Symmetric Behavior Regularization via Taylor Expansion of Symmetry

This paper introduces symmetric divergences to behavior regularization policy optimization (BRPO) to establish a novel offline RL framework. Existing methods focus on asymmetric divergences such as KL to obtain analytic regularized policies and a practical minimization objective. We show that symmetric divergences do not permit an analytic policy as regularization and can incur numerical issues as loss. We tackle these challenges by the Taylor series of $f$-divergence. Specifically, we prove that an analytic policy can be obtained with a finite series. For loss, we observe that symmetric divergences can be decomposed into an asymmetry and a conditional symmetry term, Taylor-expanding the latter alleviates numerical issues. Summing together, we propose Symmetric $f$ Actor-Critic (S$f$-AC), the first practical BRPO algorithm with symmetric divergences. Experimental results on distribution approximation and MuJoCo verify that S$f$-AC performs competitively.