forward KL from agent i to agent j . The white circle marks the agent closest from each follower, excluding itself. SAPG often shows misaligned followers, while our method keeps them well-distributed around the leader.
Appendix figures & tables9 assets
Supplementary material from the paper’s appendix.
Appendix
Figure 5: Effects of KL constraint and adversarial reward on performance. Learning curves on ShadowHand and AllegroHand tasks for three variants: full CPO (red), CPO without adversarial reward (blue), and CPO without KL constraint (green).
Figure 6: Discriminator loss under different settings. Discriminator loss during training on the ShadowHand and AllegroHand tasks for three variants: full CPO (red), CPO without adversarial reward (blue), and CPO without KL constraint (green).
Figure 7: Comparison of the transition of KL divergence between agents with different settings. Each heatmap shows the KL divergence between the leader and follower policies during training. Row i , column j indicates the forward KL from agent i to agent j . The white circle marks the agent closest from each follower, excluding itself.
Hyperparameter
Shadow Hand
Allegro Hand
Common Hyperparameters (SAPG and CPO)
Discount factor, γ
0.99
0.99
GAE smoothing factor, τ
0.95
0.95
MLP hidden layers
[512, 512, 256, 128]
[512, 256, 128]
Learning rate
5e-4
5e-4
KL threshold for LR update
0.016
0.016
Appendix
Table 3: Training hyperparameters for Shadow Hand and Allegro Hand. The upper section lists hyperparameters shared by SAPG and CPO, while the lower section lists those specific to CPO.
Hyperparameter
Regrasping
Reorientation / Two-Arms Reorientation
Throw
Common Hyperparameters (SAPG and CPO)
Discount factor, γ
0.99
0.99
0.99
GAE smoothing factor, τ
0.95
0.95
0.95
LSTM hidden units
768
768
768
MLP hidden layers
[768, 512, 256]
[768, 512, 256]
[768, 512, 256]
Learning rate
1e-4
1e-4
1e-4
Appendix
Table 4: Training hyperparameters for hand-arm dexterous manipulation tasks: AllegroKuka Regrasping, Reorientation, Throw and Two-Arms Reorientation. The upper section lists hyperparameters shared by SAPG and CPO, while the lower section lists those specific to CPO.
Hyperparameter
FrankaCubePush
FrankaCubeStack
Common Hyperparameters (SAPG and CPO)
Discount factor, γ
0.99
0.99
GAE smoothing factor, τ
0.95
0.95
LSTM hidden units
256
256
MLP hidden layers
[256, 128, 64]
[256, 128, 64]
Learning rate
5e-4
5e-4
Appendix
Table 5: Training hyperparameters for gripper-based manipulation tasks: FrankaCubePush and FrankaCubeStack. The upper section lists hyperparameters shared by SAPG and CPO, while the lower section lists those specific to CPO.
Hyperparameter
Humanoid
Anymal
Common Hyperparameters (SAPG and CPO)
Discount factor, γ
0.99
0.99
GAE smoothing factor, τ
0.95
0.95
MLP hidden layers
[768, 512, 256]
[768, 512, 256]
Learning rate
5e-4
3e-4
KL threshold for LR update
0.008
0.008
Appendix
Table 6: Training hyperparameters for locomotion tasks: Humanoid and Anymal. The upper section lists hyperparameters shared by SAPG and CPO, while the lower section lists those specific to CPO.
Figure 8: Comparison of SAPG with and without entropy regularization. The values in parentheses indicates the entropy coefficients. The effect of entropy regularization on learning performance varies across tasks.
Figure 9: Comparison of the transition of KL divergence in SAPG with and without entropy regularization. Each heatmap shows the KL divergence between the leader and follower policies during training. Row i , column j indicates the forward KL from agent i to agent j . The white circle marks the agent closest from each follower, excluding itself. It is demonstrated that entropy regularization causes follower’s misalignment from the leader policy.
We identify a new dimension for enhancing rollout diversity in Group Relative Policy Optimization (GRPO) for LLMs. While GRPO relies on diverse rollouts, prevailing strategies primarily increase diversity by injecting more token-level randomness, which may introduce step-wise noise and lead to incoherent trajectories. We uncover that smaller models within the same model family inherently exhibit higher policy-level diversity, indicated by their superior pass@k relative to larger counterparts as sample counts increase. Unlike token-level noise, this diversity is temporally correlated, preserves logical consistency, and provides structured exploration signals for gradient estimation. We thus propose S2L-PO (Small-to-Large Policy Optimization), a framework that leverages fixed small models as natural explorers to train larger models. To balance exploration and exploitation, we design a progressive annealing strategy that transitions from offline small-model rollouts to the large learner's own sampling. This shift elegantly avoids mid-training performance drops caused by the small model's capacity limits, achieving faster convergence and unlocking a higher performance ceiling. S2L-PO improves accuracy on diverse mathematical reasoning benchmarks (e.g., +8.8% on AIME 24 using a 1.7B explorer to guide the 8B model) while reducing rollout compute.
Yiming Ren, Yiran Xu, Zicheng Lin +8
Tsinghua University · Shanghai AI Laboratory · The Chinese University of Hong Kong +1
In reinforcement learning (RL), agents benefit from exploration only because they repeatedly encounter similar states: trying different actions can improve performance or reduce uncertainty; without such retries, a greedy policy is optimal. We formalize this intuition with ReMax, an objective that evaluates a policy by the expected maximum return over M samples, where M is a positive integer, while accounting for return uncertainty. Optimizing this objective induces stochastic exploration as an emergent property, without explicit bonus terms. For efficient policy optimization, we derive a new policy-gradient formulation for ReMax and introduce ReMax PPO (RePPO), a PPO variant that optimizes ReMax while generalizing the discrete retry count M to a continuous parameter m>0, enabling fine-grained control of exploration. Empirically, RePPO promotes exploration, without any explicit exploration bonuses, on the MinAtar and Craftax benchmarks.
Soichiro Nishimori, Paavo Parmas, Sotetsu Koyamada +4
The University of Tokyo, Tokyo, Japan · Kobe University, Kobe, Japan · Kyoto University, Kyoto, Japan +3
The goal of Quality-Diversity Reinforcement Learning (QD-RL) is to find a population of high-performing policies that solve a decision-making problem in diverse ways. Despite recent progress, QD-RL methods predominantly rely on evolutionary operators--including black-box optimizers, mutations, and crossovers--to facilitate exploration and induce diversity. Scaling these methods becomes increasingly costly as policies and behavior spaces grow larger. Building on the Soft QD view of quality-diversity optimization, we introduce Repulsive Population Policy Optimization (RePPO), which adapts PPO to jointly optimize a compact population of diverse, high-quality policies using a population-dependent, dynamically shaped reward. On standard continuous-control tasks, RePPO achieves a strong quality-diversity tradeoff compared with state-of-the-art QD-RL methods. Ablations further characterize this tradeoff by examining how each component affects individual quality and collective diversity. To assess RePPO's scalability, we extend our evaluation to learning from pixels and fine-tuning large language models. In pixel-based tasks, where large policies make most traditional QD-RL methods infeasible, RePPO maintains quality on par with standard PPO while achieving substantially higher diversity. Its successful application to language model fine-tuning further demonstrates, for the first time, that QD-RL methods can scale to this domain. Together, these results show that directly optimizing compact populations with RePPO provides a scalable approach to QD-RL across increasingly complex domains.
Saeed Hedayatian, Harsh Shah, Celine Mneimneh +1
Thomas Lord Department of Computer Science, University of Southern California, Los Angeles, USA · Independent Researcher