Non-monotone Adaptive Submodular Meta-Learning

Abstract

The core idea of meta-learning is to leverage prior experience to design solutions that can be quickly adapted to new, unseen tasks. Most of existing studies consider the case where the feasible parameter space is continuous. Recently, [1] develops the framework of a discrete variant of metalearning, called submodular meta-learning, and they treat each task as a discrete optimization problem, i.e., they intend to select a group of items that maximizes the average expected utility of all tasks. Motivated by their framework, we consider the submodular meta-learning problem under the adaptive setting. In particular, we assume that each item has a random state, which is drawn from some known prior distribution. One must select an item before observing its realized state. Given a task, the utility function is defined over items and states. Our goal is to adaptively select a group items, each selection is based on the feedback from the past, to maximize the average expected utility of all tasks. Following the framework of standard meta-learning, we propose an effective policy that is composed of two stages: We first pre-compute an initial set of items, called initial solution set, based on previously visited tasks, then, once a new task is revealed, we add more items to the initial solution set to complete the selection process. We show that our policy achieves a 1/32 approximation ratio if the utility function of each task is adaptive submodular. Our policy enjoys the benefits of providing a personalized solution to each task while reducing the computation cost at test time.

Streaming Adaptive Submodular Maximization

“…Very recently, they generalize their previous study and develop the first constant approximation algorithms subject to more general constraints such as knapsack constraint and k-system constraint [14]. Other variants of adaptive submodular maximization have been studied in [15,18,17,19].…”

Cascade Submodular Maximization: Question Selection and Sequencing in Online Personality Quiz

“…The worst-case performance of their solution is arbitrarily bad under our setting due to the unbounded total backward curvature of our utility function with respect to the optimal solution. Very recently, Tang and Yuan (2021) studied the cascade submodular maximization problem under the adaptive setting. They aimed at selecting a group of items sequentially based on the feedback from previously selected items.…”