Full Abstract: How can we design good goals for arbitrarily intelligent agents? Reinforcement learning (RL) is a natural approach. Unfortunately, RL does not work well for generally intelligent agents, as RL agents are incentivised to shortcut the reward sensor for maximum reward -- the so-called wireheading problem. In this paper we suggest an alternative to RL called value reinforcement learning (VRL). In VRL, agents use the reward signal to learn a utility function. The VRL setup allows us to remove the incentive to wirehead by placing a constraint on the agent's actions. The constraint is defined in terms of the agent's belief distributions, and does not require an explicit specification of which actions constitute wireheading.