We introduce Heterogeneous Agent Collaborative Reinforcement Learning (HACRL), a new Reinforcement Learning from Verifiable Reward (RLVR) problem that addresses the inefficiencies of isolated multi-agent on-policy optimization. HACRL enables collaborative optimization with independent execution: heterogeneous agents share verified rollouts during training to mutually improve, while operating independently at inference time. Unlike LLM-based multi-agent reinforcement learning (MARL), HACRL does not require coordinated deployment, and unlike on-/off-policy distillation, it enables bidirectional mutual learning among heterogeneous agents rather than one-directional homogeneous teacher-to-student transfer. Building on this problem, we propose HACPO, a collaborative RL algorithm that enables principled rollout sharing to maximize sample utilization and cross-agent knowledge transfer. To mitigate capability discrepancies and policy distribution shifts, HACPO introduces four tailored mechanisms with theoretical guarantees on unbiased advantage estimation. Extensive experiments across diverse heterogeneous model combinations and reasoning benchmarks show that HACPO consistently improves all participating agents, outperforming GSPO with double rollouts by an average of 3.6% while using only half the rollout cost.
Figures & tables
Figure 1: In HACPO, shared rollouts from multiple heterogeneous agents are leveraged for collaborative training. Built upon vanilla RL Optimization, HACPO introduces four algorithmic innovations to mitigate capability and policy distribution discrepancy.
Model
MATH-500
MATH
GSM8K
AIME2025
AMC23
Minerva
Olympiad
AVG
Qwen3-4B and Qwen3-4B-Instruct ( Heterogeneous State )
4B
0.802
0.836
0.907
0.335
0.65
0.39
0.524
0.635
4B (GRPO)
0.88
0.889
0.918
0.582
0.775
0.386
0.592
0.717
4B (GSPO)
0.854
0.87
0.925
0.485
0.675
0.412
0.564
0.684
4B (GSPO × 2)
0.876
0.875
0.923
0.522
0.675
0.39
0.579
0.691
4B (Naive)
0.728
0.737
0.891
0.378
0.6
0.353
0.394
0.583
Table 1: Main results across three heterogeneity settings (state, size and model). We compare our method against Standard Single-Agent Baselines (GRPO, GSPO), a Resource-Equivalent Baseline (GSPO × 2) and a Naive multi-agent rollout share baseline(Naive). The content in the brackets represents a comparison with GSPO × 2.
Figure 2: Training Curves of HACPO, GSPO and GSPO × 2
Model
MATH-500
MATH
GSM8K
AIME2025
AMC23
Minerva
Olympiad
AVG
1.7B(HACPO - Adv)
0.696
0.659
0.825
0.126
0.375
0.261
0.313
0.465
1.7B(HACPO)
0.69
0.674
0.822
0.225
0.45
0.279
0.314
0.493
4B(HACPO - Adv)
0.774
0.771
0.912
0.308
0.55
0.348
0.442
0.586
4B(HACPO)
0.808
0.801
0.903
0.267
0.575
0.386
0.467
0.601
Table 2: Ablation of Advantage Estimator
Model
MATH-500
math
gsm8k
aime2025
ACM23
minerva
olympiad
AVG
1.7B(HACPO - ω )
0.666
0.657
0.806
0.105
0.425
0.25
0.324
0.462
1.7B(HACPO)
0.69
0.674
0.822
0.225
0.45
0.279
0.314
0.493
4B(HACPO - ω )
0.803
0.797
0.902
0.261
0.55
0.401
0.475
0.6
4B(HACPO)
0.808
0.801
0.903
0.267
0.575
0.386
0.467
0.601
Table 3: Ablation of Model Capabilities Discrepancy Coefficient
Figure 3: Ablation of Stepwise Clipping (MATH500)
Appendix figures & tables6 assets
Supplementary material from the paper’s appendix.
