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Jiyan Jiang

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3 papers

2 author rows

ICLR Conference 2023 Conference Paper

Multi-Objective Online Learning

Jiyan Jiang
Wenpeng Zhang 0003
Shiji Zhou
Lihong Gu
Xiaodong Zeng
Wenwu Zhu 0001

This paper presents a systematic study of multi-objective online learning. We first formulate the framework of Multi-Objective Online Convex Optimization, which encompasses a novel multi-objective regret. This regret is built upon a sequence-wise extension of the commonly used discrepancy metric Pareto suboptimality gap in zero-order multi-objective bandits. We then derive an equivalent form of the regret, making it amenable to be optimized via first-order iterative methods. To motivate the algorithm design, we give an explicit example in which equipping OMD with the vanilla min-norm solver for gradient composition will incur a linear regret, which shows that merely regularizing the iterates, as in single-objective online learning, is not enough to guarantee sublinear regrets in the multi-objective setting. To resolve this issue, we propose a novel min-regularized-norm solver that regularizes the composite weights. Combining min-regularized-norm with OMD results in the Doubly Regularized Online Mirror Multiple Descent algorithm. We further derive the multi-objective regret bound for the proposed algorithm, which matches the optimal bound in the single-objective setting. Extensive experiments on several real-world datasets verify the effectiveness of the proposed algorithm.

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NeurIPS Conference 2022 Conference Paper

On the Convergence of Stochastic Multi-Objective Gradient Manipulation and Beyond

Shiji Zhou
Wenpeng Zhang
Jiyan Jiang
Wenliang Zhong
Jinjie Gu
Wenwu Zhu

The conflicting gradients problem is one of the major bottlenecks for the effective training of machine learning models that deal with multiple objectives. To resolve this problem, various gradient manipulation techniques, such as PCGrad, MGDA, and CAGrad, have been developed, which directly alter the conflicting gradients to refined ones with alleviated or even no conflicts. However, the existing design and analysis of these techniques are mainly conducted under the full-batch gradient setting, ignoring the fact that they are primarily applied with stochastic mini-batch gradients. In this paper, we illustrate that the stochastic gradient manipulation algorithms may fail to converge to Pareto optimal solutions. Firstly, we show that these different algorithms can be summarized into a unified algorithmic framework, where the descent direction is given by the composition of the gradients of the multiple objectives. Then we provide an explicit two-objective convex optimization instance to explicate the non-convergence issue under the unified framework, which suggests that the non-convergence results from the determination of the composite weights solely by the instantaneous stochastic gradients. To fix the non-convergence issue, we propose a novel composite weights determination scheme that exponentially averages the past calculated weights. Finally, we show the resulting new variant of stochastic gradient manipulation converges to Pareto optimal or critical solutions and yield comparable or improved empirical performance.

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NeurIPS Conference 2021 Conference Paper

Asynchronous Decentralized Online Learning

Jiyan Jiang
Wenpeng Zhang
Jinjie Gu
Wenwu Zhu

Most existing algorithms in decentralized online learning are conducted in the synchronous setting. However, synchronization makes these algorithms suffer from the straggler problem, i. e. , fast learners have to wait for slow learners, which significantly reduces such algorithms' overall efficiency. To overcome this problem, we study decentralized online learning in the asynchronous setting, which allows different learners to work at their own pace. We first formulate the framework of Asynchronous Decentralized Online Convex Optimization, which specifies the whole process of asynchronous decentralized online learning using a sophisticated event indexing system. Then we propose the Asynchronous Decentralized Online Gradient-Push (AD-OGP) algorithm, which performs asymmetric gossiping communication and instantaneous model averaging. We further derive a regret bound of AD-OGP, which is a function of the network topology, the levels of processing delays, and the levels of communication delays. Extensive experiments show that AD-OGP runs significantly faster than its synchronous counterpart and also verify the theoretical results.

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