Abstract: Learning expressive stochastic policies instead of deterministic ones has been proposed to achieve better stability, sample complexity and robustness. Notably, in Maximum Entropy reinforcement learning (MaxEnt RL), the policy is modeled as an expressive energy-based model (EBM) over the Q-values. However, this formulation requires the estimation of the entropy of such EBM distributions which is an open problem. To address this, previous MaxEnt RL methods either implicitly estimate the entropy, yielding high computational complexity and variance (SQL), or follow a variational inference approach that fits simplified distributions (e.g., Gaussian) for tractability (SAC). We propose Sein Soft Actor-Critic (S$^2$AC), a MaxEnt RL algorithm that learns expressive policies without compromising efficiency. S$^2$AC uses parameterized Stein Variational Gradient Descent (SVGD) as the underlying policy. At the core of S$^2$AC is a new solution to the above open challenge of entropy computation for EBMs. Our entropy formula is computationally efficient and only depends on first-order derivatives and vector products. Empirical results show that S$^2$AC yields more optimal solutions to the MaxEnt objective than SQL and SAC in the multi-goal environment, and outperforms SAC and SQL on the MuJoCo benchmark. Our code is available at: https://anonymous.4open.science/r/Stein-Soft-Actor-Critic/