Wei Pan

Zuogong Yue, Johan Thunberg, Wei Pan et al.

Performing multiple experiments is common when learning internal mechanisms of complex systems. These experiments can include perturbations to parameters or external disturbances. A challenging problem is to efficiently incorporate all collected data simultaneously to infer the underlying dynamic network. This paper addresses the reconstruction of dynamic networks from heterogeneous datasets under the assumption that underlying networks share the same Boolean structure across all experiments. Parametric models for dynamical structure functions are derived to describe causal interactions between measured variables. Multiple datasets are integrated into one regression problem with additional demands of group sparsity to assure network sparsity and structure consistency. To acquire structured group sparsity, we propose a sampling-based method, together with extended versions of l1 methods and sparse Bayesian learning. The performance of the proposed methods is benchmarked in numerical simulation. In summary, this paper presents efficient methods on network reconstruction from multiple experiments, and reveals practical experience that could guide applications.

Yang Li, Shao Zhang, Jichen Sun et al.

Zero-shot coordination in cooperative artificial intelligence (AI) remains a significant challenge, which means effectively coordinating with a wide range of unseen partners. Previous algorithms have attempted to address this challenge by optimizing fixed objectives within a population to improve strategy or behaviour diversity. However, these approaches can result in a loss of learning and an inability to cooperate with certain strategies within the population, known as cooperative incompatibility. To address this issue, we propose the Cooperative Open-ended LEarning (COLE) framework, which constructs open-ended objectives in cooperative games with two players from the perspective of graph theory to assess and identify the cooperative ability of each strategy. We further specify the framework and propose a practical algorithm that leverages knowledge from game theory and graph theory. Furthermore, an analysis of the learning process of the algorithm shows that it can efficiently overcome cooperative incompatibility. The experimental results in the Overcooked game environment demonstrate that our method outperforms current state-of-the-art methods when coordinating with different-level partners. Our demo is available at https://sites.google.com/view/cole-2023.

Yang Li, Shao Zhang, Jichen Sun et al.

Securing coordination between AI agent and teammates (human players or AI agents) in contexts involving unfamiliar humans continues to pose a significant challenge in Zero-Shot Coordination. The issue of cooperative incompatibility becomes particularly prominent when an AI agent is unsuccessful in synchronizing with certain previously unknown partners. Traditional algorithms have aimed to collaborate with partners by optimizing fixed objectives within a population, fostering diversity in strategies and behaviors. However, these techniques may lead to learning loss and an inability to cooperate with specific strategies within the population, a phenomenon named cooperative incompatibility in learning. In order to solve cooperative incompatibility in learning and effectively address the problem in the context of ZSC, we introduce the Cooperative Open-ended LEarning (COLE) framework, which formulates open-ended objectives in cooperative games with two players using perspectives of graph theory to evaluate and pinpoint the cooperative capacity of each strategy. We present two practical algorithms, specifically \algo and \algoR, which incorporate insights from game theory and graph theory. We also show that COLE could effectively overcome the cooperative incompatibility from theoretical and empirical analysis. Subsequently, we created an online Overcooked human-AI experiment platform, the COLE platform, which enables easy customization of questionnaires, model weights, and other aspects. Utilizing the COLE platform, we enlist 130 participants for human experiments. Our findings reveal a preference for our approach over state-of-the-art methods using a variety of subjective metrics. Moreover, objective experimental outcomes in the Overcooked game environment indicate that our method surpasses existing ones when coordinating with previously unencountered AI agents and the human proxy model.

Charith Peris, Lizhen Tan, Thomas Gueudre et al. · amazon-science

Teacher-student knowledge distillation is a popular technique for compressing today's prevailing large language models into manageable sizes that fit low-latency downstream applications. Both the teacher and the choice of transfer set used for distillation are crucial ingredients in creating a high quality student. Yet, the generic corpora used to pretrain the teacher and the corpora associated with the downstream target domain are often significantly different, which raises a natural question: should the student be distilled over the generic corpora, so as to learn from high-quality teacher predictions, or over the downstream task corpora to align with finetuning? Our study investigates this trade-off using Domain Classification (DC) and Intent Classification/Named Entity Recognition (ICNER) as downstream tasks. We distill several multilingual students from a larger multilingual LM with varying proportions of generic and task-specific datasets, and report their performance after finetuning on DC and ICNER. We observe significant improvements across tasks and test sets when only task-specific corpora is used. We also report on how the impact of adding task-specific data to the transfer set correlates with the similarity between generic and task-specific data. Our results clearly indicate that, while distillation from a generic LM benefits downstream tasks, students learn better using target domain data even if it comes at the price of noisier teacher predictions. In other words, target domain data still trumps teacher knowledge.

