Get our free extension to see links to code for papers anywhere online!Free add-on: code for papers everywhere!Free add-on: See code for papers anywhere!

Rui Huang, Sikun Yang, Heinz Koeppl

Modeling count-valued time series has been receiving increasing attention since count time series naturally arise in physical and social domains. Poisson gamma dynamical systems (PGDSs) are newly-developed methods, which can well capture the expressive latent transition structure and bursty dynamics behind count sequences. In particular, PGDSs demonstrate superior performance in terms of data imputation and prediction, compared with canonical linear dynamical system (LDS) based methods. Despite these advantages, PGDS cannot capture the heterogeneous overdispersed behaviours of the underlying dynamic processes. To mitigate this defect, we propose a negative-binomial-randomized gamma Markov process, which not only significantly improves the predictive performance of the proposed dynamical system, but also facilitates the fast convergence of the inference algorithm. Moreover, we develop methods to estimate both factor-structured and graph-structured transition dynamics, which enable us to infer more explainable latent structure, compared with PGDSs. Finally, we demonstrate the explainable latent structure learned by the proposed method, and show its superior performance in imputing missing data and forecasting future observations, compared with the related models.

Via

Jiahao Wang, Sikun Yang, Heinz Koeppl, Xiuzhen Cheng, Pengfei Hu, Guoming Zhang

Bayesian methodologies for handling count-valued time series have gained prominence due to their ability to infer interpretable latent structures and to estimate uncertainties, and thus are especially suitable for dealing with noisy and incomplete count data. Among these Bayesian models, Poisson-Gamma Dynamical Systems (PGDSs) are proven to be effective in capturing the evolving dynamics underlying observed count sequences. However, the state-of-the-art PGDS still falls short in capturing the time-varying transition dynamics that are commonly observed in real-world count time series. To mitigate this limitation, a non-stationary PGDS is proposed to allow the underlying transition matrices to evolve over time, and the evolving transition matrices are modeled by sophisticatedly-designed Dirichlet Markov chains. Leveraging Dirichlet-Multinomial-Beta data augmentation techniques, a fully-conjugate and efficient Gibbs sampler is developed to perform posterior simulation. Experiments show that, in comparison with related models, the proposed non-stationary PGDS achieves improved predictive performance due to its capacity to learn non-stationary dependency structure captured by the time-evolving transition matrices.

Via

Philipp Froehlich, Heinz Koeppl

In statistics and machine learning, detecting dependencies in datasets is a central challenge. We propose a novel neural network model for supervised graph structure learning, i.e., the process of learning a mapping between observational data and their underlying dependence structure. The model is trained with variably shaped and coupled simulated input data and requires only a single forward pass through the trained network for inference. By leveraging structural equation models and employing randomly generated multivariate Chebyshev polynomials for the simulation of training data, our method demonstrates robust generalizability across both linear and various types of non-linear dependencies. We introduce a novel bilinear attention mechanism (BAM) for explicit processing of dependency information, which operates on the level of covariance matrices of transformed data and respects the geometry of the manifold of symmetric positive definite matrices. Empirical evaluation demonstrates the robustness of our method in detecting a wide range of dependencies, excelling in undirected graph estimation and proving competitive in completed partially directed acyclic graph estimation through a novel two-step approach.

Via

Mengguang Li, Kai Cui, Heinz Koeppl

The standard quadrotor is one of the most popular and widely used aerial vehicle of recent decades, offering great maneuverability with mechanical simplicity. However, the under-actuation characteristic limits its applications, especially when it comes to generating desired wrench with six degrees of freedom (DOF). Therefore, existing work often compromises between mechanical complexity and the controllable DOF of the aerial system. To take advantage of the mechanical simplicity of a standard quadrotor, we propose a modular aerial system, IdentiQuad, that combines only homogeneous quadrotor-based modules. Each IdentiQuad can be operated alone like a standard quadrotor, but at the same time allows task-specific assembly, increasing the controllable DOF of the system. Each module is interchangeable within its assembly. We also propose a general controller for different configurations of assemblies, capable of tolerating rotor failures and balancing the energy consumption of each module. The functionality and robustness of the system and its controller are validated using physics-based simulations for different assembly configurations.

Via

Yannick Eich, Bastian Alt, Heinz Koeppl

This work proposes a decision-making framework for partially observable systems in continuous time with discrete state and action spaces. As optimal decision-making becomes intractable for large state spaces we employ approximation methods for the filtering and the control problem that scale well with an increasing number of states. Specifically, we approximate the high-dimensional filtering distribution by projecting it onto a parametric family of distributions, and integrate it into a control heuristic based on the fully observable system to obtain a scalable policy. We demonstrate the effectiveness of our approach on several partially observed systems, including queueing systems and chemical reaction networks.

