In recent years, multi-agent cooperation under partially observable conditions has attracted extensive attention. As a general paradigm to deal with such tasks, centralized training with decentralized execution faces the core problem of credit assignment. Value decomposition is a representative method within this paradigm. Through the mixing network, the joint state action-value function is decomposed into multiple local observation action-value functions to realize credit assignment, which performs well in many problems. However, the single point estimation of the mixing network parameters maintained by these methods lacks the representation of uncertainty and is thus difficult to effectively deal with the random factors in the environment, resulting in convergence to the suboptimal strategy. To alleviate this problem, this paper performs Bayesian analysis on the mixing network and proposes a method based on uncertainty for multi-agent credit assignment, which guides the credit assignment by explicitly quantifying the uncertainty of parameters. Considering the complex interactions among agents, this paper utilizes the Bayesian hypernetwork to implicitly model the arbitrary complex posterior distribution of the mixing network parameters, to avoid falling into the local optima by specifying the distribution type a priori. This paper compares and analyzes the performance of representative algorithms on multiple maps in StarCraft multi-agent challenge (SMAC) and verifies the effectiveness of the proposed algorithm.
[1] Bhalla S, Ganapathi Subramanian S, Crowley M. Deep multi agent reinforcement learning for autonomous driving[M]//Advances in Artificial Intelligence. Cham: Springer International Publishing, 2020: 67-78. DOI:10.1007/978-3-030-47358-7_7.
[2] Ye D Y, Zhang M J, Yang Y. A multi-agent framework for packet routing in wireless sensor networks[J]. Sensors (Basel Switzerland), 2015, 15(5):10026-10047. DOI:10.3390/s150510026.
[3] Hüttenrauch M, Šošić A, Neumann G. Guided deep reinforcement learning for swarm systems[EB/OL]. arXiv:1709.06011(2017-09-18)[2022-04-15]. https://arxiv.org/abs/1709.06011.
[4] Berner C, Brockman G, Chan B, et al. Dota 2 with large scale deep reinforcement learning[EB/OL]. arXiv:1912.06680(2019-12-13)[2022-04-15]. https://arxiv.org/abs/1912.06680.
[5] Vinyals O, Ewalds T, Bartunov S, et al. StarCraft II: a new challenge for reinforcement learning[EB/OL]. arXiv:1708.04782(2017-08-16)[2022-04-15]. https://arxiv.org/abs/1708.04782.
[6] Ye D H, Chen G B, Zhang W, et al. Towards playing full moba games with deep reinforcement learning[EB/OL]. arXiv:2011.12692(2020-12-31)[2022-04-15]. https://arxiv.org/abs/2011.12692.
[7] Gupta J K, Egorov M, Kochenderfer M. Cooperative multi-agent control using deep reinforcement learning[M]// Autonomous Agents and Multiagent Systems. Cham: Springer International Publishing, 2017: 66-83. DOI:10.1007/978-3-319-71682-4_5.
[8] Rashid T, Samvelyan M, Witt C S D, et al. QMIX: monotonic value function factorisation for deep multi-agent reinforcement learning[EB/OL]. arXiv: 1803.11485(2018-06-06)[2022-04-15]. https://arxiv.org/abs/1803.11485.
[9] Tan M. Multi-agent reinforcement learning: independent vs. cooperative agents[M]//Machine Learning Proceedings 1993. Amsterdam: Elsevier, 1993: 330-337. DOI:10.1016/b978-1-55860-307-3.50049-6.
[10] Du Y L, Han Lei, Fang M, et al. LIIR: learning individual intrinsic reward in multi-agent reinforcement learning[C/OL]//Advances in Neural Information Processing Systems, Cambridge, MIT Press, 2019: 4405-4416. (2021-06-15)[2022-04-18]. https://dl.acm.org/doi/10.5555/3454287.3454683.
[11] Foerster J, Farquhar G, Afouras T, et al. Counterfactual multi-agent policy gradients[EB/OL]. arXiv: 1705.08926(2017-12-14)[2022-04-15]. https://arxiv.org/abs/1705.08926.
