Ji Liu

Lili Wang, Ji Liu, A. Stephen Morse et al.

A simply structured distributed observer is described for estimating the state of a discrete-time, jointly observable, input-free, linear system whose sensed outputs are distributed across a time-varying network. It is explained how to construct the local estimators which comprise the observer so that their state estimation errors all converge exponentially fast to zero at a fixed, but arbitrarily chosen rate provided the network's graph is strongly connected for all time. This is accomplished by exploiting several well-known properties of invariant subspaces plus several kinds of suitably defined matrix norms.

Bipul Islam, Ji Liu, Romeil Sandhu

At the core of understanding dynamical systems is the ability to maintain and control the systems behavior that includes notions of robustness, heterogeneity, or regime-shift detection. Recently, to explore such functional properties, a convenient representation has been to model such dynamical systems as a weighted graph consisting of a finite, but very large number of interacting agents. This said, there exists very limited relevant statistical theory that is able cope with real-life data, i.e., how does perform analysis and/or statistics over a family of networks as opposed to a specific network or network-to-network variation. Here, we are interested in the analysis of network families whereby each network represents a point on an underlying statistical manifold. To do so, we explore the Riemannian structure of the tensor manifold developed by Pennec previously applied to Diffusion Tensor Imaging (DTI) towards the problem of network analysis. In particular, while this note focuses on Pennec definition of geodesics amongst a family of networks, we show how it lays the foundation for future work for developing measures of network robustness for regime-shift detection. We conclude with experiments highlighting the proposed distance on synthetic networks and an application towards biological (stem-cell) systems.

Jingxuan Zhu, Alec Koppel, Alvaro Velasquez et al.

In decentralized cooperative multi-armed bandits (MAB), each agent observes a distinct stream of rewards, and seeks to exchange information with others to select a sequence of arms so as to minimize its regret. Agents in the cooperative setting can outperform a single agent running a MAB method such as Upper-Confidence Bound (UCB) independently. In this work, we study how to recover such salient behavior when an unknown fraction of the agents can be Byzantine, that is, communicate arbitrarily wrong information in the form of reward mean-estimates or confidence sets. This framework can be used to model attackers in computer networks, instigators of offensive content into recommender systems, or manipulators of financial markets. Our key contribution is the development of a fully decentralized resilient upper confidence bound (UCB) algorithm that fuses an information mixing step among agents with a truncation of inconsistent and extreme values. This truncation step enables us to establish that the performance of each normal agent is no worse than the classic single-agent UCB1 algorithm in terms of regret, and more importantly, the cumulative regret of all normal agents is strictly better than the non-cooperative case, provided that each agent has at least 3f+1 neighbors where f is the maximum possible Byzantine agents in each agent's neighborhood. Extensions to time-varying neighbor graphs, and minimax lower bounds are further established on the achievable regret. Experiments corroborate the merits of this framework in practice.

Martin Figura, Yixuan Lin, Ji Liu et al.

In decentralized cooperative multi-agent reinforcement learning, agents can aggregate information from one another to learn policies that maximize a team-average objective function. Despite the willingness to cooperate with others, the individual agents may find direct sharing of information about their local state, reward, and value function undesirable due to privacy issues. In this work, we introduce a decentralized actor-critic algorithm with TD error aggregation that does not violate privacy issues and assumes that communication channels are subject to time delays and packet dropouts. The cost we pay for making such weak assumptions is an increased communication burden for every agent as measured by the dimension of the transmitted data. Interestingly, the communication burden is only quadratic in the graph size, which renders the algorithm applicable in large networks. We provide a convergence analysis under diminishing step size to verify that the agents maximize the team-average objective function.

Yixiong Huo, Guangfeng Jiang, Hongyang Wei et al.

3D Gaussian Splatting (3D GS) has gained popularity due to its faster rendering speed and high-quality novel view synthesis. Some researchers have explored using 3D GS for reconstructing driving scenes. However, these methods often rely on various data types, such as depth maps, 3D boxes, and trajectories of moving objects. Additionally, the lack of annotations for synthesized images limits their direct application in downstream tasks. To address these issues, we propose EGSRAL, a 3D GS-based method that relies solely on training images without extra annotations. EGSRAL enhances 3D GS's capability to model both dynamic objects and static backgrounds and introduces a novel adaptor for auto labeling, generating corresponding annotations based on existing annotations. We also propose a grouping strategy for vanilla 3D GS to address perspective issues in rendering large-scale, complex scenes. Our method achieves state-of-the-art performance on multiple datasets without any extra annotation. For example, the PSNR metric reaches 29.04 on the nuScenes dataset. Moreover, our automated labeling can significantly improve the performance of 2D/3D detection tasks. Code is available at https://github.com/jiangxb98/EGSRAL.

