Title: Online Multi-objective Convex Optimization: A Unified Framework and Joint Gradient Descent
Primary area: optimization
Keywords: online multi-objective convex optimization, Pareto front, primal-dual method

Abstract: Online Convex Optimization (OCO) usually addresses the learning task with a single objective; however, in real-world applications, multiple conflicting objectives often need to be optimized simultaneously. In this paper, we present an Online Multi-objective Convex Optimization (OMCO) framework with a novel multi-objective regret. We prove that, when the number of objectives in OMCO decreases to one, the regret is equal to the regret in OCO, thus unifying the OCO and OMCO frameworks. To facilitate the analysis of the proposed novel regret, we derive its equivalent form using the strong duality theory of convex optimization. Moreover, we propose an Online Joint Gradient Descent algorithm and prove that it achieves a sublinear multi-objective regret according to the equivalent regret form. Experimental results on several real-world datasets validate the effectiveness of our proposed algorithm.