Few-shot classification aims to learn a classifier to recognize unseen classes during training, where the learned model can easily become over-fitted based on the biased distribution formed by only a few training examples. A recent solution to this problem is calibrating the distribution of these few sample classes by transferring statistics from the base classes with sufficient examples, where how to decide the transfer weights from base classes to novel classes is the key. However, principled approaches for learning the transfer weights have not been carefully studied. To this end, we propose a novel distribution calibration method by learning the adaptive weight matrix between novel samples and base classes, which is built upon a hierarchical Optimal Transport (H-OT) framework. By minimizing the high-level OT distance between novel samples and base classes, we can view the learned transport plan as the adaptive weight information for transferring the statistics of base classes. The learning of the cost function between a base class and novel class in the high-level OT leads to the introduction of the lowlevel OT, which considers the weights of all the data samples in the base class. Experiments on standard benchmarks demonstrate that our proposed plug-andplay model outperforms competing approaches and owns desired cross-domain generalization ability, proving the effectiveness of the learned adaptive weights. 1

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.