Year: 2023
Type: preprint
Abstract: We study unconstrained Online Linear Optimization with Lipschitz losses. Motivated by the pursuit of instance optimality, we propose a new algorithm that simultaneously achieves ($i$) the AdaGrad-style second order gradient adaptivity; and ($ii$) the comparator norm adaptivity also known as "parameter freeness" in the literature. In particular, - our algorithm does not employ the impractical doubling trick, and does not require an a priori estimate of the time-uniform Lipschitz constant; - the associated regret bound has the optimal $O(\sqrt{V_T})$ dependence on the gradient variance $V_T$, without the typical logarithmic multiplicative factor; - the leading constant in the regret bound is "almost" optimal. Central to these results is a continuous time approach to online learning. We first show that the aimed simultaneous adaptivity can be achieved fairly easily in a continuous time analogue of the problem, where the environment is modeled by an arbitrary continuous semimartingale. Then, our key innovation is a new discretization argument that preserves such adaptivity in the discrete time adversarial setting. This refines a non-gradient-adaptive discretization argument from (Harvey et al., 2023), both algorithmically and analytically, which could be of independent interest.
Source: OpenBU (Boston University)
Authors: Zhang, Zhiyu, Yang, Heng, Cutkosky, Ashok, Paschalidis, Ioannis Ch.
Institutions: Harvard University, Boston University
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
Awards: G1286236842, G1863003419, G2770765901, QuBBD: From Personalized Predictions to Better Control of Chronic Health Conditions, G3024551116, G3083819904, G382641700, G42916606, G5261056217, SCH: INT: Distributed Analytics for Enhancing Fertility in Families, PIPP Phase I: Predicting and Preventing Epidemic to Pandemic Transitions, G8876996369, G969889393
OpenAlex ID: W4387210446