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Bayesian reinforcement learning Markov decision processes and approximate Bayesian computation Christos Dimitrakakis Chalmers April 16, 2015 . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 1/60 Overview Subjective probability and utility Subjective probability Rewards and preferences Bandit problems Bernoulli bandits Markov decision processes and reinforcement learning Markov processes Value functions Examples Bayesian reinforcement learning Reinforcement learning Bounds on the utility Planning: Heuristics and exact solutions Belief-augmented MDPs The expected MDP heuristic The maximum MDP heuristic Inference: Approximate Bayesian computation Properties of ABC . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 2/60 Subjectiveprobabilityandutility Subjective probability and utility Subjective probability Rewards and preferences Bandit problems Bernoulli bandits Markov decision processes and reinforcement learning Markov processes Value functions Examples Bayesian reinforcement learning Reinforcement learning Bounds on the utility Planning: Heuristics and exact solutions Belief-augmented MDPs The expected MDP heuristic The maximum MDP heuristic Inference: Approximate Bayesian computation Properties of ABC . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 3/60 Subjectiveprobabilityandutility Subjectiveprobability Objective Probability x θ P Figure: Thedoubleslitexperiment . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 4/60 Subjectiveprobabilityandutility Subjectiveprobability Objective Probability Figure: Thedoubleslitexperiment . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 4/60 Subjectiveprobabilityandutility Subjectiveprobability Objective Probability Figure: Thedoubleslitexperiment . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 4/60 Subjectiveprobabilityandutility Subjectiveprobability What about everyday life? . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 5/60 ▶ Outcomes of decisions are uncertain. ▶ How can we represent this uncertainty? Subjective probability ▶ Describe which events we think are more likely. ▶ We quantify this with probability. Why probability? ▶ Quanti(cid:12)es uncertainty in a \natural" way. ▶ A framework for drawing conclusions from data. ▶ Computationally convenient for decision making. Subjectiveprobabilityandutility Subjectiveprobability Subjective probability ▶ Making decisions requires making predictions. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 6/60 ▶ How can we represent this uncertainty? Subjective probability ▶ Describe which events we think are more likely. ▶ We quantify this with probability. Why probability? ▶ Quanti(cid:12)es uncertainty in a \natural" way. ▶ A framework for drawing conclusions from data. ▶ Computationally convenient for decision making. Subjectiveprobabilityandutility Subjectiveprobability Subjective probability ▶ Making decisions requires making predictions. ▶ Outcomes of decisions are uncertain. . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 6/60 Subjective probability ▶ Describe which events we think are more likely. ▶ We quantify this with probability. Why probability? ▶ Quanti(cid:12)es uncertainty in a \natural" way. ▶ A framework for drawing conclusions from data. ▶ Computationally convenient for decision making. Subjectiveprobabilityandutility Subjectiveprobability Subjective probability ▶ Making decisions requires making predictions. ▶ Outcomes of decisions are uncertain. ▶ How can we represent this uncertainty? . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . .. . . . ChristosDimitrakakis (Chalmers) Bayesianreinforcementlearning April16,2015 6/60

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Subjective probability. ▻ Making decisions requires making predictions. Christos Dimitrakakis (Chalmers). Bayesian reinforcement learning. April 16

Bayesian reinforcement learning - Markov decision processes and approximate Bayesian ... PDF

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Subjective probability. ▻ Making decisions requires making predictions. Christos Dimitrakakis (Chalmers). Bayesian reinforcement learning. April 16

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