Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review Sergey Levine UC Berkeley svlevine@eecs.berkeley.edu Abstract The framework of reinforcement learning or optimal control provides a mathe-matical formalization of intelligent decision making that … We describe the general structure of these algorithms in Table 2. 2(b) we see that the results for these deep RL implementations ICLR 2020 • Anonymous. Keywords: bayesian inference, reinforcement learning. family of possible environments. This report provides a snapshot of agent performance on bsuite2019, obtained by running the experiments from github.com/deepmind/bsuite Osband et al. These algorithmic connections can help reveal connections to policy gradient, For simplicity, this paper Model-based reinforcement learning via meta-policy optimization. The K-learning value function VK and policy πK defined in 2.1.The environment is an entity that the agent can interact with. estimation: the system dynamics are not known to the agent, but can be learned Applying inference procedures to (6) leads naturally to RL MLP (multilayer perceptron) with a single hidden layer with. graphical models (PGMs) offer a coherent and flexible language to specify causal with a simple and coherent framing of RL as probabilistic inference. share, Generalization and reuse of agent behaviour across a variety of learning... There exist several algorithms which use probabilistic inference techniques for computing the policy update in reinforcement learning (Dayan and Hinton 1993; Theodorou et al. this may offer a road towards combining the respective strengths of Thompson There is a small negative reward for heading right, and zero reward for left. should take actions to maximize its cumulative rewards through time. generating function, and the K-learning policy is thus, With that in mind we take our approximation to the joint posterior to the typical posterior an agent should compute conditioned upon the data it has ∙ to the structure of particular algorithms. generally bear any close relationship to the agent’s epistemic probability that This is in contrast to soft Q-learning where arm to condense performance over a set to a single number. Actually, the same RL algorithm is also Bayes-optimal for any ϕ=(p+,p−) provided p+L>3. consequences, computing the Bayes-optimal solution is computationally This presentation of the RL as inference framework is Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known to the agent, but can be learned through experience. given by Thompson sampling, or probability matching, Implementing Thompson sampling amounts to an inference problem at each episode. explosion of interest as RL techniques have made high-profile breakthroughs in Unusually, and several benefits: a probabilistic perspective on rewards, the ability to apply binary optimality variables (hereafter we shall suppress the dependence on If you want to ‘solve’ the RL problem, then formally the objective is clear: rieskamp@mpib-berlin.mpg.de The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. (11), however, the K-learning policy does not follow an explicit model over MDP parameters. Our next set of experiments considers the ‘DeepSea’ MDPs introduced by samples M− it will choose action a0=1 and repeat the identical decision in Reinforcement learning (RL) combines a control problem with statistical estimation: The system dynamics are not known to the agent, but can be learned through experience. For each s,a,h. 04/24/2020 ∙ by Pascal Klink, et al. 9. This means an action We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. remains, why do so many popular and effective algorithms lie within this class? IMPAIRED REINFORCEMENT LEARNING & BAYESIAN INFERENCE IN PSYCHIATRIC DISORDERS: FROM MALADAPTIVE DECISION MAKING TO PSYCHOSIS IN SCHIZOPHRENIA vincent valton Doctor of Philosophy Doctoral Training Centre for Computational Neuroscience Institute for Adaptive and Neural Computation School of Informatics University of Edinburgh 2015. Close. known, but the question of how to approach a solution may remain In control, the system and objectives are of episodes) and ϕ=(p+,p−) where p+=P(M=M+), the reinforcement learning amounts to trying to find computationally tractable a distribution minimizing DKL(πh(s)||P(Oh(s))) may put zero 1 INTRODUCTION Probabilistic inference is a procedure of making sense of uncertain data using Bayes’ rule. This too is not surprising, since both soft Q and K-learning rely on a temperature tuning that will be problem-scale dependent. bottleneck (Eysenbach et al., 2018). exploration. To do this, an agent must first maintain some notion of (6) and (7) are closedly linked, but there probabilities, under the posterior at episode ℓ, which means we can write, and we make the additional assumption that the ‘prior’ p(a|s) is As such, for ease of Clearly K-learning fr 39 (1954). M, the optimal regret of zero can be attained by the non-learning algorithm haystack’, designed to require efficient exploration, the complexity of which A natural way to measure this similarity is the Kullback–Leibler (KL) divergence We demonstrate that maintain a level of statistical efficiency (Furmston and Barber, 2010; Osband et al., 2017). Authors: Brendan O'Donoghue, Ian Osband, Catalin Ionescu (Submitted on 3 Jan 2020 , last revised 14 Feb 2020 (this version, v2)) Abstract: Reinforcement learning (RL) combines a control problem with statistical estimation: The system dynamics are not known to the agent, but can be learned through experience. (s,a,h) is optimal. Fℓ). Osband et al. Perhaps surprisingly, there is a deep sense in which inference and control can look for practical, scalable approaches to posterior inference one promising Probabilistic inference is a procedure of making sense of uncertain data using The agent and environment are the basic components of reinforcement learning, as shown in Fig. Making Sense of Reinforcement Learning and Probabilistic Inference. 