In this paper, we address the critical challenges of double-spending and selfish mining attacks in blockchain-based digital currencies. Double-spending is a problem where the same tender is spent multiple times during a digital currency transaction, while selfish mining is an intentional alteration of a blockchain to increase rewards to one miner or a group of miners. We introduce a new attack that combines both these attacks and propose a machine learning-based solution to mitigate the risks associated with them. Specifically, we use the learning automaton, a powerful online learning method, to develop two models, namely the SDTLA and WVBM, which can effectively defend against selfish mining attacks. Our experimental results show that the SDTLA method increases the profitability threshold of selfish mining up to 47$\%$, while the WVBM method performs even better and is very close to the ideal situation where each miner's revenue is proportional to their shared hash processing power. Additionally, we demonstrate that both methods can effectively reduce the risks of double-spending by tuning the $Z$ Parameter. Our findings highlight the potential of SDTLA and WVBM as promising solutions for enhancing the security and efficiency of blockchain networks.