Mobile edge computing pushes computationally-intensive services closer to the user to provide reduced delay due to physical proximity. This has led many to consider deploying deep learning models on the edge – commonly known as edge intelligence (EI). EI services can have many model implementations that provide different QoS. For instance, one model can perform inference faster than another (thus reducing latency) while achieving less accuracy when evaluated. In this paper, we study joint service placement and model scheduling of EI services with the goal to maximize Quality-of-Servcice (QoS) for end users where EI services have multiple implementations to serve user requests, each with varying costs and QoS benefits. We cast the problem as an integer linear program and prove that it is NP-hard. We then prove the objective is equivalent to maximizing a monotone increasing, submodular set function and thus can be solved greedily while maintaining a (1 – 1/e)-approximation guarantee. We then propose two greedy algorithms: one that theoretically guarantees this approximation and another that empirically matches its performance with greater efficiency. Finally, we thoroughly evaluate the proposed algorithm for making placement and scheduling decisions in both synthetic and real-world scenarios against the optimal solution and some baselines. In the real-world case, we consider real machine learning models using the ImageNet 2012 data-set for requests. Our numerical experiments empirically show that our more efficient greedy algorithm is able to approximate the optimal solution with a 0.904 approximation on average, while the next closest baseline achieves a 0.607 approximation on average.
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Constrained Robust Submodular Partitioning
In the robust submodular partitioning problem, we aim to allocate a set of items
into m blocks, so that the evaluation of the minimum block according to a
submodular function is maximized. Robust submodular partitioning promotes
the diversity of every block in the partition. It has many applications in machine
learning, e.g., partitioning data for distributed training so that the gradients
computed on every block are consistent. We study an extension of the robust
submodular partition problem with additional constraints (e.g., cardinality, multiple
matroids, and/or knapsack) on every block. For example, when partitioning data
for distributed training, we can add a constraint that the number of samples of each
class is the same in each partition block, ensuring data balance. We present two
classes of algorithms, i.e., Min-Block Greedy based algorithms (with an ⌦(1/m)
bound), and Round-Robin Greedy based algorithms (with a constant bound) and
show that under various constraints, they still have good approximation guarantees.
Interestingly, while normally the latter runs in only weakly polynomial time, we
show that using the two together yields strongly polynomial running time while
preserving the approximation guarantee. Lastly, we apply the algorithms on a
real-world machine learning data partitioning problem showing good results.
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- Award ID(s):
- 2106389
- NSF-PAR ID:
- 10353741
- Date Published:
- Journal Name:
- Advances in neural information processing systems
- ISSN:
- 1049-5258
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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Abstract We consider the problem of covering multiple submodular constraints. Given a finite ground set
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