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  • Variational Bayesian Reinforcement Learning with Regret Bounds
    In reinforcement learning the Q-values summarize the expected future rewards that the agent will attain However, they cannot capture the epistemic uncertainty about those rewards In this work we derive a new Bellman operator with associated fixed point we call the `knowledge values' These K-values compress both the expected future rewards and the epistemic uncertainty into a single value
  • Bandits: UCB Regret, Bayesian Bandits, and Thompson Sampling
    Bayesian Bernoulli bandit (cont’d) 21 Bayesian Bernoulli bandit with uniform prior on gives a running posterior on the mean of each arm that is μ k Beta(1+#{arm k successes},1+#{arm k failures}) (derived by Bayes rule and some algebra, see HW2) has mean (posterior mean = what we expect to be):
  • Bayesian reinforcement learning: A basic overview
    In line with the recognition that learning is essential for adaptive behaviour in multiple domains, including perception and attention, there has been emphasis on what the goal of learning is and why it is appropriate (a question living at the computational level of explanation in the terms of Marr, 1982) This complements the question of the processes involved in learning (which lie at the
  • Efficient Exploration in Average-Reward Constrained Reinforcement . . .
    Efficient Exploration in Average-Reward Constrained Reinforcement Learning: Achieving Near-Optimal Regret With Posterior Sampling Danil Provodin1 2 Maurits Kaptein1 Mykola Pechenizkiy1 3 Abstract We present a new algorithm based on posterior sampling for learning in Constrained Markov De-cision Processes (CMDP) in the infinite-horizon
  • Regret Bounds for Information-Directed Reinforcement Learning - NIPS
    As a consequence, we derive prior-free Bayesian regret bounds for vanilla-IDS which learns the whole environment under tabular finite-horizon MDPs In addition, we propose a computationally-efficient regularized-IDS that maximizes an additive form rather than the ratio form and show that it enjoys the same regret bound as vanilla-IDS
  • Model-based Reinforcement Learning for Continuous Control with . . .
    regret bound for PSRL in continuous state-action spaces can be polynomial in the episode length Hand simultaneously sub-linear in T: For the linear case, we develop a Bayesian regret bound of O~(H3=2d p T) Using feature embedding, we derive a bound of O~(H3=2d ˚ p T) Our regret bound match the order of best-known regret bound of UCB-based
  • Introduction to Regret in Reinforcement Learning
    These probabilities are computed as (Cumulative Regret for Action) Total Regret Where Total Regret is the sum of positive Cumulative Regrets of the same row In case the Total Regret is zero, we assign equal probabilities for each action (check the 2nd row)
  • Information-Theoretic Minimax Regret Bounds for Reinforcement Learning . . .
    The Bayesian regret of an MDP following a policy π, denoted by BRM(π,PΘ) is de-fined as the average regret with respect to a prior distribution of PΘ of random variable Θ The Bayesian Regret is given by BRM(π,PΘ) := EΘ∼P Θ[RM(π,Θ)] Proposition 1 Let PΘ be absolutely continuous with respect to µ with density pΘ Then, the


















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