of meta-learning is the gradient-based *Model Agnostic Meta-learning* (MAML) approach[@finn2017model]. MAML aims at learning an initialization that can be adapted to a new task after performing one (or a few) gradient-based update(s); see, e.g., [@fallah2019convergence]. This problem can be written as $$\min_{w \in W} \mathbb{E}_{a\sim P}[f_a(w-\nabla f_a(w))],$$ where $W \subseteq \mathbb{R}^d$ is the feasible set and $l$ is the probability distribution over tasks. The previous works on MAML including [@nichol2018first; @finn2018probabilistic; @DBLP:conf/iclr/GrantFLDG18; @yoon2018bayesian; @DBLP:conf/iclr/AntoniouES19; @rajeswaran2019meta; @fallah2019convergence; @collins2020distribution] consider the case where $W$ is a continuous space. In fact none of these works can be applied to the case where the feasible parameter space is discrete. In this paper, we aim to close this gap and extend the terminology of MAML to discrete settings.

**Submodular Maximization.** Submodular functions have become key concepts in numerous applications such as data summarization [@lin2011class; @wei2013using; @kirchhoff2014submodularity; @mirzasoleiman2016distributed], viral marketing [@kempe2003maximizing], sensor placement [@krause2008near], dictionary learning [@das2011submodular], and influence maximization [@kempe2003maximizing]. It is well-known that for maximizing a monotone and submodular function under the cardinality constraint, the greedy algorithm provides a $(1-1/e)$-optimal solution [@krause2014submodular; @nemhauser1978best; @wolsey1982analysis]. There has been significant effort to improve the scalability and efficiency of the greedy algorithm using lazy, stochastic, and distributed 