Yang Li, Kun Xiong, Yingping Zhang et al.

This paper presents an empirical exploration of non-transitivity in perfect-information games, specifically focusing on Xiangqi, a traditional Chinese board game comparable in game-tree complexity to chess and shogi. By analyzing over 10,000 records of human Xiangqi play, we highlight the existence of both transitive and non-transitive elements within the game's strategic structure. To address non-transitivity, we introduce the JiangJun algorithm, an innovative combination of Monte-Carlo Tree Search (MCTS) and Policy Space Response Oracles (PSRO) designed to approximate a Nash equilibrium. We evaluate the algorithm empirically using a WeChat mini program and achieve a Master level with a 99.41\% win rate against human players. The algorithm's effectiveness in overcoming non-transitivity is confirmed by a plethora of metrics, such as relative population performance and visualization results. Our project site is available at \url{https://sites.google.com/view/jiangjun-site/}.

Wenxing Liu, Hanlin Niu, Wei Pan et al.

Sim-and-real training is a promising alternative to sim-to-real training for robot manipulations. However, the current sim-and-real training is neither efficient, i.e., slow convergence to the optimal policy, nor effective, i.e., sizeable real-world robot data. Given limited time and hardware budgets, the performance of sim-and-real training is not satisfactory. In this paper, we propose a Consensus-based Sim-And-Real deep reinforcement learning algorithm (CSAR) for manipulator pick-and-place tasks, which shows comparable performance in both sim-and-real worlds. In this algorithm, we train the agents in simulators and the real world to get the optimal policies for both sim-and-real worlds. We found two interesting phenomenons: (1) Best policy in simulation is not the best for sim-and-real training. (2) The more simulation agents, the better sim-and-real training. The experimental video is available at: https://youtu.be/mcHJtNIsTEQ.

Hongpeng Zhou, Wei Pan

Discovering governing equations from data is critical for diverse scientific disciplines as they can provide insights into the underlying phenomenon of dynamic systems. This work presents a new representation for governing equations by designing the Mathematical Operation Network (MathONet) with a deep neural network-like hierarchical structure. Specifically, the MathONet is stacked by several layers of unary operations (e.g., sin, cos, log) and binary operations (e.g., +,-), respectively. An initialized MathONet is typically regarded as a super-graph with a redundant structure, a sub-graph of which can yield the governing equation. We develop a sparse group Bayesian learning algorithm to extract the sub-graph by employing structurally constructed priors over the redundant mathematical operations. By demonstrating the chaotic Lorenz system, Lotka-Volterra system, and Kolmogorov-Petrovsky-Piskunov system, the proposed method can discover the ordinary differential equations (ODEs) and partial differential equations (PDEs) from the observations given limited mathematical operations, without any prior knowledge on possible expressions of the ODEs and PDEs.

Desong Du, Naiming Qi, Yanfang Liu et al.

In the pursuit of autonomous spacecraft proximity maneuvers and docking(PMD), we introduce a novel Bayesian actor-critic reinforcement learning algorithm to learn a control policy with the stability guarantee. The PMD task is formulated as a Markov decision process that reflects the relative dynamic model, the docking cone and the cost function. Drawing from the principles of Lyapunov theory, we frame the temporal difference learning as a constrained Gaussian process regression problem. This innovative approach allows the state-value function to be expressed as a Lyapunov function, leveraging the Gaussian process and deep kernel learning. We develop a novel Bayesian quadrature policy optimization procedure to analytically compute the policy gradient while integrating Lyapunov-based stability constraints. This integration is pivotal in satisfying the rigorous safety demands of spaceflight missions. The proposed algorithm has been experimentally evaluated on a spacecraft air-bearing testbed and shows impressive and promising performance.

Minghao Han, Yuan Tian, Lixian Zhang et al.