[12] Kraemer L, Banerjee B. Multi-agent reinforcement learning as a rehearsal for decentralized planning[J]. Neurocomputing, 2016, 190: 82-94. DOI:10.1016/j.neucom.2016.01.031.
[13] Mahajan A, Rashid T, Samvelyan M, et al. MAVEN: multi-agent variational exploration[EB/OL]. arXiv: 1910.07483v2(2020-01-20)[2022-04-15]. https://arxiv.org/abs/1910.07483v2.
[14] Oliehoek F A, Spaan M T J, Vlassis N. Optimal and approximate q-value functions for decentralized POMDPs[J]. Journal of Artificial Intelligence Research, 2008, 32: 289-353. DOI:10.1613/jair.2447.
[15] Wang S C, Li B. Implicit posterior sampling reinforcement learning for continuous control[M]// Neural Information Processing. Cham: Springer International Publishing, 2020: 452-460. DOI:10.1007/978-3-030-63833-7_38.
[16] Blundell C, Cornebise J, Kavukcuoglu K, et al. Weight uncertainty in neural network[EB/OL]. arXiv: 1505.05424(2015-05-21)[2022-04-18]. https://arxiv.org/abs/1505.05424.
[17] Krueger D, Huang C W, Islam R, et al. Bayesian hypernetworks[EB/OL]. arXiv: 1710.04759(2018-04-24)[2022-04-15]. https://arxiv.org/abs/1710.04759.
[18] Pawlowski N, Brock A, Lee M C H, et al. Implicit weight uncertainty in neural networks[EB/OL]. arXiv: 1711.01297(2018-05-25)[2022-04-15]. https://arxiv.org/abs/1711.01297.
[19] Oliehoek F A, Amato C. A concise introduction to decentralized POMDPs[M]. Cham: Springer International Publishing, 2016. DOI:10.1007/978-3-319-28929-8.
[20] Wolpert D H, Tumer K. Optimal payoff functions for members of collectives[M]//Modeling Complexity in Economic and Social Systems. WORLD SCIENTIFIC, 2002: 355-369. DOI:10.1142/9789812777263_0020.
[21] Sunehag P, Lever G, Gruslys A, et al. Value-decomposition networks for cooperative multi-agent learning[EB/OL]. arXiv: 1706.05296(2017-06-16)[2022-04-15]. https://arxiv.org/abs/1706.05296.
[22] Wang J H, Zhang Y, Kim T K, et al. Shapley q-value: a local reward approach to solve global reward games[J]. Proceedings of the AAAI Conference on Artificial Intelligence, 2020, 34(5): 7285-7292. DOI:10.1609/aaai.v34i05.6220.
[23] Chalkiadakis G, Elkind E, Wooldridge M. Computational aspects of cooperative game theory[J]. Synthesis Lectures on Artificial Intelligence and Machine Learning, 2011, 5(6): 1-168. DOI:10.2200/s00355ed1v01y201107aim016.
[24] Shapely L S. A value for n-person games[J]. Annals of mathematics studies, 1953, 2: 307-318. DOI:10.7249/P0295.
[25] Son K, Kim D, Kang W J, et al. QTRAN: learning to factorize with transformation for cooperative multi-agent reinforcement learning[EB/OL]. arXiv: 1905.05408v1(2019-05-14)[2022-04-15]. https://arxiv.org/abs/1905.05408v1.
[26] Zhou M, Liu Z Y, Sui P W, et al. Learning implicit credit assignment for cooperative multi-agent reinforcement learning[EB/OL]. arXiv: 2007.02529(2020-10-22)[2022-04-15]. https://arxiv.org/abs/2007.02529.
[27] Wu Z F, Yu C, Ye D H, et al. Coordinated proximal policy optimization[EB/OL]. arXiv: 2111.04051(2021-11-07)[2022-04-15]. https://arxiv.org/abs/2111.04051.
