arXiv subjects

Suhail M. Shah

Publications and source records attributed to Suhail M. Shah.

8 recordsLinked to original sources

arXiv2023

Adaptive Consensus: A network pruning approach for decentralized optimization

We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A major challenge in decentralized optimization is the reliance on communication which remains a considerable bottleneck in many applications. To address this challenge, we propose an adaptive randomized communication-efficient algorithmic framework that reduces the volume of communication by periodically tracking the disagreement error and judiciously selecting the most influential and effective edges at each node for communication. Within this framework, we present two algorithms: Adaptive Consensus (AC) to solve the consensus problem and Adaptive Consensus based Gradient Tracking (AC-GT) to solve smooth strongly convex decentralized optimization problems. We establish strong theoretical convergence guarantees for the proposed algorithms and quantify their performance in terms of various algorithmic parameters under standard assumptions. Finally, numerical experiments showcase the effectiveness of the framework in significantly reducing the information exchange required to achieve a consensus solution.

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arXiv2023

A Stochastic Gradient Tracking Algorithm for Decentralized Optimization With Inexact Communication

Decentralized optimization is typically studied under the assumption of noise-free transmission. However, real-world scenarios often involve the presence of noise due to factors such as additive white Gaussian noise channels or probabilistic quantization of transmitted data. These sources of noise have the potential to degrade the performance of decentralized optimization algorithms if not effectively addressed. In this paper, we focus on the noisy communication setting and propose an algorithm that bridges the performance gap caused by communication noise while also mitigating other challenges like data heterogeneity. We establish theoretical results of the proposed algorithm that quantify the effect of communication noise and gradient noise on the performance of the algorithm. Notably, our algorithm achieves the optimal convergence rate for minimizing strongly convex, smooth functions in the context of inexact communication and stochastic gradients. Finally, we illustrate the superior performance of the proposed algorithm compared to its state-of-the-art counterparts on machine learning problems using MNIST and CIFAR-10 datasets.

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arXiv2022

Linearly Convergent Asynchronous Distributed ADMM via Markov Sampling

We consider the consensual distributed optimization problem and propose an asynchronous version of the Alternating Direction Method of Multipliers (ADMM) algorithm to solve it. The `asynchronous' part here refers to the fact that only one node/processor is updated (i.e. performs a minimization step) at each iteration of the algorithm. The selection of the node to be updated is decided by simulating a Markov chain. The proposed algorithm is shown to have a linear convergence property in expectation for the class of functions which are strongly convex and continuously differentiable.

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arXiv2021

Dynamic social learning under graph constraints

We introduce a model of graph-constrained dynamic choice with reinforcement modeled by positively $α$-homogeneous rewards. We show that its empirical process, which can be written as a stochastic approximation recursion with Markov noise, has the same probability law as a certain vertex reinforced random walk. We use this equivalence to show that for $α> 0$, the asymptotic outcome concentrates around the optimum in a certain limiting sense when `annealed' by letting $α\uparrow\infty$ slowly.

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arXiv2021

Making Simulated Annealing Sample Efficient for Discrete Stochastic Optimization

We study the regret of simulated annealing (SA) based approaches to solving discrete stochastic optimization problems. The main theoretical conclusion is that the regret of the simulated annealing algorithm, with either noisy or noiseless observations, depends primarily upon the rate of the convergence of the associated Gibbs measure to the optimal states. In contrast to previous works, we show that SA does not need an increased estimation effort (number of \textit{pulls/samples} of the selected \textit{arm/solution} per round for a finite horizon $n$) with noisy observations to converge in probability. By simple modifications, we can make the total number of samples per iteration required for convergence (in probability) to scale as $\mathcal{O}\big(n)$. Additionally, we show that a simulated annealing inspired heuristic can solve the problem of stochastic multi-armed bandits (MAB), by which we mean that it suffers a $\mathcal{O}(\log \,n)$ regret. Thus, our contention is that SA should be considered as a viable candidate for inclusion into the family of efficient exploration heuristics for bandit and discrete stochastic optimization problems.

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arXiv2020

Distributed Optimization on Riemannian Manifolds for multi-agent networks

We consider the consensual distributed optimization problem in the Riemannian context. Specifically, the minimization of a sum of functions form is studied where each individual function in the sum is located at the node of a network. An algorithm, which is a direct generalization of the Euclidean case, to solve the problem is proposed. The convergence analysis is carried out in full detail for geodesically convex as well as non-convex functions. The algorithm is demonstrated using some standard applications which fit the presented framework.

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arXiv2017

Stochastic Approximation on Riemannian manifolds

The standard theory of stochastic approximation (SA) is extended to the case when the constraint set is a Riemannian manifold. Specifically, the standard ODE method for analyzing SA schemes is extended to iterations constrained to stay on a manifold using a retraction mapping. In addition, for submanifolds of a Euclidean space, a framework is developed for a projected SA scheme with approximate retractions. The framework is also extended to non-differentiable constraint sets.

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arXiv2017

Distributed Stochastic Approximation with Local Projections

We propose a distributed version of a stochastic approximation scheme constrained to remain in the intersection of a finite family of convex sets. The projection to the intersection of these sets is also computed in a distributed manner and a `nonlinear gossip' mechanism is employed to blend the projection iterations with the stochastic approximation using multiple time scales

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