Reinforcement learning is showing great potentials in robotics applications, including autonomous driving, robot manipulation and locomotion. However, with complex uncertainties in the real-world environment, it is difficult to guarantee the successful generalization and sim-to-real transfer of learned policies theoretically. In this paper, we introduce and extend the idea of robust stability and $H_\infty$ control to design policies with both stability and robustness guarantee. Specifically, a sample-based approach for analyzing the Lyapunov stability and performance robustness of a learning-based control system is proposed. Based on the theoretical results, a maximum entropy algorithm is developed for searching Lyapunov function and designing a policy with provable robust stability guarantee. Without any specific domain knowledge, our method can find a policy that is robust to various uncertainties and generalizes well to different test environments. In our experiments, we show that our method achieves better robustness to both large impulsive disturbances and parametric variations in the environment than the state-of-art results in both robust and generic RL, as well as classic control. Anonymous code is available to reproduce the experimental results at https://github.com/RobustStabilityGuaranteeRL/RobustStabilityGuaranteeRL.

Wei Pan, Hao Dong, Yike Guo

Deep learning using multi-layer neural networks (NNs) architecture manifests superb power in modern machine learning systems. The trained Deep Neural Networks (DNNs) are typically large. The question we would like to address is whether it is possible to simplify the NN during training process to achieve a reasonable performance within an acceptable computational time. We presented a novel approach of optimising a deep neural network through regularisation of net- work architecture. We proposed regularisers which support a simple mechanism of dropping neurons during a network training process. The method supports the construction of a simpler deep neural networks with compatible performance with its simplified version. As a proof of concept, we evaluate the proposed method with examples including sparse linear regression, deep autoencoder and convolutional neural network. The valuations demonstrate excellent performance. The code for this work can be found in http://www.github.com/panweihit/DropNeuron

Wenjian Hao, Bowen Huang, Wei Pan et al.

This paper presents a data-driven approach to approximate the dynamics of a nonlinear time-varying system (NTVS) by a linear time-varying system (LTVS), which is resulted from the Koopman operator and deep neural networks. Analysis of the approximation error between states of the NTVS and the resulting LTVS is presented. Simulations on a representative NTVS show that the proposed method achieves small approximation errors, even when the system changes rapidly. Furthermore, simulations in an example of quadcopters demonstrate the computational efficiency of the proposed approach.

Yang Li, Junfan Chen, Feng Xue et al.

Adaptive teaming-the capability of agents to effectively collaborate with unfamiliar teammates without prior coordination-is widely explored in virtual video games but overlooked in real-world multi-robot contexts. Yet, such adaptive collaboration is crucial for real-world applications, including border surveillance, search-and-rescue, and counter-terrorism operations. To address this gap, we introduce AT-Drone, the first dedicated benchmark explicitly designed to facilitate comprehensive training and evaluation of adaptive teaming strategies in multi-drone pursuit scenarios. AT-Drone makes the following key contributions: (1) An adaptable simulation environment configurator that enables intuitive and rapid setup of adaptive teaming multi-drone pursuit tasks, including four predefined pursuit environments. (2) A streamlined real-world deployment pipeline that seamlessly translates simulation insights into practical drone evaluations using edge devices and Crazyflie drones. (3) A novel algorithm zoo integrated with a distributed training framework, featuring diverse algorithms explicitly tailored, for the first time, to multi-pursuer and multi-evader settings. (4) Standardized evaluation protocols with newly designed unseen drone zoos, explicitly designed to rigorously assess the performance of adaptive teaming. Comprehensive experimental evaluations across four progressively challenging multi-drone pursuit scenarios confirm AT-Drone's effectiveness in advancing adaptive teaming research. Real-world drone experiments further validate its practical feasibility and utility for realistic robotic operations. Videos, code and weights are available at \url{https://sites.google.com/view/at-drone}.

Desong Du, Shaohang Han, Naiming Qi et al.

Reinforcement learning (RL) exhibits impressive performance when managing complicated control tasks for robots. However, its wide application to physical robots is limited by the absence of strong safety guarantees. To overcome this challenge, this paper explores the control Lyapunov barrier function (CLBF) to analyze the safety and reachability solely based on data without explicitly employing a dynamic model. We also proposed the Lyapunov barrier actor-critic (LBAC), a model-free RL algorithm, to search for a controller that satisfies the data-based approximation of the safety and reachability conditions. The proposed approach is demonstrated through simulation and real-world robot control experiments, i.e., a 2D quadrotor navigation task. The experimental findings reveal this approach's effectiveness in reachability and safety, surpassing other model-free RL methods.

Jie Ren, Yewen Li, Zihan Ding et al.

