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In a discounted reward Markov Decision Process (MDP), the objective is to find the optimal value function, i.e., the value function corresponding to an optimal policy. This problem reduces to solving a functional equation known as the Bellman equation and a fixed point iteration scheme known as the value iteration is utilized to obtain the solution. In literature, a successive over-relaxation based value iteration scheme is proposed to speed-up the computation of the optimal value function. The speed-up is achieved by constructing a modified Bellman equation that ensures faster convergence to the optimal value function. However, in many practical applications, the model information is not known and we resort to Reinforcement Learning (RL) algorithms to obtain optimal policy and value function. One such popular algorithm is Q-learning. In this paper, we propose Successive Over-Relaxation (SOR) Q-learning. We first derive a modified fixed point iteration for SOR Q-values and utilize stochastic approximation to derive a learning algorithm to compute the optimal value function and an optimal policy. We then prove the almost sure convergence of the SOR Q-learning to SOR Q-values. Finally, through numerical experiments, we show that SOR Q-learning is faster compared to the standard Q-learning algorithm.

In this work, we consider the problem of computing optimal actions for Reinforcement Learning (RL) agents in a co-operative setting, where the objective is to optimize a common goal. However, in many real-life applications, in addition to optimizing the goal, the agents are required to satisfy certain constraints specified on their actions. Under this setting, the objective of the agents is to not only learn the actions that optimize the common objective but also meet the specified constraints. In recent times, the Actor-Critic algorithm with an attention mechanism has been successfully applied to obtain optimal actions for RL agents in multi-agent environments. In this work, we extend this algorithm to the constrained multi-agent RL setting. The idea here is that optimizing the common goal and satisfying the constraints may require different modes of attention. By incorporating different attention modes, the agents can select useful information required for optimizing the objective and satisfying the constraints separately, thereby yielding better actions. Through experiments on benchmark multi-agent environments, we show the effectiveness of our proposed algorithm.

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