Directed Exploration in Black-Box Optimization for Multi-Objective Reinforcement Learning

Usually, real-world problems involve the optimization of multiple, possibly conflicting, objectives. These problems may be addressed by Multi-objective Reinforcement learning (MORL) techniques. MORL is a generalization of standard Reinforcement Learning (RL) where the single reward signal is extended to multiple signals, in particular, one for each objective. MORL is the process of learning policies that optimize multiple objectives simultaneously. In these problems, the use of directional/gradient information can be useful to guide the exploration to better and better behaviors. However, traditional policy-gradient approaches have two main drawbacks: they require the use of a batch of episodes to properly estimate the gradient information (reducing in this way the learning speed), and they use stochastic policies which could have a disastrous impact on the safety of the learning system. In this paper, we present a novel population-based MORL algorithm for problems in which the underlying objectives are reasonably smooth. It presents two main characteristics: fast computation of the gradient information for each objective through the use of neighboring solutions, and the use of this information to carry out a geometric partition of the search space and thus direct the exploration to promising areas. Finally, the algorithm is evaluated and compared to policy gradient MORL algorithms on different multi-objective problems: the water reservoir and the biped walking problem (the latter both on simulation and on a real robot).