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Learning Automaton (LA) is an adaptive self-organized model that improves itsaction-selection through interaction with an unknown environment. LA withfinite action set can be classified into two main categories: fixed andvariable structure. Furthermore, variable action-set learning automaton (VASLA)is one of the main subsets of variable structure learning automaton. In thispaper, we propose VDHLA, a novel hybrid learning automaton model, which is acombination of fixed structure and variable action set learning automaton. Inthe proposed model, variable action set learning automaton can increase,decrease, or leave unchanged the depth of fixed structure learning automatonduring the action switching phase. In addition, the depth of the proposed modelcan change in a symmetric (SVDHLA) or asymmetric (AVDHLA) manner. To the bestof our knowledge, it is the first hybrid model that intelligently changes thedepth of fixed structure learning automaton. Several computer simulations areconducted to study the performance of the proposed model with respect to thetotal number of rewards and action switching in stationary and non-stationaryenvironments. The proposed model is compared with FSLA and VSLA. In order todetermine the performance of the proposed model in a practical application, theselfish mining attack which threatens the incentive-compatibility of aproof-of-work based blockchain environment is considered. The proposed model isapplied to defend against the selfish mining attack in Bitcoin and comparedwith the tie-breaking mechanism, which is a well-known defense. Simulationresults in all environments have shown the superiority of the proposed model.

VDHLA: Variable Depth Hybrid Learning Automaton and Its Application to Defense Against the Selfish Mining Attack in Bitcoin