Jinming Xu

Yan Huang, Ying Sun, Zehan Zhu et al.

We develop a general framework unifying several gradient-based stochastic optimization methods for empirical risk minimization problems both in centralized and distributed scenarios. The framework hinges on the introduction of an augmented graph consisting of nodes modeling the samples and edges modeling both the inter-device communication and intra-device stochastic gradient computation. By designing properly the topology of the augmented graph, we are able to recover as special cases the renowned Local-SGD and DSGD algorithms, and provide a unified perspective for variance-reduction (VR) and gradient-tracking (GT) methods such as SAGA, Local-SVRG and GT-SAGA. We also provide a unified convergence analysis for smooth and (strongly) convex objectives relying on a proper structured Lyapunov function, and the obtained rate can recover the best known results for many existing algorithms. The rate results further reveal that VR and GT methods can effectively eliminate data heterogeneity within and across devices, respectively, enabling the exact convergence of the algorithm to the optimal solution. Numerical experiments confirm the findings in this paper.

Yan Huang, Jinming Xu

We propose a flexible gradient tracking approach with adjustable computation and communication steps for solving distributed stochastic optimization problem over networks. The proposed method allows each node to perform multiple local gradient updates and multiple inter-node communications in each round, aiming to strike a balance between computation and communication costs according to the properties of objective functions and network topology in non-i.i.d. settings. Leveraging a properly designed Lyapunov function, we derive both the computation and communication complexities for achieving arbitrary accuracy on smooth and strongly convex objective functions. Our analysis demonstrates sharp dependence of the convergence performance on graph topology and properties of objective functions, highlighting the trade-off between computation and communication. Numerical experiments are conducted to validate our theoretical findings.

Zehan Zhu, Ye Tian, Yan Huang et al.

Perfect synchronization in distributed machine learning problems is inefficient and even impossible due to the existence of latency, package losses and stragglers. We propose a Robust Fully-Asynchronous Stochastic Gradient Tracking method (R-FAST), where each device performs local computation and communication at its own pace without any form of synchronization. Different from existing asynchronous distributed algorithms, R-FAST can eliminate the impact of data heterogeneity across devices and allow for packet losses by employing a robust gradient tracking strategy that relies on properly designed auxiliary variables for tracking and buffering the overall gradient vector. More importantly, the proposed method utilizes two spanning-tree graphs for communication so long as both share at least one common root, enabling flexible designs in communication architectures. We show that R-FAST converges in expectation to a neighborhood of the optimum with a geometric rate for smooth and strongly convex objectives; and to a stationary point with a sublinear rate for general non-convex settings. Extensive experiments demonstrate that R-FAST runs 1.5-2 times faster than synchronous benchmark algorithms, such as Ring-AllReduce and D-PSGD, while still achieving comparable accuracy, and outperforms existing asynchronous SOTA algorithms, such as AD-PSGD and OSGP, especially in the presence of stragglers.

Zehan Zhu, Heng Zhao, Yan Huang et al.

In this paper, we propose a Differentially Private Stochastic Gradient Push with Compressed communication (termed DP-CSGP) for decentralized learning over directed graphs. Different from existing works, the proposed algorithm is designed to maintain high model utility while ensuring both rigorous differential privacy (DP) guarantees and efficient communication. For general non-convex and smooth objective functions, we show that the proposed algorithm achieves a tight utility bound of $\mathcal{O}\left( \sqrt{d\log \left( \frac{1}δ \right)}/(\sqrt{n}Jε) \right)$ ($J$ and $d$ are the number of local samples and the dimension of decision variables, respectively) with $\left(ε, δ\right)$-DP guarantee for each node, matching that of decentralized counterparts with exact communication. Extensive experiments on benchmark tasks show that, under the same privacy budget, DP-CSGP achieves comparable model accuracy with significantly lower communication cost than existing decentralized counterparts with exact communication.

Yan Huang, Xiang Li, Yipeng Shen et al.

In this paper, we show that applying adaptive methods directly to distributed minimax problems can result in non-convergence due to inconsistency in locally computed adaptive stepsizes. To address this challenge, we propose D-AdaST, a Distributed Adaptive minimax method with Stepsize Tracking. The key strategy is to employ an adaptive stepsize tracking protocol involving the transmission of two extra (scalar) variables. This protocol ensures the consistency among stepsizes of nodes, eliminating the steady-state error due to the lack of coordination of stepsizes among nodes that commonly exists in vanilla distributed adaptive methods, and thus guarantees exact convergence. For nonconvex-strongly-concave distributed minimax problems, we characterize the specific transient times that ensure time-scale separation of stepsizes and quasi-independence of networks, leading to a near-optimal convergence rate of $\tilde{\mathcal{O}} \left( ε^{-\left( 4+δ\right)} \right)$ for any small $δ> 0$, matching that of the centralized counterpart. To our best knowledge, D-AdaST is the first distributed adaptive method achieving near-optimal convergence without knowing any problem-dependent parameters for nonconvex minimax problems. Extensive experiments are conducted to validate our theoretical results.

Jinming Xu, Nasser Lashgarian Azad, Yuan Lin

Many optimal control problems require the simultaneous output of discrete and continuous control variables. These problems are usually formulated as mixed-integer optimal control (MIOC) problems, which are challenging to solve due to the complexity of the solution space. Numerical methods such as branch-and-bound are computationally expensive and undesirable for real-time control. This paper proposes a novel hybrid-action reinforcement learning (HARL) algorithm, twin delayed deep deterministic actor-Q (TD3AQ), for MIOC problems. TD3AQ combines the advantages of both actor-critic and Q-learning methods, and can handle the discrete and continuous action spaces simultaneously. The proposed algorithm is evaluated on a plug-in hybrid electric vehicle (PHEV) energy management problem, where real-time control of the discrete variables, clutch engagement/disengagement and gear shift, and continuous variable, engine torque, is essential to maximize fuel economy while satisfying driving constraints. Simulation outcomes demonstrate that TD3AQ achieves control results close to optimality when compared with dynamic programming (DP), with just 4.69% difference. Furthermore, it surpasses the performance of baseline reinforcement learning algorithms.

Xuezhong Lin, Jingyu Pan, Jinming Xu et al.

As technology scaling is approaching the physical limit, lithography hotspot detection has become an essential task in design for manufacturability. While the deployment of pattern matching or machine learning in hotspot detection can help save significant simulation time, such methods typically demand for non-trivial quality data to build the model, which most design houses are short of. Moreover, the design houses are also unwilling to directly share such data with the other houses to build a unified model, which can be ineffective for the design house with unique design patterns due to data insufficiency. On the other hand, with data homogeneity in each design house, the locally trained models can be easily over-fitted, losing generalization ability and robustness. In this paper, we propose a heterogeneous federated learning framework for lithography hotspot detection that can address the aforementioned issues. On one hand, the framework can build a more robust centralized global sub-model through heterogeneous knowledge sharing while keeping local data private. On the other hand, the global sub-model can be combined with a local sub-model to better adapt to local data heterogeneity. The experimental results show that the proposed framework can overcome the challenge of non-independent and identically distributed (non-IID) data and heterogeneous communication to achieve very high performance in comparison to other state-of-the-art methods while guaranteeing a good convergence rate in various scenarios.