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1. Adaptive Communication Strategies to Achieve the Best Error-Runtime Trade-off in Local-update SGD

   Wang, Jianyu; Joshi, Gauri (April 2019, Systems and Machine Learning (SysML) Conference)

   Large-scale machine learning training, in particular, distributed stochastic gradient descent, needs to be robust to inherent system variability such as node straggling and random communication delays. This work considers a distributed training framework where each worker node is allowed to perform local model updates and the resulting models are averaged periodically. We analyze the true speed of error convergence with respect to wall-clock time (instead of the number of iterations) and analyze how it is affected by the frequency of averaging. The main contribution is the design of ADACOMM, an adaptive communication strategy that starts with infrequent averaging to save communication delay and improve convergence speed, and then increases the communication frequency in order to achieve a low error floor. Rigorous experiments on training deep neural networks show that ADACOMM can take 3x less time than fully synchronous SGD and still reach the same final training loss. 

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2. Convergence speed and approximation accuracy of numerical MCMC

   https://doi.org/10.1017/apr.2024.28  

   Cui, Tiangang; Dong, Jing; Jasra, Ajay; Tong, Xin T (March 2025, Advances in Applied Probability)

   Abstract When implementing Markov Chain Monte Carlo (MCMC) algorithms, perturbation caused by numerical errors is sometimes inevitable. This paper studies how the perturbation of MCMC affects the convergence speed and approximation accuracy. Our results show that when the original Markov chain converges to stationarity fast enough and the perturbed transition kernel is a good approximation to the original transition kernel, the corresponding perturbed sampler has fast convergence speed and high approximation accuracy as well. Our convergence analysis is conducted under either the Wasserstein metric or the$$\chi^2$$metric, both are widely used in the literature. The results can be extended to obtain non-asymptotic error bounds for MCMC estimators. We demonstrate how to apply our convergence and approximation results to the analysis of specific sampling algorithms, including Random walk Metropolis, Metropolis adjusted Langevin algorithm with perturbed target densities, and parallel tempering Monte Carlo with perturbed densities. Finally, we present some simple numerical examples to verify our theoretical claims. 

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3. Multi-Agent Reinforcement Learning in Stochastic Networked Systems

   Yiheng Lin, Guannan Qu (January 2021, Advances in Neural Information Processing Systems 34 (NeurIPS 2021))

   We study multi-agent reinforcement learning (MARL) in a stochastic network of agents. The objective is to find localized policies that maximize the (discounted) global reward. In general, scalability is a challenge in this setting because the size of the global state/action space can be exponential in the number of agents. Scalable algorithms are only known in cases where dependencies are static, fixed and local, e.g., between neighbors in a fixed, time-invariant underlying graph. In this work, we propose a Scalable Actor Critic framework that applies in settings where the dependencies can be non-local and stochastic, and provide a finite-time error bound that shows how the convergence rate depends on the speed of information spread in the network. Additionally, as a byproduct of our analysis, we obtain novel finite-time convergence results for a general stochastic approximation scheme and for temporal difference learning with state aggregation, which apply beyond the setting of MARL in networked systems. 

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4. Anderson acceleration for Seismic Inversion

   https://doi.org/10.1190/segam2020-3425521.1  

   Yang, Yunan (September 2020, SEG Technical Program Expanded Abstracts 2020)

   null (Ed.)

   Full waveform inversion (FWI) and least-squares reverse time migration (LSRTM) are popular imaging techniques that can be solved as PDE-constrained optimization problems. Due to the large-scale nature, gradient- and Hessian-based optimization algorithms are preferred in practice to find the optimizer iteratively. However, a balance between the evaluation cost and the rate of convergence needs to be considered. We propose the use of Anderson acceleration (AA), a popular strategy to speed up the convergence of fixed-point iterations, to accelerate a gradient descent method. We show that AA can achieve fast convergence that provides competitive results with some quasi-Newton methods. Independent of the dimensionality of the unknown parameters, the computational cost of implementing the method can be reduced to an extremely lowdimensional least-squares problem, which makes AA an attractive method for seismic inversion. 

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5. An Exponentially Convergent Primal-Dual Algorithm for Nonsmooth Composite Minimization

   https://doi.org/10.1109/CDC.2018.8619760  

   Ding, Dongsheng; Hu, Bin; Dhingra, Neil K.; Jovanovic, Mihailo R. (December 2018, 2018 IEEE Conference on Decision and Control (CDC))

   We consider a class of nonsmooth convex composite optimization problems, where the objective function is given by the sum of a continuously differentiable convex term and a potentially non-differentiable convex regularizer. In [1], the authors introduced the proximal augmented Lagrangian method and derived the resulting continuous-time primal-dual dynamics that converge to the optimal solution. In this paper, we extend these dynamics from continuous to discrete time via the forward Euler discretization. We prove explicit bounds on the exponential convergence rates of our proposed algorithm with a sufficiently small step size. Since a larger step size can improve the convergence speed, we further develop a linear matrix inequality (LMI) condition which can be numerically solved to provide rate certificates with general step size choices. In addition, we prove that a large range of step size values can guarantee exponential convergence. We close the paper by demonstrating the performance of the proposed algorithm via computational experiments. 

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