Lemma 1 (Ensemble Sample Diversity Decomposition) Given the state-action visit distribution of the ensemble policy ρ. The entropy of this distribution is H(ρ). By definition, I(ρ;z) = H(ρ) H(ρ|z) = H(z) H(z|ρ) (4) By randomly selecting the latent variable z, we consider that H(z) is a constant depending on the number of z. Lemma 3 Let X1,X2,...,XN be an infinite sequence of i.i.d. The PDF of XN:N can be derived by taking the derivative of PDF.

Transfer in reinforcement learning aims at solving a new target task with no additional learning or sample-efficiently by exploiting agents and information obtained from source tasks. We review a line of research with relevant approaches. This group of approaches reuses policies learned on source tasks for target tasks. Fernández and Veloso [17] suggest an exploration strategy for the learning of a new policy given a new task and learned source policies, where the gain of using each policy is estimated together on-line and one of the policies in the set is selected probabilistically at each step, based on the gain, but they focus on aiding the training of the target policy with samples from the target task rather than improving the zero-shot transfer performance. On the other hand, Dayan [14] introduce successor representations (SRs), state space occupancy representations disentangled from rewards, which allow linear decomposition of value functions.

Despite the rapid advance of unsupervised anomaly detection, existing methods require to train separate models for different objects. In this work, we present UniAD that accomplishes anomaly detection for multiple classes with a unified framework. Under such a challenging setting, popular reconstruction networks may fall into an "identical shortcut", where both normal and anomalous samples can be well recovered, and hence fail to spot outliers. To tackle this obstacle, we make three improvements. First, we revisit the formulations of fully-connected layer, convolutional layer, as well as attention layer, and confirm the important role of query embedding (i.e., within attention layer) in preventing the network from learning the shortcut.

Deep neural networks are parametric models able to learn complex non-linear functions from few training instances and thus can be deployed to solve many tasks. Their overparameterized architecture, characterized by a number of parameters far larger than that of training data points, enables them to retain entire datasets even with random labels [84]. Even more, this overparameterized regime makes neural network approximations of a given function not unique in the sense that multiple configurations of weights might lead to the same function. Indeed, the output of a feed forward neural network given some fixed input remains unchanged under a set of transformations. For instance, certain weight permutations and sign flips in MLPs leave the output unchanged [9].