A Reinforcement Learning Based Approach for Joint Multi-Agent Decision Making
Reinforcement Learning (RL) is being increasingly applied to optimize complex functions that may have a stochastic component. RL is extended to multi-agent systems to find policies to optimize systems that require agents to coordinate or to compete under the umbrella of Multi-Agent RL (MARL). A crucial factor in the success of RL is that the optimization problem is represented as the expected sum of rewards, which allows the use of backward induction for the solution. However, many real-world problems require a joint objective that is non-linear and dynamic programming cannot be applied directly. For example, in a resource allocation problem, one of the objective is to maximize long-term fairness among the users. This paper addresses and formalizes the problem of joint objective optimization, where not only the sum of rewards of each agent but a function of the sum of rewards of each agent needs to be optimized. The proposed algorithms at the centralized controller aims to learn the policy to dictate the actions for each agent such that the joint objective function based on average per step rewards of each agent is maximized. We propose both model-based and model-free algorithms, where the model-based algorithm is shown to achieve $\Tilde{O}(\sqrt{\frac{K}{T}})$ regret bound for $K$ agents over a time-horizon $T$, and the model-free algorithm can be implemented using deep neural networks. Further, using fairness in cellular base-station scheduling as an example, the proposed algorithms are shown to significantly outperform the state-of-the-art approaches.