Trust region methods rigorously enabled reinforcement learning (RL) agents to learn monotonically improving policies, leading to superior performance on a variety of tasks. Unfortunately, when it comes to multi-agent reinforcement learning (MARL), the property of monotonic improvement may not simply apply; this is because agents, even in cooperative games, could have conflicting directions of policy updates. As a result, achieving a guaranteed improvement on the joint policy where each agent acts individually remains an open challenge. In this paper, we extend the theory of trust region learning to MARL. Central to our findings are the multi-agent advantage decomposition lemma and the sequential policy update scheme. Based on these, we develop Heterogeneous-Agent Trust Region Policy Optimisation (HATPRO) and Heterogeneous-Agent Proximal Policy Optimisation (HAPPO) algorithms. Unlike many existing MARL algorithms, HATRPO/HAPPO do not need agents to share parameters, nor do they need any restrictive assumptions on decomposibility of the joint value function. Most importantly, we justify in theory the monotonic improvement property of HATRPO/HAPPO. We evaluate the proposed methods on a series of Multi-Agent MuJoCo and StarCraftII tasks. Results show that HATRPO and HAPPO significantly outperform strong baselines such as IPPO, MAPPO and MADDPG on all tested tasks, therefore establishing a new state of the art.

Trust Region Policy Optimisation in Multi-Agent Reinforcement Learning.

The adoption of the Fifth Generation (5G) and beyond 5G networks is driving the demand for learning approaches that enable users to co-exist harmoniously in a multi-user distributed environment. Although resource-constrained, the Cognitive Radio (CR) has been identified as a key enabler of distributed 5G and beyond networks due to its cognitive abilities and ability to access idle spectrum opportunistically. Reinforcement learning is well suited to meet the demand for learning in 5G and beyond 5G networks because it does not require the learning agent to have prior information about the environment in which it operates. Intuitively, CRs should be enabled to implement reinforcement learning to efficiently gain opportunistic access to spectrum and co-exist with each other. However, the application of reinforcement learning is straightforward in a single-agent environment and complex and resource intensive in a multi-agent and multi-objective learning environment. In this paper, (1) we present a brief history and overview of reinforcement learning and its limitations; (2) we provide a review of recent multi-agent learning methods proposed and multi-agent learning algorithms applied in Cognitive Radio (CR) networks; and (3) we further present a novel framework for multi-CR reinforcement learning and conclude with a synopsis of future research directions and recommendations. 

/pdf/towards-a-multi-agent-reinforcement-learning-approach-for-59kt3uqh.pdf

Towards a multi-agent reinforcement learning approach for joint sensing and sharing in cognitive radio networks

Constructing earth-fixed cells with low-earth orbit (LEO) satellites in non-terrestrial networks (NTNs) has been the most promising paradigm to enable global coverage. The limited computing capabilities on LEO satellites however render tackling resource optimization within a short duration a critical challenge. Although the sufficient computing capabilities of the ground infrastructures can be utilized to assist the LEO satellite, different time-scale control cycles and coupling decisions between the space- and ground-segments still obstruct the joint optimization design for computing agents at different segments. To address the above challenges, in this paper, a multi-time-scale deep reinforcement learning (DRL) scheme is developed for achieving the radio resource optimization in NTNs, in which the LEO satellite and user equipment (UE) collaborate with each other to perform individual decision-making tasks with different control cycles. Specifically, the UE updates its policy toward improving value functions of both the satellite and UE, while the LEO satellite only performs finite-step rollout for decision-makings based on the reference decision trajectory provided by the UE. Most importantly, rigorous analysis to guarantee the performance convergence of the proposed scheme is provided. Comprehensive simulations are conducted to justify the effectiveness of the proposed scheme in balancing the transmission performance and computational complexity.

Collaborative Computing in Non-Terrestrial Networks: A Multi-Time-Scale Deep Reinforcement Learning Approach

We present Coordinated Proximal Policy Optimization (CoPPO), an algorithm that extends the original Proximal Policy Optimization (PPO) to the multi-agent setting. The key idea lies in the coordinated adaptation of step size during the policy update process among multiple agents. We prove the monotonicity of policy improvement when optimizing a theoretically-grounded joint objective, and derive a simplified optimization objective based on a set of approximations. We then interpret that such an objective in CoPPO can achieve dynamic credit assignment among agents, thereby alleviating the high variance issue during the concurrent update of agent policies. Finally, we demonstrate that CoPPO outperforms several strong baselines and is competitive with the latest multi-agent PPO method (i.e. MAPPO) under typical multi-agent settings, including cooperative matrix games and the StarCraft II micromanagement tasks.