Daochen Zha, Wenye Ma, Lei Yuan et al.

Exploration under sparse reward is a long-standing challenge of model-free reinforcement learning. The state-of-the-art methods address this challenge by introducing intrinsic rewards to encourage exploration in novel states or uncertain environment dynamics. Unfortunately, methods based on intrinsic rewards often fall short in procedurally-generated environments, where a different environment is generated in each episode so that the agent is not likely to visit the same state more than once. Motivated by how humans distinguish good exploration behaviors by looking into the entire episode, we introduce RAPID, a simple yet effective episode-level exploration method for procedurally-generated environments. RAPID regards each episode as a whole and gives an episodic exploration score from both per-episode and long-term views. Those highly scored episodes are treated as good exploration behaviors and are stored in a small ranking buffer. The agent then imitates the episodes in the buffer to reproduce the past good exploration behaviors. We demonstrate our method on several procedurally-generated MiniGrid environments, a first-person-view 3D Maze navigation task from MiniWorld, and several sparse MuJoCo tasks. The results show that RAPID significantly outperforms the state-of-the-art intrinsic reward strategies in terms of sample efficiency and final performance. The code is available at https://github.com/daochenzha/rapid

Xiaohan Ding, Tianxiang Hao, Jianchao Tan et al.

We propose ResRep, a novel method for lossless channel pruning (a.k.a. filter pruning), which slims down a CNN by reducing the width (number of output channels) of convolutional layers. Inspired by the neurobiology research about the independence of remembering and forgetting, we propose to re-parameterize a CNN into the remembering parts and forgetting parts, where the former learn to maintain the performance and the latter learn to prune. Via training with regular SGD on the former but a novel update rule with penalty gradients on the latter, we realize structured sparsity. Then we equivalently merge the remembering and forgetting parts into the original architecture with narrower layers. In this sense, ResRep can be viewed as a successful application of Structural Re-parameterization. Such a methodology distinguishes ResRep from the traditional learning-based pruning paradigm that applies a penalty on parameters to produce sparsity, which may suppress the parameters essential for the remembering. ResRep slims down a standard ResNet-50 with 76.15% accuracy on ImageNet to a narrower one with only 45% FLOPs and no accuracy drop, which is the first to achieve lossless pruning with such a high compression ratio. The code and models are at https://github.com/DingXiaoH/ResRep.

Shaojie Min, Ji Liu

Analytical explorations on complex networks and cubes (i.e., multi-dimensional datasets) are currently two separate research fields with different strategies. To gain more insights into cube dynamics via unique network-domain methodologies and to obtain abundant synthetic networks, we need a transformation approach from cubes into associated networks. To this end, we propose FGM, a fast generic model converting cubes into interrelated networks, whereby samples are remodeled into nodes and network dynamics are guided under the concept of nearest-neighbor searching. Through comparison with previous models, we show that FGM can cost-efficiently generate networks exhibiting typical patterns more closely aligned to factual networks, such as more authentic degree distribution, power-law average nearest-neighbor degree dependency, and the influence decay phenomenon we consider vital for networks. Furthermore, we evaluate the networks that FGM generates through various cubes. Results show that FGM is resilient to input perturbations, producing networks with consistent fine properties.

Wesley A. Suttle, Vipul K. Sharma, Krishna C. Kosaraju et al.

We develop provably safe and convergent reinforcement learning (RL) algorithms for control of nonlinear dynamical systems, bridging the gap between the hard safety guarantees of control theory and the convergence guarantees of RL theory. Recent advances at the intersection of control and RL follow a two-stage, safety filter approach to enforcing hard safety constraints: model-free RL is used to learn a potentially unsafe controller, whose actions are projected onto safe sets prescribed, for example, by a control barrier function. Though safe, such approaches lose any convergence guarantees enjoyed by the underlying RL methods. In this paper, we develop a single-stage, sampling-based approach to hard constraint satisfaction that learns RL controllers enjoying classical convergence guarantees while satisfying hard safety constraints throughout training and deployment. We validate the efficacy of our approach in simulation, including safe control of a quadcopter in a challenging obstacle avoidance problem, and demonstrate that it outperforms existing benchmarks.

Xusheng Li, Chengliang Wang, Shumao Wang et al.

