Why Goal-Conditioned Reinforcement Learning Works: Relation to Dual Control

Goal-conditioned reinforcement learning (RL) concerns the problem of training an agent to maximize the probability of reaching target goal states. This paper presents an analysis of the goal-conditioned setting based on optimal control. In particular, we derive an optimality gap between more classical, often quadratic, objectives and the goal-conditioned reward, elucidating the success of goal-conditioned RL and why classical ``dense'' rewards can falter. We then consider the partially observed Markov decision setting and connect state estimation to our probabilistic reward, making the goal-conditioned reward well suited to dual control problems. The advantages of goal-conditioned policies are validated on nonlinear and uncertain environments using both RL and predictive control techniques.