Coordinated Proximal Policy Optimization

Trust region methods are widely applied in single-agent reinforcement learning problems due to their monotonic performance-improvement guarantee at every iteration. Nonetheless, when applied in multi-agent settings, the guarantee of trust region methods no longer holds because an agent's payoff is also affected by other agents' adaptive behaviors. To tackle this problem, we conduct a game-theoretical analysis in the policy space, and propose a multi-agent trust region learning method (MATRL), which enables trust region optimization for multi-agent learning. Specifically, MATRL finds a stable improvement direction that is guided by the solution concept of Nash equilibrium at the meta-game level. We derive the monotonic improvement guarantee in multi-agent settings and empirically show the local convergence of MATRL to stable fixed points in the two-player rotational differential game. To test our method, we evaluate MATRL in both discrete and continuous multiplayer general-sum games including checker and switch grid worlds, multi-agent MuJoCo, and Atari games. Results suggest that MATRL significantly outperforms strong multi-agent reinforcement learning baselines.

A Game-Theoretic Approach to Multi-Agent Trust Region Optimization.

Trust-region methods are widely used in single-agent reinforcement learning. One advantage is that they guarantee a lower bound of monotonic payoff improvement for policy optimization at each iteration. Nonetheless, when applied in multi-agent settings, such guarantee is lost because an agent's payoff is also determined by other agents' adaptive behaviors. In fact, measuring agents' payoff improvements in multi-agent reinforcement learning (MARL) scenarios is still challenging. Although game-theoretical solution concepts such as Nash equilibrium can be applied, the algorithm (e.g., Nash-Q learning) suffers from poor scalability beyond two-player discrete games. To mitigate the above measurability and tractability issues, in this paper, we propose Multi-Agent Trust Region Learning (MATRL) method. MATRL augments the single-agent trust-region optimization process with the multi-agent solution concept of stable fixed point that is computed at the policy-space meta-game level. When multiple agents learn simultaneously, stable fixed points at the meta-game level can effectively measure agents' payoff improvements, and, importantly, a meta-game representation enjoys better scalability for multi-player games. We derive the lower bound of agents' payoff improvements for MATRL methods, and also prove the convergence of our method on the meta-game fixed points. We evaluate the MATRL method on both discrete and continuous multi-player general-sum games; results suggest that MATRL significantly outperforms strong MARL baselines on grid worlds, multi-agent MuJoCo, and Atari games.

/pdf/multi-agent-trust-region-learning-3sk8n2k5pw.pdf

Multi-Agent Trust Region Learning

Reward shaping (RS) is a powerful method in reinforcement learning (RL) for overcoming the problem of sparse or uninformative rewards. However, RS typically relies on manually engineered shaping-reward functions whose construction is time-consuming and error-prone. It also requires domain knowledge which runs contrary to the goal of autonomous learning. We introduce Reinforcement Learning Optimal Shaping Algorithm (ROSA), an automated RS framework in which the shaping-reward function is constructed in a novel Markov game between two agents. A reward-shaping agent (Shaper) uses switching controls to determine which states to add shaping rewards and their optimal values while the other agent (Controller) learns the optimal policy for the task using these shaped rewards. We prove that ROSA, which easily adopts existing RL algorithms, learns to construct a shaping-reward function that is tailored to the task thus ensuring efficient convergence to high performance policies. We demonstrate ROSA's congenial properties in three carefully designed experiments and show its superior performance against state-of-the-art RS algorithms in challenging sparse reward environments.

Learning to Shape Rewards using a Game of Switching Controls.

Reward shaping (RS) is a powerful method in reinforcement learning (RL) for overcoming the problem of sparse or uninformative rewards. However, RS typically relies on manually engineered shaping-reward functions whose construction is time-consuming and error-prone. It also requires domain knowledge which runs contrary to the goal of autonomous learning. We introduce Reinforcement Learning Optimising Shaping Algorithm (ROSA), an automated RS framework in which the shaping-reward function is constructed in a novel Markov game between two agents. A reward-shaping agent (Shaper) uses switching controls to determine which states to add shaping rewards and their optimal values while the other agent (Controller) learns the optimal policy for the task using these shaped rewards. We prove that ROSA, which easily adopts existing RL algorithms, learns to construct a shaping-reward function that is tailored to the task thus ensuring efficient convergence to high performance policies. We demonstrate ROSA's congenial properties in three carefully designed experiments and show its superior performance against state-of-the-art RS algorithms in challenging sparse reward environments.

Learning to Shape Rewards using a Game of Two Partners.

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A Game-Theoretic Approach to Multi-Agent Trust Region Optimization.

Multi-Agent Trust Region Learning

Learning to Shape Rewards using a Game of Switching Controls.

Learning to Shape Rewards using a Game of Two Partners.