Via

Christian Fabian, Kai Cui, Heinz Koeppl

Learning the behavior of large agent populations is an important task for numerous research areas. Although the field of multi-agent reinforcement learning (MARL) has made significant progress towards solving these systems, solutions for many agents often remain computationally infeasible and lack theoretical guarantees. Mean Field Games (MFGs) address both of these issues and can be extended to Graphon MFGs (GMFGs) to include network structures between agents. Despite their merits, the real world applicability of GMFGs is limited by the fact that graphons only capture dense graphs. Since most empirically observed networks show some degree of sparsity, such as power law graphs, the GMFG framework is insufficient for capturing these network topologies. Thus, we introduce the novel concept of Graphex MFGs (GXMFGs) which builds on the graph theoretical concept of graphexes. Graphexes are the limiting objects to sparse graph sequences that also have other desirable features such as the small world property. Learning equilibria in these games is challenging due to the rich and sparse structure of the underlying graphs. To tackle these challenges, we design a new learning algorithm tailored to the GXMFG setup. This hybrid graphex learning approach leverages that the system mainly consists of a highly connected core and a sparse periphery. After defining the system and providing a theoretical analysis, we state our learning approach and demonstrate its learning capabilities on both synthetic graphs and real-world networks. This comparison shows that our GXMFG learning algorithm successfully extends MFGs to a highly relevant class of hard, realistic learning problems that are not accurately addressed by current MARL and MFG methods.

Via

Anam Tahir, Kai Cui, Bastian Alt, Amr Rizk, Heinz Koeppl

The significance of the freshness of sensor and control data at the receiver side, often referred to as Age of Information (AoI), is fundamentally constrained by contention for limited network resources. Evidently, network congestion is detrimental for AoI, where this congestion is partly self-induced by the sensor transmission process in addition to the contention from other transmitting sensors. In this work, we devise a decentralized AoI-minimizing transmission policy for a number of sensor agents sharing capacity-limited, non-FIFO duplex channels that introduce random delays in communication with a common receiver. By implementing the same policy, however with no explicit inter-agent communication, the agents minimize the expected AoI in this partially observable system. We cater to the partial observability due to random channel delays by designing a bootstrap particle filter that independently maintains a belief over the AoI of each agent. We also leverage mean-field control approximations and reinforcement learning to derive scalable and optimal solutions for minimizing the expected AoI collaboratively.

Via

Anam Tahir, Kai Cui, Heinz Koeppl

Scalable load balancing algorithms are of great interest in cloud networks and data centers, necessitating the use of tractable techniques to compute optimal load balancing policies for good performance. However, most existing scalable techniques, especially asymptotically scaling methods based on mean field theory, have not been able to model large queueing networks with strong locality. Meanwhile, general multi-agent reinforcement learning techniques can be hard to scale and usually lack a theoretical foundation. In this work, we address this challenge by leveraging recent advances in sparse mean field theory to learn a near-optimal load balancing policy in sparsely connected queueing networks in a tractable manner, which may be preferable to global approaches in terms of communication overhead. Importantly, we obtain a general load balancing framework for a large class of sparse bounded-degree topologies. By formulating a novel mean field control problem in the context of graphs with bounded degree, we reduce the otherwise difficult multi-agent problem to a single-agent problem. Theoretically, the approach is justified by approximation guarantees. Empirically, the proposed methodology performs well on several realistic and scalable network topologies. Moreover, we compare it with a number of well-known load balancing heuristics and with existing scalable multi-agent reinforcement learning methods. Overall, we obtain a tractable approach for load balancing in highly localized networks.

Via

Kai Cui, Gökçe Dayanıklı, Mathieu Laurière, Matthieu Geist, Olivier Pietquin, Heinz Koeppl

Recent techniques based on Mean Field Games (MFGs) allow the scalable analysis of multi-player games with many similar, rational agents. However, standard MFGs remain limited to homogeneous players that weakly influence each other, and cannot model major players that strongly influence other players, severely limiting the class of problems that can be handled. We propose a novel discrete time version of major-minor MFGs (M3FGs), along with a learning algorithm based on fictitious play and partitioning the probability simplex. Importantly, M3FGs generalize MFGs with common noise and can handle not only random exogeneous environment states but also major players. A key challenge is that the mean field is stochastic and not deterministic as in standard MFGs. Our theoretical investigation verifies both the M3FG model and its algorithmic solution, showing firstly the well-posedness of the M3FG model starting from a finite game of interest, and secondly convergence and approximation guarantees of the fictitious play algorithm. Then, we empirically verify the obtained theoretical results, ablating some of the theoretical assumptions made, and show successful equilibrium learning in three example problems. Overall, we establish a learning framework for a novel and broad class of tractable games.

Via

Jannis Weil, Gizem Ekinci, Heinz Koeppl, Tobias Meuser

Information exchange in multi-agent systems improves the cooperation among agents, especially in partially observable settings. In the real world, communication is often carried out over imperfect channels. This requires agents to handle uncertainty due to potential information loss. In this paper, we consider a cooperative multi-agent system where the agents act and exchange information in a decentralized manner using a limited and unreliable channel. To cope with such channel constraints, we propose a novel communication approach based on independent Q-learning. Our method allows agents to dynamically adapt how much information to share by sending messages of different sizes, depending on their local observations and the channel's properties. In addition to this message size selection, agents learn to encode and decode messages to improve their jointly trained policies. We show that our approach outperforms approaches without adaptive capabilities in a novel cooperative digit-prediction environment and discuss its limitations in the traffic junction environment.

Via