Death & Suicide in Universal Artificial Intelligence J.Martin T.Everitt M.Hutter Artificial General Intelligence, 2016 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 1 / 19
Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 2 / 19
Defining Death for Agents Motivations Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 3 / 19
Defining Death for Agents Motivations Generally Intelligent Agents and Death Why AIXI, and why agent death? Why do we need theoretical models of generally intelligent agents? Guiding the construction of agents. Understanding agent reasoning and behaviour. Developing control strategies. Why study agent death? AI safety and the shutdown problem. Tripwire control strategies. Why a subjective definition of death? Objective definition difficult (even for biological organisms). Want to understand how the agent itself will reason about its death. J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 4 / 19
Defining Death for Agents Agents and Environments Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 5 / 19
Defining Death for Agents Agents and Environments The Agent-Environment Model States vs. History Sequences Agent is a policy π : maps a history æ < t to an action a t ∈ A Environment µ : maps a history æ < t a t to a percept e t ∈ E History Model State Model (MDP) . . . a t − 2 e t − 2 a t − 1 e t − 1 Agent π Agent π e t a t s t a t Environment µ Environment µ . . . a t − 2 e t − 2 a t − 1 e t − 1 a t J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 6 / 19
Defining Death for Agents Agents and Environments Two Generally Intelligent Agents AI µ and AIXI Definition (The Value Function) The value (expected total future reward) of policy π in environment ν : ∞ ν ( æ < t a t ) = 1 V π � � γ k r k ν ( e t : k | æ < t a t : k ) Γ t k = t e t : k Definition (AI µ : knows the true environment) For the true environment µ , the agent AI µ is a µ -optimal policy π µ ( æ < t ) := arg max V π µ ( æ < t ) . π Definition (AIXI: must learn the environment) The agent AIXI models the environment using a mixture ξ . It is a ξ -optimal policy: π ξ ( æ < t ) := arg max V π ξ ( æ < t ) . π J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 7 / 19
Defining Death for Agents Death as a Death-state Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 8 / 19
Defining Death for Agents Death as a Death-state Defining a Death-State in an MDP In an MDP we can define a special accepting state as the death state. The agent remains in the death state no matter what actions it takes. a 2 a 1 a 1 , a 2 S 1 S 2 S d a 1 a 2 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 9 / 19
Defining Death for Agents Death as a Death-state Defining a Death-State in a General Environment ¯ In general environments, we e t can’t explicitly define a æ < t ¯ a ¯ a death state . æ < t e t Must instead define it via a æ < t a ′ æ < t a ′ e d a ′ death-percept e d e d ≡ ( o d , r d ). Definition (Death-state in a general environment) Given a true environment µ and a history æ < t a t , we say that the agent is in a death-state at time t if for all t ′ ≥ t and all a ( t +1): t ′ ∈ A ∗ , µ ( e d t ′ | æ < t æ d t : t ′ − 1 a t ′ ) = 1 . An agent dies at time t if the agent is not in the death-state at t − 1 and is in the death-state at t . J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 10 / 19
Defining Death for Agents Death-probability and Semimeasure Loss Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 11 / 19
Defining Death for Agents Death-probability and Semimeasure Loss Semimeasures and Semimeasure Loss Definition (Semimeasure) A semimeasure over an alphabet X is a function ν : X ∗ → [0 , 1] such that � (1) ν ( ǫ ) ≤ 1, and (2) 1 ≥ ν ( y | x ) . y ∈X ν ( x ) is the probability that a sequence starts with the string x . ν may not be a proper probability measure as it need not sum to 1. There may be some probability the sequence will just terminate. Definition (Instantaneous measure loss) The instantaneous measure loss of a semimeasure ν at time t given a history æ < t a t is: � L ν ( æ < t a t ) = 1 − ν ( e t | æ < t a t ) e t J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 12 / 19
Defining Death for Agents Death-probability and Semimeasure Loss Measure Loss as Death-Probability Definition (Semimeasure-death) An agent dies at time t in an environment µ if, given a history æ < t a t , µ does not produce a percept e t (i.e. if the history sequence terminates). The µ -probability of death at t given a history æ < t a t is equal to L µ ( æ < t a t ), the instantaneous µ -measure loss at t . Advantages of this definition: ¯ e t Simple/Intuitive: No need to define æ < t ¯ a ¯ a a bizarre death-percept or æ < t death-state. e t æ < t a ′ a ′ General: Any sequence of death-probabilities captured by losses of some semimeasure µ . Equivalence of Behaviour: agents behave identically w.r.t semi-measure death and death-state. J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 13 / 19
Results Known Environments: AI µ Outline Defining Death for Agents 1 Motivations Agents and Environments Death as a Death-state Death-probability and Semimeasure Loss Results 2 Known Environments: AI µ Unknown Environments: AIXI Conclusion 3 J.Martin, T.Everitt, M.Hutter (Research School of Information Sciences and Engineering Australian National University) Death & Suicide in Universal Artificial Intelligence Artificial General Intelligence, 2016 14 / 19
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