[28] Schulman J, Wolski F, Dhariwal P, et al. Proximal policy optimization algorithms[EB/OL]. arXiv:1707.06347(2017-08-28)[2022-04-15]. https://arxiv.org/abs/1707.06347.
[29] Shao J Z, Zhang H C, Jiang Y C, et al. Credit assignment with meta-policy gradient for multi-agent reinforcement learning[EB/OL]. arXiv: 2102.12957(2021-02-24)[2022-04-15]. https://arxiv.org/abs/2102.12957.
[30] Xu Z W, Hasselt H, Silver D. Meta-gradient reinforcement learning[C/OL]//Advances in International Conference on Neural Information Processing Systems, Cambridge, MIT Press, 2018: 2396-2407. (2018-12-03)[2022-04-18]. https://dl.acm.org/doi/10.5555/3327144.3327166.
[31] Xu Z W, Li D P, Bai Y P, et al. MMD-MIX: value function factorisation with maximum mean discrepancy for cooperative multi-agent reinforcement learning[C]//2021 International Joint Conference on Neural Networks (IJCNN). July 18-22, 2021, Shenzhen, China. IEEE, 2021:1-7. DOI:10.1109/IJCNN52387.2021.9533636.
[32] Bellemare M G, Dabney W, Munos R. A distributional perspective on reinforcement learning[EB/OL]. arXiv: 1707.06887(2017-07-21)[2022-04-15]. https://arxiv.org/abs/1707.06887.
[33] Ahn H, Lee D, Cha S, et al. Uncertainty-based continual learning with adaptive regularization[EB/OL]. arXiv: 1905.11614(2019-11-14)[2022-04-18]. https://arxiv.org/abs/1905.11614.
[34] Lipton Z C, Li X J, Gao J F, et al. BBQ-networks: efficient exploration in deep reinforcement learning for task-oriented dialogue systems[EB/OL]. arXiv: 1608.05081(2017-11-23)[2022-04-15]. https://arxiv.org/abs/1608.05081.
[35] Hinton G E, van Camp D. Keeping the neural networks simple by minimizing the description length of the weights[C]//Proceedings of the sixth annual conference on Computational learning theory - COLT '93. July 26-28, 1993. Santa Cruz, California, USA. New York: ACM Press, 1993: 5-13. DOI:10.1145/168304.168306.
[36] Moerland T M, Broekens J, Jonker C. Efficient exploration with double uncertain value networks[EB/OL]. arXiv:1711.10789(2017-11-29)[2022-04-15]. https://arxiv.org/abs/1711.10789.
[37] Fortunato M, Azar M G, Piot B, et al. Noisy networks for exploration[EB/OL]. arXiv:1706.10295(2019-07-09)[2022-04-15]. https://arxiv.org/abs/1706.10295.
[38] Jiang B, Xu T Y, Wong W H. Approximate bayesian computation with kullback-leibler divergence as data discrepancy[C/OL]//Proceedings of the 21st International Conference on Artificial Intelligence and Statistics (AISTATS) 2018, Lanzarote, Spain. JMLR: Volume 84. 2018: 1711-1721. (2018-03-31)[2022-04-18]. http://proceedings.mlr.press/v84/jiang18a/jiang18a.pdf.
[39] Samvelyan M, Rashid T, de Witt C S, et al. The StarCraft multi-agent challenge[EB/OL]. arXiv: 1902.04043(2019-12-09)[2022-04-18]. https://arxiv.org/abs/1902.04043.
[40] Hu J, Wu H, Harding S A, et al. RIIT: Rethinking the importance of implementation tricks in multi-agent reinforcement learning[EB/OL]. arXiv: 2102.03479(2022-01-01)[2022-04-15]. https://arxiv.org/abs/2102.03479.
[41] Yao M, Yin Q Y, Yu T T, et al. The partially observable asynchronous multi-agent cooperation challenge[EB/OL]// arXiv: 2112.03809(2021-12-07)[2022-04-15]. https://arxiv.org/abs/2112.03809.
