Bi-level Actor-Critic for Multi-agent Coordination

Coordination is one of the essential problems in multi-agent systems. Typically multi-agent reinforcement learning (MARL) methods treat agents equally and the goal is to solve the Markov game to an arbitrary Nash equilibrium (NE) when multiple equilibra exist, thus lacking a solution for NE selection. In this paper, we treat agents \emph{unequally} and consider Stackelberg equilibrium as a potentially better convergence point than Nash equilibrium in terms of Pareto superiority, especially in cooperative environments. Under Markov games, we formally define the bi-level reinforcement learning problem in finding Stackelberg equilibrium. We propose a novel bi-level actor-critic learning method that allows agents to have different knowledge base (thus intelligent), while their actions still can be executed simultaneously and distributedly. The convergence proof is given, while the resulting learning algorithm is tested against the state of the arts. We found that the proposed bi-level actor-critic algorithm successfully converged to the Stackelberg equilibria in matrix games and find an asymmetric solution in a highway merge environment

Independent Learning Approaches: Overcoming Multi-Agent Learning Pathologies In Team-Games

Deep Neural Networks enable Reinforcement Learning (RL) agents to learn behaviour policies directly from high-dimensional observations. As a result, the field of Deep Reinforcement Learning (DRL) has seen a great number of successes. Recently the sub-field of Multi-Agent DRL (MADRL) has received an increased amount of attention. However, considerations are required when using RL in Multi-Agent Systems. For instance Independent Learners (ILs) lack the convergence guarantees of many single-agent RL approaches, even in domains that do not require a MADRL approach. Furthermore, ILs must often overcome a number of learning pathologies to converge upon an optimal joint-policy. Numerous IL approaches have been proposed to facilitate cooperation, including hysteretic Q-learning (Matignon et al., 2007) and leniency (Panait et al., 2006). Recently LMRL2, a variation of leniency, proved robust towards a number of pathologies in low-dimensional domains, including miscoordination, relative overgeneralization, stochasticity, the alter-exploration problem and the moving target problem (Wei and Luke, 2016). In contrast, the majority of work on ILs in MADRL focuses on an amplified moving target problem, caused by neural networks being trained with potentially obsolete samples drawn from experience replay memories. In this thesis we combine advances from research on ILs with DRL algorithms. However, first we evaluate the robustness of tabular approaches along each of the above pathology dimensions. Upon identifying a number of weaknesses that prevent LMRL2 from consistently converging upon optimal joint-policies we propose a new version of leniency, Distributed-Lenient Q-learning (DLQ). We find DLQ delivers state of the art performances in strategic-form and Markov games from Multi-Agent Reinforcement Learning literature. We subsequently scale leniency to MADRL, introducing Lenient (Double) Deep Q-Network (LDDQN). We empirically evaluate LDDQN with extensions of the Cooperative Multi-Agent Object Transportation Problem (Bucsoniu et al., 2010), finding that LDDQN outperforms hysteretic deep Q-learners in domains with multiple dropzones yielding stochastic rewards. Finally, to evaluate deep ILs along each pathology dimension we introduce a new MADRL environment: the Apprentice Firemen Game (AFG). We find lenient and hysteretic approaches fail to consistently learn near optimal joint-policies in the AFG. To address these pathologies we introduce Negative Update Intervals-DDQN (NUI-DDQN), a MADRL algorithm which discards episodes yielding cumulative rewards outside the range of expanding intervals. NUI-DDQN consistently gravitates towards optimal joint-policies in deterministic and stochastic reward settings of the AFG, overcoming the outlined pathologies