Convergence rates of the stochastic alternating algorithm for bi-objective optimization

• URL: http://arxiv.org/abs/2203.10605v1
• Date: Sun, 20 Mar 2022 17:31:08 GMT
• Title: Convergence rates of the stochastic alternating algorithm for bi-objective optimization
• Authors: Suyun Liu and Luis Nunes Vicente
• Abstract summary: We show that alternating algorithms achieve a sublinear convergence rate of $mathcalO (1/sqrtT)$ under strong convexity. Importantly, by varying the proportion of steps applied to each function, one can determine an approximation to the front.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Stochastic alternating algorithms for bi-objective optimization are considered when optimizing two conflicting functions for which optimization steps have to be applied separately for each function. Such algorithms consist of applying a certain number of steps of gradient or subgradient descent on each single objective at each iteration. In this paper, we show that stochastic alternating algorithms achieve a sublinear convergence rate of $\mathcal{O}(1/T)$, under strong convexity, for the determination of a minimizer of a weighted-sum of the two functions, parameterized by the number of steps applied on each of them. An extension to the convex case is presented for which the rate weakens to $\mathcal{O}(1/\sqrt{T})$. These rates are valid also in the non-smooth case. Importantly, by varying the proportion of steps applied to each function, one can determine an approximation to the Pareto front.

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