Optimization from Structured Samples for Coverage and Influence Functions

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2022 Data-driven Optimization Workshop: Optimization from Structured Samples for Coverage and Influence Functions

Speaker: Zhijie Zhang, Fuzhou University

We revisit the optimization from samples (OPS) model, which studies the problem of optimizing objective functions directly from the sample data. Previous results showed that we cannot obtain a constant approximation ratio for the maximum coverage problem using polynomial independent samples of the form {S_i,f(S_i )}_(i=1)^t (BRS, STOC17), even if coverage functions are (1-ϵ)-PMAC learnable using these samples (BDF+, SODA12). In this work, to circumvent the impossibility result of OPS, we propose a stronger model called optimization from structured samples (OPSS), where the data samples encode the structural information of the functions. We show that under OPSS model, the maximum coverage problem enjoys constant approximation under mild assumptions on the sample distribution. We further generalize the result and show that influence maximization also enjoys constant approximation under this model.

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