The multi-line LiDAR is widely used in autonomous vehicles, so point cloud-based 3D detectors are essential for autonomous driving. Extracting rich multi-scale features is crucial for point cloud-based 3D detectors in autonomous driving due to significant differences in the size of different types of objects. However, because of the real-time requirements, large-size convolution kernels are rarely used to extract large-scale features in the backbone. Current 3D detectors commonly use feature pyramid networks to obtain large-scale features; however, some objects containing fewer point clouds are further lost during down-sampling, resulting in degraded performance. Since pillar-based schemes require much less computation than voxel-based schemes, they are more suitable for constructing real-time 3D detectors. Hence, we propose the *, a pillar-based scheme. We redesigned the feature encoding, the backbone, and the neck of the 3D detector. We propose the Voxel2Pillar feature encoding, which uses a sparse convolution constructor to construct pillars with richer point cloud features, especially height features. The Voxel2Pillar adds more learnable parameters to the feature encoding, enabling the initial pillars to have higher performance ability. We extract multi-scale and large-scale features in the proposed fully sparse backbone, which does not utilize large-size convolutional kernels; the backbone consists of the proposed multi-scale feature extraction module. The neck consists of the proposed sparse ConvNeXt, whose simple structure significantly improves the performance. We validate the effectiveness of the proposed * on the Waymo Open Dataset, and the object detection accuracy for vehicles, pedestrians, and cyclists is improved. We also verify the effectiveness of each proposed module in detail through ablation studies.

Yu Zhao, Huaming Du, Ying Liu et al.

Stock Movement Prediction (SMP) aims at predicting listed companies' stock future price trend, which is a challenging task due to the volatile nature of financial markets. Recent financial studies show that the momentum spillover effect plays a significant role in stock fluctuation. However, previous studies typically only learn the simple connection information among related companies, which inevitably fail to model complex relations of listed companies in the real financial market. To address this issue, we first construct a more comprehensive Market Knowledge Graph (MKG) which contains bi-typed entities including listed companies and their associated executives, and hybrid-relations including the explicit relations and implicit relations. Afterward, we propose DanSmp, a novel Dual Attention Networks to learn the momentum spillover signals based upon the constructed MKG for stock prediction. The empirical experiments on our constructed datasets against nine SOTA baselines demonstrate that the proposed DanSmp is capable of improving stock prediction with the constructed MKG.

Yixuan Lin, Vijay Gupta, Ji Liu

This paper considers a novel multi-agent linear stochastic approximation algorithm driven by Markovian noise and general consensus-type interaction, in which each agent evolves according to its local stochastic approximation process which depends on the information from its neighbors. The interconnection structure among the agents is described by a time-varying directed graph. While the convergence of consensus-based stochastic approximation algorithms when the interconnection among the agents is described by doubly stochastic matrices (at least in expectation) has been studied, less is known about the case when the interconnection matrix is simply stochastic. For any uniformly strongly connected graph sequences whose associated interaction matrices are stochastic, the paper derives finite-time bounds on the mean-square error, defined as the deviation of the output of the algorithm from the unique equilibrium point of the associated ordinary differential equation. For the case of interconnection matrices being stochastic, the equilibrium point can be any unspecified convex combination of the local equilibria of all the agents in the absence of communication. Both the cases with constant and time-varying step-sizes are considered. In the case when the convex combination is required to be a straight average and interaction between any pair of neighboring agents may be uni-directional, so that doubly stochastic matrices cannot be implemented in a distributed manner, the paper proposes a push-sum-type distributed stochastic approximation algorithm and provides its finite-time bound for the time-varying step-size case by leveraging the analysis for the consensus-type algorithm with stochastic matrices and developing novel properties of the push-sum algorithm. Distributed temporal difference learning is discussed as an illustrative application.

Weicong Ding, Hanlin Tang, Jingshuo Feng et al.

Real-world recommendation systems often consist of two phases. In the first phase, multiple predictive models produce the probability of different immediate user actions. In the second phase, these predictions are aggregated according to a set of 'strategic parameters' to meet a diverse set of business goals, such as longer user engagement, higher revenue potential, or more community/network interactions. In addition to building accurate predictive models, it is also crucial to optimize this set of 'strategic parameters' so that primary goals are optimized while secondary guardrails are not hurt. In this setting with multiple and constrained goals, this paper discovers that a probabilistic strategic parameter regime can achieve better value compared to the standard regime of finding a single deterministic parameter. The new probabilistic regime is to learn the best distribution over strategic parameter choices and sample one strategic parameter from the distribution when each user visits the platform. To pursue the optimal probabilistic solution, we formulate the problem into a stochastic compositional optimization problem, in which the unbiased stochastic gradient is unavailable. Our approach is applied in a popular social network platform with hundreds of millions of daily users and achieves +0.22% lift of user engagement in a recommendation task and +1.7% lift in revenue in an advertising optimization scenario comparing to using the best deterministic parameter strategy.

Zhaowei Zhu, Jingxuan Zhu, Ji Liu et al.

