Joint Optimization of Concave Scalarized Multi-Objective Reinforcement Learning with Policy Gradient Based Algorithm

Many engineering problems have multiple objectives, and the overall aim is to optimize a non-linear function of these objectives. In this paper, we formulate the problem of maximizing a non-linear concave function of multiple long-term objectives. A policy-gradient based model-free algorithm is proposed for the problem. To compute an estimate of the gradient, an asymptotically biased estimator is proposed. The proposed algorithm is shown to achieve convergence to within an ε of the global optima after sampling O(M4 σ2/(1-γ)8ε4) trajectories where γ is the discount factor and M is the number of the agents, thus achieving the same dependence on ε as the policy gradient algorithm for the standard reinforcement learning.