Actively Learning Reinforcement Learning: A Stochastic Optimal Control Approach

In this paper we propose a framework towards achieving two intertwined objectives: (i) equipping reinforcement learning with active exploration and deliberate information gathering, such that it regulates state and parameter uncertainties resulting from modeling mismatches and noisy sensory; and (ii) overcoming the huge computational cost of stochastic optimal control. We approach both objectives by using reinforcement learning to attain the stochastic optimal control law. On one hand, we avoid the curse of dimensionality prohibiting the direct solution of the stochastic dynamic programming equation. On the other hand, the resulting stochastic control inspired reinforcement learning agent admits the behavior of a dual control, namely, caution and probing, that is, regulating the state estimate together with its estimation quality. Unlike exploration and exploitation, caution and probing are employed automatically by the controller in real-time, even after the learning process is concluded. We use the proposed approach on a numerical example of a model that belongs to an emerging class in system identification. We show how, for the dimensionality of the stochastic version of this model, Dynamic Programming is prohibitive, Model Predictive Control requires an expensive nonlinear optimization, and a Linear Quadratic Regulator with the certainty equivalence assumption leads to poor performance and filter divergence, all contrasting our approach which is shown to be both: computationally convenient, stabilizing and of an acceptable performance.