In this paper, we study \emph{Federated Bandit}, a decentralized Multi-Armed Bandit problem with a set of $N$ agents, who can only communicate their local data with neighbors described by a connected graph $G$. Each agent makes a sequence of decisions on selecting an arm from $M$ candidates, yet they only have access to local and potentially biased feedback/evaluation of the true reward for each action taken. Learning only locally will lead agents to sub-optimal actions while converging to a no-regret strategy requires a collection of distributed data. Motivated by the proposal of federated learning, we aim for a solution with which agents will never share their local observations with a central entity, and will be allowed to only share a private copy of his/her own information with their neighbors. We first propose a decentralized bandit algorithm Gossip_UCB, which is a coupling of variants of both the classical gossiping algorithm and the celebrated Upper Confidence Bound (UCB) bandit algorithm. We show that Gossip_UCB successfully adapts local bandit learning into a global gossiping process for sharing information among connected agents, and achieves guaranteed regret at the order of $O(\max\{ \texttt{poly}(N,M) \log T, \texttt{poly}(N,M)\log_{λ_2^{-1}} N\})$ for all $N$ agents, where $λ_2\in(0,1)$ is the second largest eigenvalue of the expected gossip matrix, which is a function of $G$. We then propose Fed_UCB, a differentially private version of Gossip_UCB, in which the agents preserve $ε$-differential privacy of their local data while achieving $O(\max \{\frac{\texttt{poly}(N,M)}ε\log^{2.5} T, \texttt{poly}(N,M) (\log_{λ_2^{-1}} N + \log T) \})$ regret.

Hanlin Tang, Shaoduo Gan, Samyam Rajbhandari et al.

Adam is the important optimization algorithm to guarantee efficiency and accuracy for training many important tasks such as BERT and ImageNet. However, Adam is generally not compatible with information (gradient) compression technology. Therefore, the communication usually becomes the bottleneck for parallelizing Adam. In this paper, we propose a communication efficient {\bf A}DAM {\bf p}reconditioned {\bf M}omentum SGD algorithm-- named APMSqueeze-- through an error compensated method compressing gradients. The proposed algorithm achieves a similar convergence efficiency to Adam in term of epochs, but significantly reduces the running time per epoch. In terms of end-to-end performance (including the full-precision pre-condition step), APMSqueeze is able to provide {sometimes by up to $2-10\times$ speed-up depending on network bandwidth.} We also conduct theoretical analysis on the convergence and efficiency.

Shikai Fang, Zheng Wang, Zhimeng Pan et al.

Despite the success of existing tensor factorization methods, most of them conduct a multilinear decomposition, and rarely exploit powerful modeling frameworks, like deep neural networks, to capture a variety of complicated interactions in data. More important, for highly expressive, deep factorization, we lack an effective approach to handle streaming data, which are ubiquitous in real-world applications. To address these issues, we propose SPIDER, a Streaming ProbabilistIc Deep tEnsoR factorization method. We first use Bayesian neural networks (NNs) to construct a deep tensor factorization model. We assign a spike-and-slab prior over the NN weights to encourage sparsity and prevent overfitting. We then use Taylor expansions and moment matching to approximate the posterior of the NN output and calculate the running model evidence, based on which we develop an efficient streaming posterior inference algorithm in the assumed-density-filtering and expectation propagation framework. Our algorithm provides responsive incremental updates for the posterior of the latent factors and NN weights upon receiving new tensor entries, and meanwhile select and inhibit redundant/useless weights. We show the advantages of our approach in four real-world applications.

Bo Liu, Ian Gemp, Mohammad Ghavamzadeh et al.

In this paper, we introduce proximal gradient temporal difference learning, which provides a principled way of designing and analyzing true stochastic gradient temporal difference learning algorithms. We show how gradient TD (GTD) reinforcement learning methods can be formally derived, not by starting from their original objective functions, as previously attempted, but rather from a primal-dual saddle-point objective function. We also conduct a saddle-point error analysis to obtain finite-sample bounds on their performance. Previous analyses of this class of algorithms use stochastic approximation techniques to prove asymptotic convergence, and do not provide any finite-sample analysis. We also propose an accelerated algorithm, called GTD2-MP, that uses proximal ``mirror maps'' to yield an improved convergence rate. The results of our theoretical analysis imply that the GTD family of algorithms are comparable and may indeed be preferred over existing least squares TD methods for off-policy learning, due to their linear complexity. We provide experimental results showing the improved performance of our accelerated gradient TD methods.