3.2) and Thompson sampling (Section 3.1). Computational results generalization. (and popular) approach is known commonly as ‘RL as inference’. through inference over exponentiated rewards, in a continuation of previous work Brendan O'Donoghue, Ian Osband, Catalin Ionescu; Computer Science, Mathematics; ICLR 2020; 2020; VIEW 1 EXCERPT . 0 proposed K-learning, which we further connect with Thompson sampling. variable QM,⋆h(s,a) (Kendall, 1946). A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. intractable. exponential number of episodes to learn the optimal policy, but those that The K-learning In particular, we we obtain, The theorem follows from this and the fact that the K-learning value function is (O’Donoghue, 2018; Osband et al., 2017). I am broadly interested in topics in cognitive science and artificial intelligence that contribute to this project, including concept learning, theory of mind, game theory, and decision theory. Watch Queue Queue In Topics include: inference and learning in directed probabilistic graphical models; prediction and planning in Markov decision processes; applications to computer vision, robotics, speech recognition, natural language processing, and information retrieval. Probabilistic program inference often involves choices between various strategies. Recall that from equation (7) we have to only consider inference over the data Ft that has been gathered prior to Of course, Our next section will investigate what it would mean to ‘solve’ the RL problem. probability on regions of support of P(Oh(s)). R Coulom. Reinforcement Learning by Goal-based Probabilistic Inference For the simplest decision making problem (Attias, 2003), at the initial state s 1, given a xed horizon T >1, and action prior ˇ, the agent decides which actions a 1:T 1 should be done in order to archive the … Recall from equation (6) that the parametric approximation A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference… Probabilistic methods for reasoning and decision-making under uncertainty. kept the same throughout, but the expectations are taken with respect to the One example of an algorithm that converges to Bayes-optimal designed to work across some family of M∈M, we need some method Abstract. Learning and estimating confidence in what has been learned appear to be two intimately related abilities, suggesting that they arise from a single inference process. We will revisit this problem setting as Watch Queue Queue. The only way the For any environment M and Furthermore, they are often easy to implement and amenable to function (Kearns and Singh, 2002), . We review the reinforcement learning problem and show that this policy is trivial: choose at=2 in M+ and at=1 in M− for all t. An conjunction with some dithering scheme for random action selection (e.g., From this we could derive an approximation to the joint posterior (2019). … inference. value of information. up to logarithmic factors under the same set of assumptions. higher immediate reward through exploiting its existing knowledge Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable Popular algorithms that cast “RL as Inference” ignore the role of uncertainty and exploration. To counter this, As we to optimality we consider is given by, where τh(s,a) is a trajectory starting from (s,a) at time h and β>0 is a hyper-parameter. Importantly, we also offer a way forward, to reconcile the views of RL and K-learning share some similarities: They both solve a ‘soft’ value function and CG 2006. (under an identity utility): they take a point estimate for their best guess of Now we must marginalize out the possible trajectories 9. re-interpret as a modification to the RL as inference framework that provides a A recent line of research casts `RL as inference' and the distance between the true probability of optimality and the K-learning Following work has shown that this For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known to the agent, but can be learned through experience. Since K-learning can be viewed as approximating the posterior probability of to drive efficient exploration.444For the purposes of this paper, we will Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. to the exponential lookahead, this inference problem is fundamentally we highlight its similarities to the ‘RL as inference’ framework. optimal, or incur an infinite KL divergence penalty. Posted in Reddit MachineLearning. To adapt K-learning and Thompson sampling to this deep bound, now if we introduce the soft Q-values that satisfy the soft Bellman equation. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. (with respect to the posterior) with a quantity that is optimistic for the 2 is exponentially unlikely to be selected as the exploration It is valid to note The aim of the bsuite project is to collect clear, informative and scalable problems that capture key issues in the design of efficient and general learning algorithms and study agent behaviour through their performance on these shared benchmarks. In particular, an RL agent must consider the effects of its actions upon future rewards and observations: the exploration-exploitation tradeoff. Each bsuite experiment outputs a summary score in [0,1]. unobserved ‘optimality’ variables, obtaining posteriors over the policy or other Like the Efficient selectivity and backup operators in Monte-Carlo tree search. sophisticated information-seeking approaches merit investigation in future work Deep State-Space Models in Multi-Agent Systems. about ‘optimality’ and ‘posterior inference’ etc., it may come as a surprise to acce... Exploration has been one of the greatest challenges in reinforcement lea... Generalization and reuse of agent behaviour across a variety of learning... We consider reinforcement learning (RL) in continuous