Mirror Descent Actor Critic via Bounded Advantage Learning

Regularization is a core component of recent Reinforcement Learning (RL) algorithms. Mirror Descent Value Iteration (MDVI) uses both Kullback-Leibler divergence and entropy as regularizers in its value and policy updates. Despite its empirical success in discrete action domains and strong theoretical guarantees, the performance of a MDVI-based method does not surpass an entropy-only-regularized method in continuous action domains. In this study, we propose Mirror Descent Actor Critic (MDAC) as an actor-critic style instantiation of MDVI for continuous action domains, and show that its empirical performance is significantly boosted by bounding the actor's log-density terms in the critic's loss function, compared to a non-bounded naive instantiation. Further, we relate MDAC to Advantage Learning by recalling that the actor's log-probability is equal to the regularized advantage function in tabular cases, and theoretically discuss when and why bounding the advantage terms is validated and beneficial. We also empirically explore a good choice for the bounding function, and show that MDAC perfoms better than strong non-regularized and entropy-only-regularized methods with an appropriate choice of the bounding function.

@article{iwaki2025_2502.03854,
  title={ Mirror Descent Actor Critic via Bounded Advantage Learning },
  author={ Ryo Iwaki },
  journal={arXiv preprint arXiv:2502.03854},
  year={ 2025 }
}