A policy in deep reinforcement learning (RL), either deterministic or stochastic, is commonly parameterized as a Gaussian distribution alone, limiting the learned behavior to be unimodal. However, the nature of many practical decision-making problems favors a multimodal policy that facilitates robust exploration of the environment and thus to address learning challenges arising from sparse rewards, complex dynamics, or the need for strategic adaptation to varying contexts. This issue is exacerbated in continuous control domains where exploration usually takes place in the vicinity of the predicted optimal action, either through an additive Gaussian noise or the sampling process of a stochastic policy. In this paper, we introduce Categorical Policies to model multimodal behavior modes with an intermediate categorical distribution, and then generate output action that is conditioned on the sampled mode. We explore two sampling schemes that ensure differentiable discrete latent structure while maintaining efficient gradient-based optimization. By utilizing a latent categorical distribution to select the behavior mode, our approach naturally expresses multimodality while remaining fully differentiable via the sampling tricks. We evaluate our multimodal policy on a set of DeepMind Control Suite environments, demonstrating that through better exploration, our learned policies converge faster and outperform standard Gaussian policies. Our results indicate that the Categorical distribution serves as a powerful tool for structured exploration and multimodal behavior representation in continuous control.

For on-policy reinforcement learning, discretizing action space for continuous control can easily express multiple modes and is straightforward to optimize. However, without considering the inherent ordering between the discrete atomic actions, the explosion in the number of discrete actions can possess undesired properties and induce a higher variance for the policy gradient estimator. In this paper, we introduce a straightforward architecture that addresses this issue by constraining the discrete policy to be unimodal using Poisson probability distributions. This unimodal architecture can better leverage the continuity in the underlying continuous action space using explicit unimodal probability distributions. We conduct extensive experiments to show that the discrete policy with the unimodal probability distribution provides significantly faster convergence and higher performance for on-policy reinforcement learning algorithms in challenging control tasks, especially in highly complex tasks such as Humanoid. We provide theoretical analysis on the variance of the policy gradient estimator, which suggests that our attentively designed unimodal discrete policy can retain a lower variance and yield a stable learning process.