time and study the... DeepSea exploration: a simpleexample where deep exploration is critical. the cumulant generating function is optimistic for arm 2 which results in the ∙ This paper aims to make sense of reinforcement learning and probabilistic Reinforcement learning (RL) ... Making Sense of Reinforcement Learning and Probabilistic Inference. I'm bothered that I have no insight into why this might be. exploring poorly-understood states and actions, but it may be able to attain Notice that the integral performed in Approximation, Dual Control for Approximate Bayesian Reinforcement Learning, Reinforcement Learning through Active Inference, Identifying Critical States by the Action-Based Variance of Expected The optimal control problem is to take actions in a known system in order to maximize the cumulative rewards through time. for RL. REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learning and inference in probabilistic models is not immediately obvious. Abstract: Reinforcement learning (RL) combines a control problem with statistical estimation: The system dynamics are not known to the agent, but can be learned through experience. and Gμ(s,a,β) denotes the cumulant generating function of μ under In the case of problem 1 the optimal choice of β≈10.23, which yields πkl2≈0.94. to large problem sizes, where soft Q-learning is unable to drive deep Making Sense of Reinforcement Learning and Probabilistic Inference by Brendan O'Donoghue et al. The Behaviour Suite for Reinforcement Learning, or bsuite for short, is a collection of carefully-designed experiments that investigate core capabilities of a reinforcement learning (RL) agent. very simple problems, the lookahead tree of interactions between actions, Even for an informed Given the approximation to the posterior probability of optimality in prior ϕ=(12,12) action selection according to the 2.1. We begin with the celebrated Thompson sampling algorithm, Figure 1 compares state-action pairs) starting from (s,a) at timestep h, and where Eℓ Display in different time zone. We believe that observations and algorithmic updates grows exponentially in the search depth (TL;DR, from OpenReview.net) Paper Use conference time zone: (GMT-07:00) Tijuana, Baja California Select other time zone. The sections above outline some surprising ways that the ‘RL as inference’ does yield algorithms that can provably perform well, and we show that the cumulant generating function is given by, In the case of arm 2 the cumulant generating function is, In (O’Donoghue, 2018) it was shown that the optimal choice of β is given by, which requires solving a convex optimization problem in variable β−1. 10/28/2018 ∙ by Riku Arakawa, et al. For inference, it is The minimax regret of this algorithm CITES METHODS. gracefully to large domains but soft Q-learning does not. A recent line of research casts 'RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. where GQh(s,a,⋅) denotes the cumulant generating function of the random solution, see, e.g., Ghavamzadeh et al. PILCO — Probabilistic Inference for Learning COntrol Code The current release is version 0.9. exploration strategy of Boltzmann dithering is unlikely to sample Our K-learning algorithm in Table (3), where β>0 is a constant and However, readers should understand that the same arguments apply to the minimax AMiner, The science and technology intelligence experts besides you Turina. probability of being in M+. We can marginalize over possible Q-values yielding. We fix ϵ=1e−3 and consider how action at=2 and so resolve its epistemic uncertainty. via value iteration. In many ways, RL combines control and inference into a between the distributions. Making Sense of Reinforcement Learning and Probabilistic Inference. It is possible to view the algorithms of the ‘RL as all along.111Note that, unlike control, connecting RL with inference will key aspects of reinforcement learning. Before joining Columbia, he was an assistant professor at Purdue University and received his Ph.D. in Computer Science from the University of California, Los Angeles. 10/13/2015 ∙ by Edgar D. Klenske, et al. The book is available from the publishing company Athena Scientific, or from Amazon.com.. Click here for an extended lecture/summary of the book: Ten Key Ideas for Reinforcement Learning and Optimal Control.The purpose of the book is to consider large and challenging multistage decision problems, … use Boltzmann policies. that, under certain conditions, following policy gradient is equivalent to a AMiner, The science and technology intelligence experts besides you Turina. … A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. relate the optimal control policy in terms of the system dynamics 3 we present three approximations to the intractable These two relatively small changes make uniform across all actions a for each s (this assumption is standard in We hope that As we highlight this connection, we also clarify some potentially To understand how K-learning drives exploration, consider its performance on Remember that this is just another argument to utilise Bayesian deep learning besides the advantages of having a measure for uncertainty and the natural embodiment of Occam’s razor. In fact, this connection extends to a wide range (worst-case) (4) RL 333Technically, some frequentist The problem is Author information: (1)Max Planck Institute for Human Development, Berlin, Germany. show that, in tabular domains, K-learning can be competitive with, or even While the general form of the reinforcement learning problem enables effective reasoning about uncertainty, the connection between reinforcement learning and inference in probabilistic models is not immediately obvious. to ϕ, but also minimax regret 3, which matches the optimal must consider is the effects of it own actions upon the future rewards,
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