Abstract
Reinforcement learning (RL) is a general paradigm for studying intelligent behaviour, with applications ranging from artificial intelligence to psychology and economics. AIXI is a universal solution to the RL problem; it can learn any computable environment. A technical subtlety of AIXI is that it is defined using a mixture over semimeasures that need not sum to 1, rather than over proper probability measures. In this work we argue that the shortfall of a semimeasure can naturally be interpreted as the agent’s estimate of the probability of its death. We formally define death for generally intelligent agents like AIXI, and prove a number of related theorems about their behaviour. Notable discoveries include that agent behaviour can change radically under positive linear transformations of the reward signal (from suicidal to dogmatically self-preserving), and that the agent’s posterior belief that it will survive increases over time.
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Notes
- 1.
For simplicity we hereafter simply refer to the environment itself as \(\nu \).
- 2.
Note that \(\nu \) is not a distribution over actions, so the presence of actions in the condition of \(\nu (e_t\mid \ae _{<t})\) is an abuse of notation we adopt for simplicity.
- 3.
For technical reasons we require that \(e^d \notin \mathcal {E}\).
- 4.
To compare an agent’s behaviour in \(\mu \) with that in \(\mu '\), we should also augment its policy \(\pi \) so that it is defined over \((\mathcal {A}\times \mathcal {E}_d)^*\). Since actions taken once in the death-state are inconsequential, however, this modification is purely technical and for simplicity we still refer to the augmented policy as \(\pi \).
- 5.
If the two formalisations predicted different behaviour, or were only applicable in incomparable environment classes, we might worry that our results were more reflective of our model choice than of any general property of intelligent agents.
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Martin, J., Everitt, T., Hutter, M. (2016). Death and Suicide in Universal Artificial Intelligence. In: Steunebrink, B., Wang, P., Goertzel, B. (eds) Artificial General Intelligence. AGI 2016. Lecture Notes in Computer Science(), vol 9782. Springer, Cham. https://doi.org/10.1007/978-3-319-41649-6_3
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DOI: https://doi.org/10.1007/978-3-319-41649-6_3
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