Zeroth-order non-convex learning via hierarchical dual averaging

• URL: http://arxiv.org/abs/2109.05829v1
• Date: Mon, 13 Sep 2021 09:59:06 GMT
• Title: Zeroth-order non-convex learning via hierarchical dual averaging
• Authors: Am\'elie H\'eliou and Matthieu Martin and Panayotis Mertikopoulos and Thibaud Rahier
• Abstract summary: We propose a hierarchical version of dual dynamic averaging for zeroth-order online non- norm optimization. We derive tight bounds for both the learners static dynamic regret - i.e., the best policy in hindsight the play.
• Score: 26.023679256204737
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We propose a hierarchical version of dual averaging for zeroth-order online non-convex optimization - i.e., learning processes where, at each stage, the optimizer is facing an unknown non-convex loss function and only receives the incurred loss as feedback. The proposed class of policies relies on the construction of an online model that aggregates loss information as it arrives, and it consists of two principal components: (a) a regularizer adapted to the Fisher information metric (as opposed to the metric norm of the ambient space); and (b) a principled exploration of the problem's state space based on an adapted hierarchical schedule. This construction enables sharper control of the model's bias and variance, and allows us to derive tight bounds for both the learner's static and dynamic regret - i.e., the regret incurred against the best dynamic policy in hindsight over the horizon of play.

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