Deep reinforcement learning (DRL) has successfully solved various problems recently, typically with a unimodal policy representation. However, grasping distinguishable skills for some tasks with non-unique optima can be essential for further improving its learning efficiency and performance, which may lead to a multimodal policy represented as a mixture-of-experts (MOE). To our best knowledge, present DRL algorithms for general utility do not deploy this method as policy function approximators due to the potential challenge in its differentiability for policy learning. In this work, we propose a probabilistic mixture-of-experts (PMOE) implemented with a Gaussian mixture model (GMM) for multimodal policy, together with a novel gradient estimator for the indifferentiability problem, which can be applied in generic off-policy and on-policy DRL algorithms using stochastic policies, e.g., Soft Actor-Critic (SAC) and Proximal Policy Optimisation (PPO). Experimental results testify the advantage of our method over unimodal polices and two different MOE methods, as well as a method of option frameworks, based on the above two types of DRL algorithms, on six MuJoCo tasks. Different gradient estimations for GMM like the reparameterisation trick (Gumbel-Softmax) and the score-ratio trick are also compared with our method. We further empirically demonstrate the distinguishable primitives learned with PMOE and show the benefits of our method in terms of exploration.

Liang Hu, Yujie Tang, Zhipeng Zhou et al.

This paper presents a deep reinforcement learning (DRL) algorithm for orientation estimation using inertial sensors combined with magnetometer. The Lyapunov method in control theory is employed to prove the convergence of orientation estimation errors. Based on the theoretical results, the estimator gains and a Lyapunov function are parametrized by deep neural networks and learned from samples. The DRL estimator is compared with three well-known orientation estimation methods on both numerical simulations and real datasets collected from commercially available sensors. The results show that the proposed algorithm is superior for arbitrary estimation initialization and can adapt to very large angular velocities for which other algorithms can be hardly applicable. To the best of our knowledge, this is the first DRL-based orientation estimation method with estimation error boundedness guarantee.

Minghao Han, Yuan Tian, Lixian Zhang et al.

Reinforcement learning (RL) is promising for complicated stochastic nonlinear control problems. Without using a mathematical model, an optimal controller can be learned from data evaluated by certain performance criteria through trial-and-error. However, the data-based learning approach is notorious for not guaranteeing stability, which is the most fundamental property for any control system. In this paper, the classic Lyapunov's method is explored to analyze the uniformly ultimate boundedness stability (UUB) solely based on data without using a mathematical model. It is further shown how RL with UUB guarantee can be applied to control dynamic systems with safety constraints. Based on the theoretical results, both off-policy and on-policy learning algorithms are proposed respectively. As a result, optimal controllers can be learned to guarantee UUB of the closed-loop system both at convergence and during learning. The proposed algorithms are evaluated on a series of robotic continuous control tasks with safety constraints. In comparison with the existing RL algorithms, the proposed method can achieve superior performance in terms of maintaining safety. As a qualitative evaluation of stability, our method shows impressive resilience even in the presence of external disturbances.

Liang Hu, Chengwei Wu, Wei Pan

In this paper, we consider the state estimation problem for nonlinear stochastic discrete-time systems. We combine Lyapunov's method in control theory and deep reinforcement learning to design the state estimator. We theoretically prove the convergence of the bounded estimate error solely using the data simulated from the model. An actor-critic reinforcement learning algorithm is proposed to learn the state estimator approximated by a deep neural network. The convergence of the algorithm is analysed. The proposed Lyapunov-based reinforcement learning state estimator is compared with a number of existing nonlinear filtering methods through Monte Carlo simulations, showing its advantage in terms of estimate convergence even under some system uncertainties such as covariance shift in system noise and randomly missing measurements. To the best of our knowledge, this is the first reinforcement learning based nonlinear state estimator with bounded estimate error performance guarantee.

Bruno Brito, Hai Zhu, Wei Pan et al.

Prediction of human motions is key for safe navigation of autonomous robots among humans. In cluttered environments, several motion hypotheses may exist for a pedestrian, due to its interactions with the environment and other pedestrians. Previous works for estimating multiple motion hypotheses require a large number of samples which limits their applicability in real-time motion planning. In this paper, we present a variational learning approach for interaction-aware and multi-modal trajectory prediction based on deep generative neural networks. Our approach can achieve faster convergence and requires significantly fewer samples comparing to state-of-the-art methods. Experimental results on real and simulation data show that our model can effectively learn to infer different trajectories. We compare our method with three baseline approaches and present performance results demonstrating that our generative model can achieve higher accuracy for trajectory prediction by producing diverse trajectories.