Appendix
Model Combination
α
1- δ
δstep
Qwen3-4B and Qwen3-4B-Instruct
3.0
0.8
0.01
Qwen3-1.7B-Base and Qwen3-4B-Base
1.0
0.8
0.025
Qwen3-4B-Base and Qwen3-8B-Base
3.0
0.8
0.025
Llama3.2-1B-Instruct and Llama3.2-3B-Instruct
1.0
0.9
0.01
Qwen3-1.7B-Base and Llama3.2-1B-Instruct
1.0
0.8
0.025
Qwen3-4B-Base and Llama3.2-3B-Instruct
1.0
0.8
0.025
Appendix
Table 4: The Details of Hyperparameter
Model
mean
max
min
range
shomo
1.00002
1.00020
0.99960
0.00060
shete
0.89550
0.93615
0.86198
0.07417
Appendix
Table 5: st,i(1,1) and st,i(1,2) of Qwen3-1.7B-Base in all steps
Cooperative tasks in Multi-Agent Reinforcement Learning (MARL) require agents to collectively maximize a shared return. Under the Centralized Training with Decentralized Execution (CTDE) paradigm, policy gradients have remained difficult to compute directly. Prior methods largely follow two approaches: independent factorized updates with centralized critics, which lack general joint-improvement guarantees without value decomposition assumptions, or alternating best-response updates, which can converge to suboptimal Nash Equilibria. In this paper, we show the joint policy gradient admits an exact decentralized decomposition of per-agent terms, each formed from per-agent score functions and decentralized critics. Based on this decomposition, we develop Agent-Chained Policy Optimization (ACPO), where actors are trained independently, with their updates together constituting a single step on the joint policy gradient. Central to this result is a serialized view of the simultaneous joint decision in which agents commit actions one at a time, each conditioning on a belief over preceding actions. The belief acts as the coordination mechanism which ties the independent per-agent updates into a joint gradient step. We evaluate ACPO on Multi-Robot Warehouse, SMACv2, and MA-MuJoCo, where it outperforms strong baselines, with the gap widening as the number of agents grows.
Daiki E. Matsunaga, Junho Na, Tri Wahyu Guntara +4
To improve generalization and resilience in human-robot collaboration (HRC), robots must contend with diverse combinations of human behaviors and contexts, motivating multi-agent reinforcement learning (MARL). However, inherent heterogeneity between robots and humans creates a rationality gap (RG), where decentralized policy updates deviate from cooperative joint optimization. The resulting learning problem is a general-sum differentiable game, so independent policy-gradient updates can oscillate or diverge without added structure. We propose heterogeneous-agent Lyapunov policy optimization (HALO), a framework that stabilizes decentralized MARL by enforcing Lyapunov-based contraction in policy-parameter space. Unlike Lyapunov-based safe RL, which targets state/trajectory constraints in constrained Markov decision processes, HALO uses Lyapunov certification to stabilize decentralized policy learning. HALO rectifies decentralized gradients via optimal quadratic projections, ensuring monotonic contraction of RG and enabling effective exploration of open-ended interaction spaces. Extensive simulations and real-world humanoid-robot experiments show that this certified stability improves generalization and robustness in collaborative corner cases. Our project website is available at https://HaoZhang-THU.github.io/HALO/.
Hao Zhang, Yaru Niu, Yikai Wang +2
ETAIC Lab, Department of Electrical Engineering, University of Texas at Arlington, USA · Safe AI Lab, Department of Mechanical Engineering, Carnegie Mellon University, USA.
Cooperative Multi-Agent Reinforcement Learning (MARL) solves complex tasks that require coordination from multiple agents, but is often limited to either local (independent learning) or global (centralized learning) perspectives. In this paper, we introduce a novel sequential training scheme and MARL architecture, which learns from multiple perspectives on different hierarchy levels. We propose the Hierarchical Lead Critic (HLC) - inspired by natural emerging distributions in team structures, where following high-level objectives combines with low-level execution. HLC demonstrates that introducing multiple hierarchies, leveraging local and global perspectives, can lead to improved performance with high sample efficiency and robust policies. Experimental results conducted on cooperative, non-communicative, and partially observable MARL benchmarks demonstrate that HLC outperforms single hierarchy baselines and scales robustly with increasing amounts of agents and difficulty.