In Section 3.1, the difference between the performance of two joint policies is expressed as follows: In Section 3.1, we claim that We represent the policy using its parameter, i.e. From Proposition 4.7 in (Levin and Peres, 2017), if we have two distributions Then, the following can be derived using Eq. Now we provide a detailed proof. Section 3.2 mentions that there exists a risk of high variance in estimating the policy gradient when Now we use mathematical induction to prove the fact. In Section 3.3, the difference between CoPPO and MAPPO is simplified to the difference between Similar to Appendix A.5, the decentralized policies can be viewed independently, thus The details of our CoPPO algorithm are given in Algorithm 1.

In contrast to regular (simple) networks, hyper networks possess the ability to depict more complex relationships among nodes and store extensive information. Such networks are commonly found in real-world applications, such as in social interactions. Learning embedded representations for nodes involves a process that translates network structures into more simplified spaces, thereby enabling the application of machine learning approaches designed for vector data to be extended to network data. Nevertheless, there remains a need to delve into methods for learning embedded representations that prioritize structural aspects. This research introduces HyperS2V, a node embedding approach that centers on the structural similarity within hyper networks. Initially, we establish the concept of hyper-degrees to capture the structural properties of nodes within hyper networks. Subsequently, a novel function is formulated to measure the structural similarity between different hyper-degree values. Lastly, we generate structural embeddings utilizing a multi-scale random walk framework. Moreover, a series of experiments, both intrinsic and extrinsic, are performed on both toy and real networks. The results underscore the superior performance of HyperS2V in terms of both interpretability and applicability to downstream tasks.

Aerodynamic performance evaluation is an important part of the aircraft aerodynamic design optimization process; however, traditional methods are costly and time-consuming. Despite the fact that various machine learning methods can achieve high accuracy, their application in engineering is still difficult due to their poor generalization performance and "black box" nature. In this paper, a knowledge-embedded meta learning model, which fully integrates data with the theoretical knowledge of the lift curve, is developed to obtain the lift coefficients of an arbitrary supercritical airfoil under various angle of attacks. In the proposed model, a primary network is responsible for representing the relationship between the lift and angle of attack, while the geometry information is encoded into a hyper network to predict the unknown parameters involved in the primary network. Specifically, three models with different architectures are trained to provide various interpretations. Compared to the ordinary neural network, our proposed model can exhibit better generalization capability with competitive prediction accuracy. Afterward, interpretable analysis is performed based on the Integrated Gradients and Saliency methods. Results show that the proposed model can tend to assess the influence of airfoil geometry to the physical characteristics. Furthermore, the exceptions and shortcomings caused by the proposed model are analysed and discussed in detail.

Neural control of memory-constrained, agile robots requires small, yet highly performant models. We leverage graph hyper networks to learn graph hyper policies trained with off-policy reinforcement learning resulting in networks that are two orders of magnitude smaller than commonly used networks yet encode policies comparable to those encoded by much larger networks trained on the same task. We show that our method can be appended to any off-policy reinforcement learning algorithm, without any change in hyperparameters, by showing results across locomotion and manipulation tasks. Further, we obtain an array of working policies, with differing numbers of parameters, allowing us to pick an optimal network for the memory constraints of a system. Training multiple policies with our method is as sample efficient as training a single policy. Finally, we provide a method to select the best architecture, given a constraint on the number of parameters. Project website: https://sites.google.com/usc.edu/graphhyperpolicy

The majority of artificial intelligence (AI) is a game of numbers. Deep neural networks, a type of AI that learns to recognize patterns in data, began outperforming standard algorithms 10 years ago because we ultimately had enough data and processing capabilities to fully utilize them. Today's neural nets are even more data and power-hungry. Training them necessitates fine-tuning the values of millions, if not billions, of parameters that define these networks and represent the strength of interconnections between artificial neurons. The goal is to obtain near-ideal settings for them, a process called optimization, but teaching the networks to get there is difficult.

In this paper, we consider the problem of multi-agent navigation in partially observable grid environments. This problem is challenging for centralized planning approaches as they, typically, rely on the full knowledge of the environment. We suggest utilizing the reinforcement learning approach when the agents, first, learn the policies that map observations to actions and then follow these policies to reach their goals. To tackle the challenge associated with learning cooperative behavior, i.e. in many cases agents need to yield to each other to accomplish a mission, we use a mixing Q-network that complements learning individual policies. In the experimental evaluation, we show that such approach leads to plausible results and scales well to large number of agents.

In this work, we propose a novel probabilistic sequence model that excels at capturing high variability in time series data, both across sequences and within an individual sequence. Our method uses temporal latent variables to capture information about the underlying data pattern and dynamically decodes the latent information into modifications of weights of the base decoder and recurrent model. The efficacy of the proposed method is demonstrated on a range of synthetic and real-world sequential data that exhibit large scale variations, regime shifts, and complex dynamics.