Cooperative multi-agent reinforcement learning (MARL) has been proposed for multi-agent collaborations toaccomplish manychallenging tasks[1,2,3,4].

Statistical learning theory is the foundation of machine learning, providing theoretical bounds for the risk of models learned from a (single) training set, assumed to issue from an unknown probability distribution.

Despite its popularity, self-training is well-believed to be unreliable and often leads to training instability.

JS is also a special case of a general familyofdivergences,thef-divergences[20].

Based on this observation, we adopt ageneralized version ofthe JensenShannon divergence for multiple distributions to encourage consistency around data points. Using this loss function, we show state-of-the-art results on both synthetic(CIFAR),andreal-world(e.g.WebVision)noisewithvaryingnoiserates.

It is not clear, however, whether these theoretical results apply to actual distributions such as images.

For`, we construct the systems of hyperrectangles by4 first precomputing anapproximate k-NN distance estimate using Ball Trees foreachdata point, andthen clustering5 the top-q densest data points intoT partitions using the k-means algorithm, where we binary search for the optimal6 parameterq.

The ability of machine learning to generate structured objects has progressed dramatically in the lastfewyears.