Pure profit-oriented continuous influence maximization considering cost budget: A gradient descent-based approach

Abstract

Continuous influence maximization (CIM) has been commonly applied in online viral marketing. To maximize the sales revenue, CIM assigns each user a continuous weight reflecting the likelihood and cost for him becoming a seed. Most of the existing studies on CIM aim to maximize the revenue from the sale of products, but do not pay attention to its net profit, which is the revenue minus the cost of promotion. However, in real-world marketing, the fundamental goal of business is to maximize net profit, rather than simply maximizing sales revenue. Moreover, traditional CIM assumes a budget to limit the total cost of all users. This assumption does not tenable in practical applications. In practice, it is not necessary to incur costs for all the users. Instead, the budget should be set only for the cost associated with the seed set. In this paper, an extended CIM problem of budget-constrained cost distribution for profit maximization (BCDPM) is defined. BCDPM aims to maximize the expected net profit by assigning different costs to the customers according to their ability to spread influence of the product, ensuring that the cost of each potential seed set does not exceed the budget. We prove the NP-hardness of BCDPM and the non-monotonicity and non-modularity of its objective function. By formulating the BCDPM problem into a constrained optimization, we present a gradient descent-based algorithm to determine the optimal cost distribution for this problem. An algorithm is presented to compute the gradient for maximizing the increment of profit in each iteration of the gradient descent. To avoid the time-consuming simulations, we design an effective algorithm to get the largest profit increment of each seed set. Experiment results on real and synthetic networks show that the proposed algorithm can obtain much larger expected net profit than other algorithms.