# Weibull-Open-World (WOW) Multi-Type Novelty Detection in CartPole3D
## 6 Related Work  
A recent unifying formalization for defining novelty was introduced in [4]. In that paper, they briefly considered 2D CartPole, but with either a simple Euclidean distance of state features or a very complex dissimilarity measure computed as expectations over the normal world. Their definition used a pairwise comparison of each new state with all training states, which was computationally impractical; in addition, that paper lacked any suggestions for defining when the dissimilarity was abnormal. The dissimilarity measures considered herein are more straightforward and support multiple subtypes of novelty. Importantly, we introduce using Extreme Value Theory as the core algorithm for deciding when dissimilarity departs from normal, which, as distributional models, are efficient while still modeling uncertainty in the decision. Another general framework for defining novel worlds based on a generative framework is presented in [15], which defines novelty in terms of the construction or generation of defined worlds and states. While we consider it a formally closed world model, the framework can be used in our expanded model. Other frameworks measure novelty \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & & & & & \\ \cline{3-5}  & & easy & 0.30 & 0.70 & 2.53 \\ \cline{2-5}  & & medium & 0.33 & 0.67 & 2.40 \\ \cline{2-5}  & & hard & 0.20 & 0.80 & 3.07 \\ \cline{2-5}  & & Subtotal & 0.28 & 0.72 & 2.67 \\ \hline \multirow{4}{*}{
\begin{tabular}{c} \end{tabular} } & & easy & 0.33 & 0.67 & 4.43 \\ \cline{2-5}  & & medium & 0.17 & 0.83 & 5.27 \\ \cline{1-1} \cline{2-5}  & & hard & 0.20 & 0.80 & 5.03 \\ \cline{1-1} \cline{2-5}  & & Subtotal & 0.23 & 0.77 & 4.91 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Detection performance of Gaussian-based detection in 1&2 step lookahead WOW-agent. With the Gaussian-based novelty detection we see a significant fraction of false positives, and lower correct detection rate compared to the EVT-based detection, both of which are significant. They use the same WOW-agent and so robustness and control performance were not statistically significantly different and are not shown. based on the complexity of agents able to recover some level of task performance in novel worlds [16; 17] or based on agent-independent representations of the world [18]. The major distinction is that our approach does not have to reason about how the changes happen, just about what observations change, and how that can be used to classify subtypes of novelty. Novelty detection has many variations among signal processing, computer vision, and machine learning [19; 20; 21; 22; 23; 24; 25]. Still, almost all of these view novelty detection as a one-class problem--detecting things different from training. Recent work continues this one-class view but looks at how one can improve the process with learned features [26] or by using GANs [27]. Out-of-Distribution (OOD), similar to novelty detection, detects inputs that have not been seen before, but this body of work also treats the OOD as a single group somehow different from training [28; 29], with substantial aspects of the work focusing on uncertainty modeling. These all differ from our work, as we focus on how to define/detect multiple subtypes of novelty. Open-set and open-world recognition [8] are also related problems and the most related algorithms. While that family or work has many known classes, they initially treat all \"unknowns\" as a single group. In open-world recognition, they detect unknowns and then get human-supplied labels and learn the new classes. In contrast, our model attempts to define a subclass of novelty based on anticipated properties of the novel, not human-supplied labels after detection. And while those papers also use EVT-based models, they convert all of the high-dimensional representations to a single dimension, while the approach in this paper uses EVT-based models per dimension, and combines probabilities over dimensions to define subtypes of novelty.