Shripad Gade, Ji Liu, Nitin H. Vaidya

This paper studies a system of linear equations, denoted as $Ax = b$, which is horizontally partitioned (rows in $A$ and $b$) and stored over a network of $m$ devices connected in a fixed directed graph. We design a fast distributed algorithm for solving such a partitioned system of linear equations, that additionally, protects the privacy of local data against an honest-but-curious adversary that corrupts at most $τ$ nodes in the network. First, we present TITAN, privaTe fInite Time Average coNsensus algorithm, for solving a general average consensus problem over directed graphs, while protecting statistical privacy of private local data against an honest-but-curious adversary. Second, we propose a distributed linear system solver that involves each agent/devices computing an update based on local private data, followed by private aggregation using TITAN. Finally, we show convergence of our solver to the least squares solution in finite rounds along with statistical privacy of local linear equations against an honest-but-curious adversary provided the graph has weak vertex-connectivity of at least $τ+1$. We perform numerical experiments to validate our claims and compare our solution to the state-of-the-art methods by comparing computation, communication and memory costs.

Bipul Islam, Ji Liu, Anthony Yezzi et al.

The ability to accurately reconstruct the 3D facets of a scene is one of the key problems in robotic vision. However, even with recent advances with machine learning, there is no high-fidelity universal 3D reconstruction method for this optimization problem as schemes often cater to specific image modalities and are often biased by scene abnormalities. Simply put, there always remains an information gap due to the dynamic nature of real-world scenarios. To this end, we demonstrate a feedback control framework which invokes operator inputs (also prone to errors) in order to augment existing reconstruction schemes. For proof-of-concept, we choose a classical region-based stereoscopic reconstruction approach and show how an ill-posed model can be augmented with operator input to be much more robust to scene artifacts. We provide necessary conditions for stability via Lyapunov analysis and perhaps more importantly, we show that the stability depends on a notion of absolute curvature. Mathematically, this aligns with previous work that has shown Ricci curvature as proxy for functional robustness of dynamical networked systems. We conclude with results that show how our method can improve standalone reconstruction schemes.

Hanlin Tang, Xiangru Lian, Shuang Qiu et al.

Communication is a key bottleneck in distributed training. Recently, an \emph{error-compensated} compression technology was particularly designed for the \emph{centralized} learning and receives huge successes, by showing significant advantages over state-of-the-art compression based methods in saving the communication cost. Since the \emph{decentralized} training has been witnessed to be superior to the traditional \emph{centralized} training in the communication restricted scenario, therefore a natural question to ask is "how to apply the error-compensated technology to the decentralized learning to further reduce the communication cost." However, a trivial extension of compression based centralized training algorithms does not exist for the decentralized scenario. key difference between centralized and decentralized training makes this extension extremely non-trivial. In this paper, we propose an elegant algorithmic design to employ error-compensated stochastic gradient descent for the decentralized scenario, named $\texttt{DeepSqueeze}$. Both the theoretical analysis and the empirical study are provided to show the proposed $\texttt{DeepSqueeze}$ algorithm outperforms the existing compression based decentralized learning algorithms. To the best of our knowledge, this is the first time to apply the error-compensated compression to the decentralized learning.

Wesley Suttle, Zhuoran Yang, Kaiqing Zhang et al.

In this paper, we present a probability one convergence proof, under suitable conditions, of a certain class of actor-critic algorithms for finding approximate solutions to entropy-regularized MDPs using the machinery of stochastic approximation. To obtain this overall result, we prove the convergence of policy evaluation with general regularizers when using linear approximation architectures and show convergence of entropy-regularized policy improvement.

Yixuan Lin, Kaiqing Zhang, Zhuoran Yang et al.

This paper considers a distributed reinforcement learning problem in which a network of multiple agents aim to cooperatively maximize the globally averaged return through communication with only local neighbors. A randomized communication-efficient multi-agent actor-critic algorithm is proposed for possibly unidirectional communication relationships depicted by a directed graph. It is shown that the algorithm can solve the problem for strongly connected graphs by allowing each agent to transmit only two scalar-valued variables at one time.

Wesley Suttle, Zhuoran Yang, Kaiqing Zhang et al.

This paper extends off-policy reinforcement learning to the multi-agent case in which a set of networked agents communicating with their neighbors according to a time-varying graph collaboratively evaluates and improves a target policy while following a distinct behavior policy. To this end, the paper develops a multi-agent version of emphatic temporal difference learning for off-policy policy evaluation, and proves convergence under linear function approximation. The paper then leverages this result, in conjunction with a novel multi-agent off-policy policy gradient theorem and recent work in both multi-agent on-policy and single-agent off-policy actor-critic methods, to develop and give convergence guarantees for a new multi-agent off-policy actor-critic algorithm.

Kaiqing Zhang, Yang Liu, Ji Liu et al.