Qingrui Zhang, Hao Dong, Wei Pan

Decentralized multi-agent control has broad applications, ranging from multi-robot cooperation to distributed sensor networks. In decentralized multi-agent control, systems are complex with unknown or highly uncertain dynamics, where traditional model-based control methods can hardly be applied. Compared with model-based control in control theory, deep reinforcement learning (DRL) is promising to learn the controller/policy from data without the knowing system dynamics. However, to directly apply DRL to decentralized multi-agent control is challenging, as interactions among agents make the learning environment non-stationary. More importantly, the existing multi-agent reinforcement learning (MARL) algorithms cannot ensure the closed-loop stability of a multi-agent system from a control-theoretic perspective, so the learned control polices are highly possible to generate abnormal or dangerous behaviors in real applications. Hence, without stability guarantee, the application of the existing MARL algorithms to real multi-agent systems is of great concern, e.g., UAVs, robots, and power systems, etc. In this paper, we aim to propose a new MARL algorithm for decentralized multi-agent control with a stability guarantee. The new MARL algorithm, termed as a multi-agent soft-actor critic (MASAC), is proposed under the well-known framework of "centralized-training-with-decentralized-execution". The closed-loop stability is guaranteed by the introduction of a stability constraint during the policy improvement in our MASAC algorithm. The stability constraint is designed based on Lyapunov's method in control theory. To demonstrate the effectiveness, we present a multi-agent navigation example to show the efficiency of the proposed MASAC algorithm.

Qingrui Zhang, Wei Pan, Vasso Reppa

This paper presents a novel model-reference reinforcement learning algorithm for the intelligent tracking control of uncertain autonomous surface vehicles with collision avoidance. The proposed control algorithm combines a conventional control method with reinforcement learning to enhance control accuracy and intelligence. In the proposed control design, a nominal system is considered for the design of a baseline tracking controller using a conventional control approach. The nominal system also defines the desired behaviour of uncertain autonomous surface vehicles in an obstacle-free environment. Thanks to reinforcement learning, the overall tracking controller is capable of compensating for model uncertainties and achieving collision avoidance at the same time in environments with obstacles. In comparison to traditional deep reinforcement learning methods, our proposed learning-based control can provide stability guarantees and better sample efficiency. We demonstrate the performance of the new algorithm using an example of autonomous surface vehicles.

Baozhou Zhu, Zaid Al-Ars, Wei Pan

Binary Convolutional Neural Networks (CNNs) can significantly reduce the number of arithmetic operations and the size of memory storage, which makes the deployment of CNNs on mobile or embedded systems more promising. However, the accuracy degradation of single and multiple binary CNNs is unacceptable for modern architectures and large scale datasets like ImageNet. In this paper, we proposed a Piecewise Approximation (PA) scheme for multiple binary CNNs which lessens accuracy loss by approximating full precision weights and activations efficiently and maintains parallelism of bitwise operations to guarantee efficiency. Unlike previous approaches, the proposed PA scheme segments piece-wisely the full precision weights and activations, and approximates each piece with a scaling coefficient. Our implementation on ResNet with different depths on ImageNet can reduce both Top-1 and Top-5 classification accuracy gap compared with full precision to approximately 1.0%. Benefited from the binarization of the downsampling layer, our proposed PA-ResNet50 requires less memory usage and two times Flops than single binary CNNs with 4 weights and 5 activations bases. The PA scheme can also generalize to other architectures like DenseNet and MobileNet with similar approximation power as ResNet which is promising for other tasks using binary convolutions. The code and pretrained models will be publicly available.

Minghao Han, Lixian Zhang, Jun Wang et al.

Reinforcement Learning (RL) and its integration with deep learning have achieved impressive performance in various robotic control tasks, ranging from motion planning and navigation to end-to-end visual manipulation. However, stability is not guaranteed in model-free RL by solely using data. From a control-theoretic perspective, stability is the most important property for any control system, since it is closely related to safety, robustness, and reliability of robotic systems. In this paper, we propose an actor-critic RL framework for control which can guarantee closed-loop stability by employing the classic Lyapunov's method in control theory. First of all, a data-based stability theorem is proposed for stochastic nonlinear systems modeled by Markov decision process. Then we show that the stability condition could be exploited as the critic in the actor-critic RL to learn a controller/policy. At last, the effectiveness of our approach is evaluated on several well-known 3-dimensional robot control tasks and a synthetic biology gene network tracking task in three different popular physics simulation platforms. As an empirical evaluation on the advantage of stability, we show that the learned policies can enable the systems to recover to the equilibrium or way-points when interfered by uncertainties such as system parametric variations and external disturbances to a certain extent.

