Closing the Gap between TD Learning and Supervised Learning with $Q$-Conditioned Maximization

Recently, supervised learning (SL) methodology has emerged as an effective approach for offline reinforcement learning (RL) due to their simplicity, stability, and efficiency. However, recent studies show that SL methods lack the trajectory stitching capability, typically associated with temporal difference (TD)-based approaches. A question naturally surfaces: $\mathit{\text{How}}\mathit{\text{can}}\mathit{\text{we}}\mathit{\text{endow}}\mathit{\text{SL}}\mathit{\text{methods}}\mathit{\text{with}}\mathit{\text{stitching}}\mathit{\text{capability}}\mathit{\text{and}}\mathit{\text{close}}\mathit{\text{its}}\mathit{\text{performance}}\mathit{\text{gap}}\mathit{\text{with}}\mathit{\text{TD}}\mathit{\text{learning?}}$ To answer this question, we introduce $Q$-conditioned maximization supervised learning for offline goal-conditioned RL, which enhances SL with the stitching capability through $Q$-conditioned policy and $Q$-conditioned maximization. Concretely, we propose $\mathbf{\text{G}}$oal-$\mathbf{\text{C}}$onditioned $\mathit{\text{Rein}}$forced $\mathbf{\text{S}}$upervised $\mathbf{\text{L}}$earning ($\mathbf{\text{GC}}\mathit{\text{Rein}}\mathbf{\text{SL}}$), which consists of (1) estimating the $Q$-function by Normalizing Flows from the offline dataset and (2) finding the maximum $Q$-value within the data support by integrating $Q$-function maximization with Expectile Regression. In inference time, our policy chooses optimal actions based on such a maximum $Q$-value. Experimental results from stitching evaluations on offline RL datasets demonstrate that our method outperforms prior SL approaches with stitching capabilities and goal data augmentation techniques.