This paper addresses the problem of distributed learning of average belief with sequential observations, in which a network of $n>1$ agents aim to reach a consensus on the average value of their beliefs, by exchanging information only with their neighbors. Each agent has sequentially arriving samples of its belief in an online manner. The neighbor relationships among the $n$ agents are described by a graph which is possibly time-varying, whose vertices correspond to agents and whose edges depict neighbor relationships. Two distributed online algorithms are introduced for undirected and directed graphs, which are both shown to converge to the average belief almost surely. Moreover, the sequences generated by both algorithms are shown to reach consensus with an $O(1/t)$ rate with high probability, where $t$ is the number of iterations. For undirected graphs, the corresponding algorithm is modified for the case with quantized communication and limited precision of the division operation. It is shown that the modified algorithm causes all $n$ agents to either reach a quantized consensus or enter a small neighborhood around the average of their beliefs. Numerical simulations are then provided to corroborate the theoretical results.

Bo Liu, Luwan Zhang, Ji Liu

Dantzig Selector (DS) is widely used in compressed sensing and sparse learning for feature selection and sparse signal recovery. Since the DS formulation is essentially a linear programming optimization, many existing linear programming solvers can be simply applied for scaling up. The DS formulation can be explained as a basis pursuit denoising problem, wherein the data matrix (or measurement matrix) is employed as the denoising matrix to eliminate the observation noise. However, we notice that the data matrix may not be the optimal denoising matrix, as shown by a simple counter-example. This motivates us to pursue a better denoising matrix for defining a general DS formulation. We first define the optimal denoising matrix through a minimax optimization, which turns out to be an NPhard problem. To make the problem computationally tractable, we propose a novel algorithm, termed as Optimal Denoising Dantzig Selector (ODDS), to approximately estimate the optimal denoising matrix. Empirical experiments validate the proposed method. Finally, a novel sparse reinforcement learning algorithm is formulated by extending the proposed ODDS algorithm to temporal difference learning, and empirical experimental results demonstrate to outperform the conventional vanilla DS-TD algorithm.

Chen Yu, Hanlin Tang, Cedric Renggli et al.

Most of today's distributed machine learning systems assume {\em reliable networks}: whenever two machines exchange information (e.g., gradients or models), the network should guarantee the delivery of the message. At the same time, recent work exhibits the impressive tolerance of machine learning algorithms to errors or noise arising from relaxed communication or synchronization. In this paper, we connect these two trends, and consider the following question: {\em Can we design machine learning systems that are tolerant to network unreliability during training?} With this motivation, we focus on a theoretical problem of independent interest---given a standard distributed parameter server architecture, if every communication between the worker and the server has a non-zero probability $p$ of being dropped, does there exist an algorithm that still converges, and at what speed? The technical contribution of this paper is a novel theoretical analysis proving that distributed learning over unreliable network can achieve comparable convergence rate to centralized or distributed learning over reliable networks. Further, we prove that the influence of the packet drop rate diminishes with the growth of the number of \textcolor{black}{parameter servers}. We map this theoretical result onto a real-world scenario, training deep neural networks over an unreliable network layer, and conduct network simulation to validate the system improvement by allowing the networks to be unreliable.

Peng Sun, Xinghai Sun, Lei Han et al.

Starcraft II (SC2) is widely considered as the most challenging Real Time Strategy (RTS) game. The underlying challenges include a large observation space, a huge (continuous and infinite) action space, partial observations, simultaneous move for all players, and long horizon delayed rewards for local decisions. To push the frontier of AI research, Deepmind and Blizzard jointly developed the StarCraft II Learning Environment (SC2LE) as a testbench of complex decision making systems. SC2LE provides a few mini games such as MoveToBeacon, CollectMineralShards, and DefeatRoaches, where some AI agents have achieved the performance level of human professional players. However, for full games, the current AI agents are still far from achieving human professional level performance. To bridge this gap, we present two full game AI agents in this paper - the AI agent TStarBot1 is based on deep reinforcement learning over a flat action structure, and the AI agent TStarBot2 is based on hard-coded rules over a hierarchical action structure. Both TStarBot1 and TStarBot2 are able to defeat the built-in AI agents from level 1 to level 10 in a full game (1v1 Zerg-vs-Zerg game on the AbyssalReef map), noting that level 8, level 9, and level 10 are cheating agents with unfair advantages such as full vision on the whole map and resource harvest boosting. To the best of our knowledge, this is the first public work to investigate AI agents that can defeat the built-in AI in the StarCraft II full game.

Hongyu Xu, Zhangyang Wang, Haichuan Yang et al.

