The training is stalled if the size of the replay buffer is smaller than the minibatch size, i.e., if |B|< M. Algorithms 3 and 4 show the critic network update and the actor network and uncertainty parameter sampler update, respectively. Although we write the gradient-based update in the form of a mini-batch stochastic gradient update for simplicity, we employ an adaptive approach such as Adam [16]. The update of pk follows the exponential moving average with the momentum (1/Tlast), where Tlast is the number of steps spent in the last episode (Tlast is set to 1000 for the first episode). The reason behind this design choice is as follows. The short episode is a meaning that a bad uncertainty parameter ω is used in the last episode.

Figure 7: Learningcurvesof ATOC (left) and CommNet (right) during learningonpredator -prey.

We demonstrate the smoothing effect of SD3 on the optimization landscape in this section, where experimental setup is the same as in Section 4.1 in the text for the comparative study of SD2 and Experimental details can be found in Section B.2. The performance comparison of SD3 and TD3 is shown in Figure 1(a), where SD3 significantly outperforms TD3. So far, we have demonstrated the smoothing effect of SD3 over TD3. Hyperparameters of DDPG and SD2 are summarized in Table 1. Assume that the actor is a local maximizer with respect to the critic.