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When trying to liquidate a large quantity of a particular stock, the price of that stock is likely to be affected by trades, thus leading to a reduced expected return if we were to sell the entire quantity at once. This leads to the problem of optimal execution, where the aim is to split the sell order into several smaller sell orders over the course of a period of time, to optimally balance stock price with market risk. This problem can be defined in terms of difference equations. Here, we show how we can reformulate this as a multi-objective problem, which we solve with a novel multi-armed bandit algorithm.