The thresholded feature has recently emerged as an extremely efficient, yet rough empirical approximation, of the time-consuming sparse coding inference process. Such an approximation has not yet been rigorously examined, and standard dictionaries often lead to non-optimal performance when used for computing thresholded features. In this paper, we first present two theoretical recovery guarantees for the thresholded feature to exactly recover the nonzero support of the sparse code. Motivated by them, we then formulate the Dictionary Learning for Thresholded Features (DLTF) model, which learns an optimized dictionary for applying the thresholded feature. In particular, for the $(k, 2)$ norm involved, a novel proximal operator with log-linear time complexity $O(m\log m)$ is derived. We evaluate the performance of DLTF on a vast range of synthetic and real-data tasks, where DLTF demonstrates remarkable efficiency, effectiveness and robustness in all experiments. In addition, we briefly discuss the potential link between DLTF and deep learning building blocks.

Tian Li, Jie Zhong, Ji Liu et al.

We present ease.ml, a declarative machine learning service platform we built to support more than ten research groups outside the computer science departments at ETH Zurich for their machine learning needs. With ease.ml, a user defines the high-level schema of a machine learning application and submits the task via a Web interface. The system automatically deals with the rest, such as model selection and data movement. In this paper, we describe the ease.ml architecture and focus on a novel technical problem introduced by ease.ml regarding resource allocation. We ask, as a "service provider" that manages a shared cluster of machines among all our users running machine learning workloads, what is the resource allocation strategy that maximizes the global satisfaction of all our users? Resource allocation is a critical yet subtle issue in this multi-tenant scenario, as we have to balance between efficiency and fairness. We first formalize the problem that we call multi-tenant model selection, aiming for minimizing the total regret of all users running automatic model selection tasks. We then develop a novel algorithm that combines multi-armed bandits with Bayesian optimization and prove a regret bound under the multi-tenant setting. Finally, we report our evaluation of ease.ml on synthetic data and on one service we are providing to our users, namely, image classification with deep neural networks. Our experimental evaluation results show that our proposed solution can be up to 9.8x faster in achieving the same global quality for all users as the two popular heuristics used by our users before ease.ml.

Wei Qian, Wending Li, Yasuhiro Sogawa et al.

Sparsity learning with known grouping structure has received considerable attention due to wide modern applications in high-dimensional data analysis. Although advantages of using group information have been well-studied by shrinkage-based approaches, benefits of group sparsity have not been well-documented for greedy-type methods, which much limits our understanding and use of this important class of methods. In this paper, generalizing from a popular forward-backward greedy approach, we propose a new interactive greedy algorithm for group sparsity learning and prove that the proposed greedy-type algorithm attains the desired benefits of group sparsity under high dimensional settings. An estimation error bound refining other existing methods and a guarantee for group support recovery are also established simultaneously. In addition, we incorporate a general M-estimation framework and introduce an interactive feature to allow extra algorithm flexibility without compromise in theoretical properties. The promising use of our proposal is demonstrated through numerical evaluations including a real industrial application in human activity recognition at home. Supplementary materials for this article are available online.

Haichuan Yang, Shupeng Gui, Chuyang Ke et al.

The cardinality constraint is an intrinsic way to restrict the solution structure in many domains, for example, sparse learning, feature selection, and compressed sensing. To solve a cardinality constrained problem, the key challenge is to solve the projection onto the cardinality constraint set, which is NP-hard in general when there exist multiple overlapped cardinality constraints. In this paper, we consider the scenario where the overlapped cardinality constraints satisfy a Three-view Cardinality Structure (TVCS), which reflects the natural restriction in many applications, such as identification of gene regulatory networks and task-worker assignment problem. We cast the projection into a linear programming, and show that for TVCS, the vertex solution of this linear programming is the solution for the original projection problem. We further prove that such solution can be found with the complexity proportional to the number of variables and constraints. We finally use synthetic experiments and two interesting applications in bioinformatics and crowdsourcing to validate the proposed TVCS model and method.

Yijun Huang, Ji Liu

Many practical applications such as gene expression analysis, multi-task learning, image recognition, signal processing, and medical data analysis pursue a sparse solution for the feature selection purpose and particularly favor the nonzeros \emph{evenly} distributed in different groups. The exclusive sparsity norm has been widely used to serve to this purpose. However, it still lacks systematical studies for exclusive sparsity norm optimization. This paper offers two main contributions from the optimization perspective: 1) We provide several efficient algorithms to solve exclusive sparsity norm minimization with either smooth loss or hinge loss (non-smooth loss). All algorithms achieve the optimal convergence rate $O(1/k^2)$ ($k$ is the iteration number). To the best of our knowledge, this is the first time to guarantee such convergence rate for the general exclusive sparsity norm minimization; 2) When the group information is unavailable to define the exclusive sparsity norm, we propose to use the random grouping scheme to construct groups and prove that if the number of groups is appropriately chosen, the nonzeros (true features) would be grouped in the ideal way with high probability. Empirical studies validate the efficiency of proposed algorithms, and the effectiveness of random grouping scheme on the proposed exclusive SVM formulation.