Qingrui Zhang, Wei Pan, Vasso Reppa

This paper presents a novel model-reference reinforcement learning control method for uncertain autonomous surface vehicles. The proposed control combines a conventional control method with deep reinforcement learning. With the conventional control, we can ensure the learning-based control law provides closed-loop stability for the overall system, and potentially increase the sample efficiency of the deep reinforcement learning. With the reinforcement learning, we can directly learn a control law to compensate for modeling uncertainties. In the proposed control, a nominal system is employed for the design of a baseline control law using a conventional control approach. The nominal system also defines the desired performance for uncertain autonomous vehicles to follow. In comparison with traditional deep reinforcement learning methods, our proposed learning-based control can provide stability guarantees and better sample efficiency. We demonstrate the performance of the new algorithm via extensive simulation results.

Hongpeng Zhou, Chahine Ibrahim, Wei Pan

Nonlinear system identification is important with a wide range of applications. The typical approaches for nonlinear system identification include Volterra series models, nonlinear autoregressive with exogenous inputs models, block-structured models, state-space models and neural network models. Among them, neural networks (NN) is an important black-box method thanks to its universal approximation capability and less dependency on prior information. However, there are several challenges associated with NN. The first one lies in the design of a proper neural network structure. A relatively simple network cannot approximate the feature of the system, while a complex model may lead to overfitting. The second lies in the availability of data for some nonlinear systems. For some systems, it is difficult to collect enough data to train a neural network. This raises the challenge that how to train a neural network for system identification with a small dataset. In addition, if the uncertainty of the NN parameter could be obtained, it would be also beneficial for further analysis. In this paper, we propose a sparse Bayesian deep learning approach to address the above problems. Specifically, the Bayesian method can reinforce the regularization on neural networks by introducing introduced sparsity-inducing priors. The Bayesian method can also compute the uncertainty of the NN parameter. An efficient iterative re-weighted algorithm is presented in this paper. We also test the capacity of our method to identify the system on various ratios of the original dataset. The one-step-ahead prediction experiment on Cascaded Tank System shows the effectiveness of our method. Furthermore, we test our algorithm with more challenging simulation experiment on this benchmark, which also outperforms other methods.

Hongpeng Zhou, Minghao Yang, Jun Wang et al.

One-Shot Neural Architecture Search (NAS) is a promising method to significantly reduce search time without any separate training. It can be treated as a Network Compression problem on the architecture parameters from an over-parameterized network. However, there are two issues associated with most one-shot NAS methods. First, dependencies between a node and its predecessors and successors are often disregarded which result in improper treatment over zero operations. Second, architecture parameters pruning based on their magnitude is questionable. In this paper, we employ the classic Bayesian learning approach to alleviate these two issues by modeling architecture parameters using hierarchical automatic relevance determination (HARD) priors. Unlike other NAS methods, we train the over-parameterized network for only one epoch then update the architecture. Impressively, this enabled us to find the architecture on CIFAR-10 within only 0.2 GPU days using a single GPU. Competitive performance can be also achieved by transferring to ImageNet. As a byproduct, our approach can be applied directly to compress convolutional neural networks by enforcing structural sparsity which achieves extremely sparse networks without accuracy deterioration.

Ying Wen, Yaodong Yang, Rui Luo et al.

Humans are capable of attributing latent mental contents such as beliefs or intentions to others. The social skill is critical in daily life for reasoning about the potential consequences of others' behaviors so as to plan ahead. It is known that humans use such reasoning ability recursively by considering what others believe about their own beliefs. In this paper, we start from level-$1$ recursion and introduce a probabilistic recursive reasoning (PR2) framework for multi-agent reinforcement learning. Our hypothesis is that it is beneficial for each agent to account for how the opponents would react to its future behaviors. Under the PR2 framework, we adopt variational Bayes methods to approximate the opponents' conditional policies, to which each agent finds the best response and then improve their own policies. We develop decentralized-training-decentralized-execution algorithms, namely PR2-Q and PR2-Actor-Critic, that are proved to converge in the self-play scenarios when there exists one Nash equilibrium. Our methods are tested on both the matrix game and the differential game, which have a non-trivial equilibrium where common gradient-based methods fail to converge. Our experiments show that it is critical to reason about how the opponents believe about what the agent believes. We expect our work to contribute a new idea of modeling the opponents to the multi-agent reinforcement learning community.

