Efficient Projection-Free Online Methods with Stochastic Recursive Gradient

Xie, Jiahao; Shen, Zebang; Zhang, Chao; Wang, Boyu; Qian, Hui

doi:10.1609/aaai.v34i04.6116

Cited by 20 publications

(19 citation statements)

References 13 publications

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“…We first introduce the setup of the communication graph for the multi-agent network. More specifically, we consider that 𝑁 agents communicate in a random network [23,33], where each two agents are linked with probability 0.5 (discard the graphs that are not connected). And the weight matrix 𝑊 is defined based on the Metropolis rule [26]:…”

Section: Methodsmentioning

confidence: 99%

“…To tackle this challenge and also accelerate online meta-learning, we take a closer look to the distributed networklevel OCO in this section, and devise a distributed OGD algorithm with gradient tracking. For ease of exposition, we consider a more general formulation [3,5,12,33] for the distributed network-level OCO (3): In iteration 𝑡 the agent 𝑖 makes a local model prediction 𝑥 𝑡,𝑖 from a convex compact set K ⊂ R 𝑑 and incurs convex loss 𝑓 𝑡,𝑖 (𝑥 𝑡,𝑖 ) that follows some unknown distribution P, i.e., 𝑓 𝑡,𝑖 ∼ P, for any 𝑡 and 𝑖 ∈ N . The stochastic assumption about the loss function corresponds to the underlying task distribution P T of meta-learning in an implicit manner.…”

Section: Distributed Network-level Online Convex Optimizationmentioning

confidence: 99%

“…Next, we evaluate the performance of MAOML in both convex and nonconvex setups: (1) Convex setup: we consider the online multiclass logistic regression [33] on the MNIST dataset as an online learning task T 𝑡,𝑛 at each agent. .…”

Section: Performance Of Maomlmentioning

confidence: 99%

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Accelerating Distributed Online Meta-Learning via Multi-Agent Collaboration under Limited Communication

Lin

Dedeoğlu

Zhang

2020

Preprint

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Online meta-learning is emerging as an enabling technique for achieving edge intelligence in the IoT ecosystem. Nevertheless, to learn a good meta-model for within-task fast adaptation, a single agent alone has to learn over many tasks, and this is the so-called 'cold-start' problem. Observing that in a multi-agent network the learning tasks across different agents often share some model similarity, we ask the following fundamental question: "Is it possible to accelerate the online meta-learning across agents via limited communication and if yes how much benefit can be achieved? " To answer this question, we propose a multi-agent online metalearning framework and cast it as an equivalent two-level nested online convex optimization (OCO) problem. By characterizing the upper bound of the agent-task-averaged regret, we show that the performance of multi-agent online meta-learning depends heavily on how much an agent can benefit from the distributed networklevel OCO for meta-model updates via limited communication, which however is not well understood. To tackle this challenge, we devise a distributed online gradient descent algorithm with gradient tracking where each agent tracks the global gradient using only one communication step with its neighbors per iteration, and it results in an average regret 𝑂 ( √︁ 𝑇 /𝑁 ) per agent, indicating that a factor of √︁ 1/𝑁 speedup over the optimal single-agent regret 𝑂 ( √ 𝑇 ) after 𝑇 iterations, where 𝑁 is the number of agents. Building on this sharp performance speedup, we next develop a multi-agent online meta-learning algorithm and show that it can achieve the optimal task-average regret at a faster rate of 𝑂 (1/ √ 𝑁𝑇 ) via limited communication, compared to single-agent online meta-learning. Extensive experiments corroborate the theoretic results.

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Section: Methodsmentioning

confidence: 99%

Section: Distributed Network-level Online Convex Optimizationmentioning

confidence: 99%

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Accelerating Distributed Online Meta-Learning via Multi-Agent Collaboration under Limited Communication

Lin

Dedeoğlu

Zhang

2020

Preprint

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“…It has been further improved in [4] by introducing the lazy conditional gradient. Xie et al [25] introduced the recursive variance reduction technique to reduce noise in stochastic gradients prediction. Although these methods have enjoyed success in reducing projection cost, they require either at least one projection or linear optimization both of which can be prohibitive in large scale learning problems.…”

Section: Related Workmentioning

confidence: 99%

Fully Projection-Free Proximal Stochastic Gradient Method With Optimal Convergence Rates

2020

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Proximal stochastic gradient plays an important role in large-scale machine learning and big data analysis. It needs to iteratively update models within a feasible set until convergence. The computational cost is usually high due to the projection over the feasible set. To reduce complexity, many projection-free methods such as Frank-Wolfe methods have been proposed. However, those projection-free methods have to solve a linear programming problem for every update of models which still leads to high computational cost for a complex feasible set, and can be unbearable in practical scenarios. Motivated by this problem, we propose a fully projection-free proximal stochastic gradient method, which has two advantages over previous methods. First, it enjoys high efficiency. The proposed method does not conduct projection directly but finds an approximately correct projection point with a very low computational cost. Second, it achieves tight and optimal convergence rates. Our theoretical analysis shows that the proposed method achieves convergence rates of O 1 √ T and O log T T for convex and strongly convex functions, respectively. These convergence rates successfully match with the known lower bounds. Therefore, in this paper, we provide a valuable insight that some loss of accuracy of projection can improve the efficiency significantly, but does not impair convergence rates. Finally, empirical studies show that the proposed method achieves more than 5× speedup than previous methods.

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“…Recently, several variants have also been developed to improve its performance [36,38,21,18,4,9]. When f is nonconvex, [35] showed that FW converges to a stationary point at a rate O(1/ √ t) in the gap max v∈C x t − v, ∇f (x t ) [28], which has inspired a line of work in stochastic optimization [48,52,51,10,53].…”

Section: Introductionmentioning

confidence: 99%

Complexity of Linear Minimization and Projection on Some Sets

Combettes¹,

Pokutta²

2021

Preprint

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The Frank-Wolfe algorithm is a method for constrained optimization that relies on linear minimizations, as opposed to projections. Therefore, a motivation put forward in a large body of work on the Frank-Wolfe algorithm is the computational advantage of solving linear minimizations instead of projections. However, the discussions supporting this advantage are often too succinct or incomplete. In this paper, we review the complexity bounds for both tasks on several sets commonly used in optimization. Projection methods onto the p-ball, p ∈ ]1, 2[ ∪ ]2, +∞[, and the Birkhoff polytope are also proposed.

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Efficient Projection-Free Online Methods with Stochastic Recursive Gradient

Cited by 20 publications

References 13 publications

Accelerating Distributed Online Meta-Learning via Multi-Agent Collaboration under Limited Communication

Accelerating Distributed Online Meta-Learning via Multi-Agent Collaboration under Limited Communication

Fully Projection-Free Proximal Stochastic Gradient Method With Optimal Convergence Rates

Complexity of Linear Minimization and Projection on Some Sets

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