While it is well known that arithmetic circuits can be used for efficient probabilistic inference, arithmetic circuits can also be used for other tasks. In this paper, we show how arithmetic circuits in a semiring setting (i.e., algebraic circuits) can solve decision theoretic inference tasks and a utility learning task under partial observability. The former involves finding the set of decisions that maximises the expected utility. We introduce two approaches for this, both applying algebraic circuits. The learning task involves learning unknown utility values from partially observed interpretations of which the total utility is given. We provide the necessary theory and also perform an experimental evaluation of the approaches.