Hao Dong, Akara Supratak, Wei Pan et al.

This paper proposes a practical approach to addressing limitations posed by use of single active electrodes in applications for sleep stage classification. Electroencephalography (EEG)-based characterizations of sleep stage progression contribute the diagnosis and monitoring of the many pathologies of sleep. Several prior reports have explored ways of automating the analysis of sleep EEG and of reducing the complexity of the data needed for reliable discrimination of sleep stages in order to make it possible to perform sleep studies at lower cost in the home (rather than only in specialized clinical facilities). However, these reports have involved recordings from electrodes placed on the cranial vertex or occiput, which can be uncomfortable or difficult for subjects to position. Those that have utilized single EEG channels which contain less sleep information, have showed poor classification performance. We have taken advantage of Rectifier Neural Network for feature detection and Long Short-Term Memory (LSTM) network for sequential data learning to optimize classification performance with single electrode recordings. After exploring alternative electrode placements, we found a comfortable configuration of a single-channel EEG on the forehead and have shown that it can be integrated with additional electrodes for simultaneous recording of the electroocuolgram (EOG). Evaluation of data from 62 people (with 494 hours sleep) demonstrated better performance of our analytical algorithm for automated sleep classification than existing approaches using vertex or occipital electrode placements. Use of this recording configuration with neural network deconvolution promises to make clinically indicated home sleep studies practical.

J. Jin, Y. Yuan, W. Pan et al.

This paper begins with considering the identification of sparse linear time-invariant networks described by multivariable ARX models. Such models possess relatively simple structure thus used as a benchmark to promote further research. With identifiability of the network guaranteed, this paper presents an identification method that infers both the Boolean structure of the network and the internal dynamics between nodes. Identification is performed directly from data without any prior knowledge of the system, including its order. The proposed method solves the identification problem using Maximum a posteriori estimation (MAP) but with inseparable penalties for complexity, both in terms of element (order of nonzero connections) and group sparsity (network topology). Such an approach is widely applied in Compressive Sensing (CS) and known as Sparse Bayesian Learning (SBL). We then propose a novel scheme that combines sparse Bayesian and group sparse Bayesian to efficiently solve the problem. The resulted algorithm has a similar form of the standard Sparse Group Lasso (SGL) while with known noise variance, it simplifies to exact re-weighted SGL. The method and the developed toolbox can be applied to infer networks from a wide range of fields, including systems biology applications such as signaling and genetic regulatory networks.

Wei Pan, Ye Yuan, Lennart Ljung et al.

In this paper, we propose a new method to identify biochemical reaction networks (i.e. both reactions and kinetic parameters) from heterogeneous datasets. Such datasets can contain (a) data from several replicates of an experiment performed on a biological system; (b) data measured from a biochemical network subjected to different experimental conditions, for example, changes/perturbations in biological inductions, temperature, gene knock-out, gene over-expression, etc. Simultaneous integration of various datasets to perform system identification has the potential to avoid non-identifiability issues typically arising when only single datasets are used.

Wei Pan, Aivar Sootla, Guy-Bart Stan

In this paper, we present a distributed algorithm for the reconstruction of large-scale nonlinear networks. In particular, we focus on the identification from time-series data of the nonlinear functional forms and associated parameters of large-scale nonlinear networks. Recently, a nonlinear network reconstruction problem was formulated as a nonconvex optimisation problem based on the combination of a marginal likelihood maximisation procedure with sparsity inducing priors. Using a convex-concave procedure (CCCP), an iterative reweighted lasso algorithm was derived to solve the initial nonconvex optimisation problem. By exploiting the structure of the objective function of this reweighted lasso algorithm, a distributed algorithm can be designed. To this end, we apply the alternating direction method of multipliers (ADMM) to decompose the original problem into several subproblems. To illustrate the effectiveness of the proposed methods, we use our approach to identify a network of interconnected Kuramoto oscillators with different network sizes (500~100,000 nodes).