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High-powered electric vehicle (EV) charging can significantly increase charging costs due to peak-demand charges. This paper proposes a novel charging algorithm which exploits typically long plugin sessions for domestic chargers and reduces the overall charging power by boost charging the EV for a short duration, followed by low-power charging for the rest of the plugin session. The optimal parameters for boost and low-power charging phases are obtained using reinforcement learning by training on EV's past charging sessions. Compared to some prior work, the proposed algorithm does not attempt to predict the plugin session duration, which can be difficult to accurately predict in practice due to the nature of human behavior, as shown in the analysis. Instead, the charging parameters are controlled directly and are adapted transparently to the user's charging behavior over time. The performance evaluation on a UK dataset of 3.1 million charging sessions from 22,731 domestic charge stations, demonstrates that the proposed algorithm results in 31% of aggregate peak reduction. The experiments also demonstrate the impact of history size on learning behavior and conclude with a case study by applying the algorithm to a specific charge point.