Xudong Chen, Ji Liu, M. -A. Belabbas et al.

We consider in this paper a networked system of opinion dynamics in continuous time, where the agents are able to evaluate their self-appraisals in a distributed way. In the model we formulate, the underlying network topology is described by a rooted digraph. For each ordered pair of agents $(i,j)$, we assign a function of self-appraisal to agent $i$, which measures the level of importance of agent $i$ to agent $j$. Thus, by communicating only with her neighbors, each agent is able to calculate the difference between her level of importance to others and others' level of importance to her. The dynamical system of self-appraisals is then designed to drive these differences to zero. We show that for almost all initial conditions, the trajectory generated by this dynamical system asymptotically converges to an equilibrium point which is exponentially stable.

Ji Liu, Ryohei Fujimaki, Jieping Ye

We consider forward-backward greedy algorithms for solving sparse feature selection problems with general convex smooth functions. A state-of-the-art greedy method, the Forward-Backward greedy algorithm (FoBa-obj) requires to solve a large number of optimization problems, thus it is not scalable for large-size problems. The FoBa-gdt algorithm, which uses the gradient information for feature selection at each forward iteration, significantly improves the efficiency of FoBa-obj. In this paper, we systematically analyze the theoretical properties of both forward-backward greedy algorithms. Our main contributions are: 1) We derive better theoretical bounds than existing analyses regarding FoBa-obj for general smooth convex functions; 2) We show that FoBa-gdt achieves the same theoretical performance as FoBa-obj under the same condition: restricted strong convexity condition. Our new bounds are consistent with the bounds of a special case (least squares) and fills a previously existing theoretical gap for general convex smooth functions; 3) We show that the restricted strong convexity condition is satisfied if the number of independent samples is more than $\bar{k}\log d$ where $\bar{k}$ is the sparsity number and $d$ is the dimension of the variable; 4) We apply FoBa-gdt (with the conditional random field objective) to the sensor selection problem for human indoor activity recognition and our results show that FoBa-gdt outperforms other methods (including the ones based on forward greedy selection and L1-regularization).

Ji Liu, Lei Yuan, Jieping Ye

We consider the following signal recovery problem: given a measurement matrix $Φ\in \mathbb{R}^{n\times p}$ and a noisy observation vector $c\in \mathbb{R}^{n}$ constructed from $c = Φθ^* + ε$ where $ε\in \mathbb{R}^{n}$ is the noise vector whose entries follow i.i.d. centered sub-Gaussian distribution, how to recover the signal $θ^*$ if $Dθ^*$ is sparse {\rca under a linear transformation} $D\in\mathbb{R}^{m\times p}$? One natural method using convex optimization is to solve the following problem: $$\min_θ {1\over 2}\|Φθ- c\|^2 + λ\|Dθ\|_1.$$ This paper provides an upper bound of the estimate error and shows the consistency property of this method by assuming that the design matrix $Φ$ is a Gaussian random matrix. Specifically, we show 1) in the noiseless case, if the condition number of $D$ is bounded and the measurement number $n\geq Ω(s\log(p))$ where $s$ is the sparsity number, then the true solution can be recovered with high probability; and 2) in the noisy case, if the condition number of $D$ is bounded and the measurement increases faster than $s\log(p)$, that is, $s\log(p)=o(n)$, the estimate error converges to zero with probability 1 when $p$ and $s$ go to infinity. Our results are consistent with those for the special case $D=\bold{I}_{p\times p}$ (equivalently LASSO) and improve the existing analysis. The condition number of $D$ plays a critical role in our analysis. We consider the condition numbers in two cases including the fused LASSO and the random graph: the condition number in the fused LASSO case is bounded by a constant, while the condition number in the random graph case is bounded with high probability if $m\over p$ (i.e., $#text{edge}\over #text{vertex}$) is larger than a certain constant. Numerical simulations are consistent with our theoretical results.

Ji Liu, Stephen J. Wright

We consider the reconstruction problem in compressed sensing in which the observations are recorded in a finite number of bits. They may thus contain quantization errors (from being rounded to the nearest representable value) and saturation errors (from being outside the range of representable values). Our formulation has an objective of weighted $\ell_2$-$\ell_1$ type, along with constraints that account explicitly for quantization and saturation errors, and is solved with an augmented Lagrangian method. We prove a consistency result for the recovered solution, stronger than those that have appeared to date in the literature, showing in particular that asymptotic consistency can be obtained without oversampling. We present extensive computational comparisons with formulations proposed previously, and variants thereof.