Abstract
In this paper, we study the constrained stochastic submodular maximization problem with state-dependent costs. The input of our problem is a set of items whose states (i.e., the marginal contribution and the cost of an item) are drawn from a known probability distribution. The only way to know the realized state of an item is to select that item. We consider two constraints, i.e., inner and outer constraints. Recall that each item has a state-dependent cost, and the inner constraint states that the total realized cost of all selected items must not exceed a give budget. Thus, inner constraint is state-dependent. The outer constraint, on the other hand, is state-independent. It can be represented as a downward-closed family of sets of selected items regardless of their states. Our objective is to maximize the objective function subject to both inner and outer constraints. Under the assumption that larger cost indicates larger “utility”, we present a constant approximate solution to this problem.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
For simplicity, we only consider deterministic policy. However, all results can be easily extended to random policies.
References
Adamczyk, M., Sviridenko, M., Ward, J.: Submodular stochastic probing on matroids. Math. Oper. Res. 41(3), 1022–1038 (2016)
Asadpour, A., Nazerzadeh, H.: Maximizing stochastic monotone submodular functions. Manage. Sci. 62(8), 2374–2391 (2016)
Chekuri, C., Vondrák, J., Zenklusen, R.: Submodular function maximization via the multilinear relaxation and contention resolution schemes. SIAM J. Comput. 43(6), 1831–1879 (2014)
Fukunaga, T., Konishi, T., Fujita, S., Kawarabayashi, K.I.: Stochastic submodular maximization with performance-dependent item costs. In: Proceedings of the AAAI Conference on Artificial Intelligence, vol. 33, pp. 1485–1494 (2019)
Golovin, D., Krause, A.: Adaptive submodularity: theory and applications in active learning and stochastic optimization. J. Artif. Intell. Res. 42, 427–486 (2011)
Gupta, A., Krishnaswamy, R., Molinaro, M., Ravi, R.: Approximation algorithms for correlated knapsacks and non-martingale bandits. In: 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science, pp. 827–836. IEEE (2011)
Tang, S.: Stochastic coupon probing in social networks. In: Proceedings of the 27th ACM International Conference on Information and Knowledge Management, pp. 1023–1031 (2018)
Tang, S.: Beyond pointwise submodularity: non-monotone adaptive submodular maximization in linear time. Theoret. Comput. Sci. 850, 249–261 (2021)
Tang, S.: Beyond pointwise submodularity: non-monotone adaptive submodular maximization subject to Knapsack and k-system constraints. In: Le Thi, H.A., Pham Dinh, T., Le, H.M. (eds.) MCO 2021. LNNS, vol. 363, pp. 16–27. Springer, Cham (2022). https://doi.org/10.1007/978-3-030-92666-3_2
Tang, S.: Stochastic submodular probing with state-dependent costs. In: Wu, W., Du, H. (eds.) AAIM 2021. LNCS, vol. 13153, pp. 170–178. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-93176-6_15
Tang, S., Yuan, J.: Influence maximization with partial feedback. Oper. Res. Lett. 48(1), 24–28 (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this paper
Cite this paper
Tang, S. (2022). Constrained Stochastic Submodular Maximization with State-Dependent Costs. In: Ni, Q., Wu, W. (eds) Algorithmic Aspects in Information and Management. AAIM 2022. Lecture Notes in Computer Science, vol 13513. Springer, Cham. https://doi.org/10.1007/978-3-031-16081-3_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-16081-3_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-16080-6
Online ISBN: 978-3-031-16081-3
eBook Packages: Computer ScienceComputer Science (R0)