Optimizing Infill Drilling Decisions Using Multi-armed Bandits: Application in a Long-Term, Multi-element Stockpile
Every mining operation faces a decision regarding additional drilling at some point during its lifetime. The two questions that always arise upon making this decision are whether more drilling is required and, if so, where the additional drill holes should be located. The method presented in this paper addresses both of these questions through an optimization in a multi-armed bandit (MAB) framework. The MAB optimizes for the best infill drilling pattern while taking geological uncertainty into account by using multiple conditional simulations for the deposit under consideration. MAB formulations are commonly used in many applications where decisions have to be made between different alternatives with stochastic outcomes, such as Internet advertising, clinical trials and others. The application of the proposed method to a long-term, multi-element stockpile, which is a part of a gold mining complex in Nevada, USA, demonstrates its practical aspects.
KeywordsDownside Risk Average Reward Cutoff Grade Kriging Variance Geological Uncertainty
We thank Newmont Mining Corporation for providing us with the data necessary to conduct this research and the organizations that funded this research: the Natural Sciences and Engineering Research Council of Canada (NSERC) Discovery Grant 239019 and the COSMO Mining Industry Consortium (AngloGold Ashanti, Barrick Gold, BHP Billiton, De Beers Canada, Kinross Gold, Newmont Mining and Vale) supporting the COSMO laboratory.
- Agrawal S, Goyal N (2012) Analysis of Thompson sampling for the multi-armed bandit problem. Proceedings of the 25th Annual Conference on Learning Theory (COLT)Google Scholar
- Chorn LG, Carr PP (1997) The value of purchasing information to reduce risk in capital investments. SPE hydrocarbon economics and evaluation symposium. Society of Petroleum EngineersGoogle Scholar
- Diehl P, David M (1982) Classification of ore reserves/resources based on geostatistical methods. CIM Bull 75(838):127–136Google Scholar
- Goovaerts P (1997) Geostatistics for natural resources evaluation. Oxford University Press, New YorkGoogle Scholar
- Goria S, Armstrong M, Galli A (2001) Quantifying the impact of additional drilling on an openpit gold project. 2001 annual conference of the IAMG. CancunGoogle Scholar
- May BC, Korda N, Lee A, Leslie DS (2012) Optimistic Bayesian sampling in contextual-bandit problems. J Mach Learn Res 13(1):2069–2106Google Scholar
- Menabde M, Froyland G, Stone P, Yeates G (2007) Mining schedule optimisation for conditionally simulated orebodies. In Orebody modelling and strategic mine planning. p 379–384Google Scholar
- Ravenscroft PJ (1992) Risk analysis of mine scheduling by conditional simulation. Trans Inst Min Metall Sect A 101:A104–A108Google Scholar
- Switzer P, Green AA (1984) Min/max autocorrelation factors for multivariate spatial imagery. Stanford University, Department of Statistics, StandfordGoogle Scholar