Abstract Many sequential decision-making problems require an agent to reason about both multiple objectives and uncertainty regarding the environment’s state. Such problems can be naturally modelled as multi-objective partially observable Markov decision processes (MOPOMDPs). We propose optimistic linear support with alpha reuse (OLSAR), which computes a bounded approximation of the optimal solution set for all possible weightings of the objectives. The main idea is to solve a series of scalarized single-objective POMDPs, each corresponding to a different weighting of the objectives. A key insight underlying OLSAR is that the policies and value functions produced when solving scalarized POMDPs in earlier iterations can be reused to more quickly solve scalarized POMDPs in later iterations. We show experimentally that OLSAR outperforms, both in terms of runtime and approximation quality, alternative methods and a variant of OLSAR that does not leverage reuse.