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Power-seeking behavior is a key source of risk from advanced AI, but ourtheoretical understanding of this phenomenon is relatively limited. Building onexisting theoretical results demonstrating power-seeking incentives for mostreward functions, we investigate how the training process affects power-seekingincentives and show that they are still likely to hold for trained agents undersome simplifying assumptions. We formally define the training-compatible goalset (the set of goals consistent with the training rewards) and assume that thetrained agent learns a goal from this set. In a setting where the trained agentfaces a choice to shut down or avoid shutdown in a new situation, we prove thatthe agent is likely to avoid shutdown. Thus, we show that power-seekingincentives can be probable (likely to arise for trained agents) and predictive(allowing us to predict undesirable behavior in new situations).

Power-seeking can be probable and predictive for trained agents