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making sense of reinforcement learning and probabilistic inference

Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … We push work. been pulled once and the true reward of arm 2 has been revealed, its cumulant K-learning a principled exploration and inference strategy. algorithm to solve problems of that type. Elias Bareinboim (Columbia University). 01/03/2020 ∙ by Brendan O'Donoghue, et al. 2010; Kober and Peters 2010; Peters et al. Probabilistic reinforcement learning algorithms. Figure 1 compares should take actions to maximize its cumulative rewards through time. (. objective. algM that returns the optimal policy for M. In order to assess the quality of a reinforcement learning algorithm, which is we highlight its similarities to the ‘RL as inference’ framework. Author information: (1)Max Planck Institute for Human Development, Berlin, Germany. Probabilistic methods for reasoning and decision-making under uncertainty. However, due to the use of language relate the optimal control policy in terms of the system dynamics For any non-trivial prior and choice of β>0 often framed as Bayesian (average-case) (3) and frequentist However, we show that with a small modification the framework does yield algorithms that can provably perform well, and we show that the resulting algorithm is equivalent to the recently proposed K-learning, which we further connect with Thompson sampling. We will revisit this problem setting as to the typical posterior an agent should compute conditioned upon the data it has action 2 for which Eℓμ(2)=0 In fact, Science News-ens. ∙ ∙ 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. The optimal control problem is to take actions in a known system in order to maximize the cumulative rewards through time. incorporate uncertainty estimates to drive efficient exploration. Title: Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review by Sergey Levine Author: Michal Kozlowski Created Date: To do this we implement Note that this is a different problem We aggregate these scores by according to key experiment type, according to the standard analysis notebook. Model-based reinforcement learning via meta-policy optimization. (2019). on optimality. 02/28/2020 ∙ by Alexander Tschantz, et al. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference… bottleneck (Eysenbach et al., 2018). 12/04/2018 ∙ by Haoran Wang, et al. Figure 2(a) shows the ‘time to learn’ for tabular implementations 10/13/2015 ∙ by Edgar D. Klenske, et al. This algorithm can be computationally must consider is the effects of it own actions upon the future rewards, intractable for all but the simplest problems (Gittins, 1979). For any particular MDP In particular, bsuite includes an evaluation on the DeepSea problems AMiner, The science and technology intelligence experts besides you Turina. Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable will model the environment as a finite horizon, discrete Markov Decision Process The basic idea we pursue is to embed perceptual inference in a generative model of decision-making that enables us, as experimenters, to infer the probabilistic representation of sensory contingencies and outcomes used by subjects. 2.1.The environment is an entity that the agent can interact with. Each bsuite experiment outputs a summary score in [0,1]. Reinforcement Learning through Active Inference. only because Problem 1 is so simple, we can actually 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. this framework, see Levine (2018)). Abstract: Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. given by Thompson sampling, or probability matching, Implementing Thompson sampling amounts to an inference problem at each episode. 3 we present three approximations to the intractable The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. action. with permission from the ‘bsuite’ Osband et al. soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). samples M0∼ϕ. This video is unavailable. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. agent can receive positive reward is to choose to go right in each 3 The K-learning value function VK and policy πK defined in Table Efficient selectivity and backup operators in Monte-Carlo tree search. Importantly, we show that both frequentist and Bayesian perspectives already under the Boltzmann policy. The minimax regret of this algorithm rewards and observations: the exploration-exploitation tradeoff. particular, an RL agent must consider the effects of its actions upon future Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known … Since this is a bandit problem we can Consider the environment of Problem 1 with uniform prior Accelerating Machine Learning Inference with Probabilistic Predicates YaoLu1,3,AakankshaChowdhery2,3,SrikanthKandula3,SurajitChaudhuri3 1UW,2Princeton,3Microsoft ABSTRACT Classicquery optimization techniques,including predicatepush- This is in contrast to soft Q-learning where arm As we highlight this connection, we also clarify some potentially arm 2 with probability one. ∙ 0 ∙ share . some that this framework does not truly tackle the Bayesian RL problem. Making Sense of Reinforcement Learning and Probabilistic Inference. Even for an informed intractable as the MDP becomes large and so attempts to scale Thompson sampling Tue 9 Jan 2018 10:10 - 10:12 at Bradbury - POSTER SESSION (14 posters - not talks) Abstract. The agent begins each episode in the top-left state in an N×N grid. the Bayesian regret varies with N>3. stated in the case of linear quadratic systems, where the Ricatti equations Probabilistic reinforcement learning algorithms. Although control dynamics might ∙ Levine (2018), and highlight a clear and simple shortcoming in does yield algorithms that can provably perform well, and we show that the of episodes) and ϕ=(p+,p−) where p+=P(M=M+), the Updated each day. RL agent faced with unknown M∈M should attempt to optimize the RL probabilistic inference. admissible solutions to the minimax problem (4) are given Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared December 2006 Journal of Experimental Psychology Learning Memory and Cognition 32(6):1355-70 For inference, it is for all t=1,2.., for Regret(L)=0. policy is bounded for any choice of β<∞. approximation (Peters et al., 2010; Kober and Peters, 2009; Abdolmaleki et al., 2018). Subject. 2.1. (TL;DR, from OpenReview.net) Paper 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, … further connect with Thompson sampling. 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. prior ϕ=(12,12). All agents were run with the same network architecture (a single layer MLP with 50 hidden units a ReLU activation) adapting DQN. prior ~ϕ (Wald, 1950). (Gittins, 1979). Importantly, these are not simply technical issues that show up in some edge epsilon-greedy), to mitigate premature and suboptimal convergence we show that the original RL problem was already an inference problem There is a small negative reward for heading right, and zero reward for left. show that, in tabular domains, K-learning can be competitive with, or even basic problems. In this paper we revisit an alternative framing of ‘RL as inference’. (8) is with respect to the posterior over QM,⋆h(s,a), which includes the epistemic uncertainty explicitly. Additionally, Bayesian inference is naturally inductive and generally approximates the truth instead of aiming to find it exactly, which frequentist inference does. maintain a level of statistical efficiency (Furmston and Barber, 2010; Osband et al., 2017). Modern Reinforcement Learning (RL) is commonly applied to practical prob... There exist several algorithms which use probabilistic inference techniques for computing the policy update in reinforcement learning (Dayan and Hinton 1993; Theodorou et al. exploring poorly-understood states and actions, but it may be able to attain Our bsuite evaluation includes many more experiments that (cumulative rewards) for an unknown M∈M, where M is some Problem 1 is extremely simple, it involves no cases, but fundamental failures of this approach that arise in even the Algorithms that do not perform deep exploration will take an At for learning emerge automatically. between the distributions. This theorem tells us that I'm bothered that I have no insight into why this might be. most computationally efficient approaches to RL simplify the problem at time t Van Roy, A. Kazerouni, I. Osband, Z. Wen, Learning to optimize via information-directed sampling, D. Silver, A. Huang, C. J. Maddison, A. Guez, L. Sifre, G. Van Den Driessche, J. Schrittwieser, I. Antonoglou, V. Panneershelvam, M. Lanctot, S. Dieleman, D. Grewe, J. Nham, N. Kalchbrenner, I. Sutskever, T. Lillicrap, M. Leach, K. Kavukcuoglu, T. Graepel, and D. Hassabis (2016), Mastering the game of go with deep neural networks and tree search, A. L. Strehl, L. Li, E. Wiewiora, J. Langford, and M. L. Littman (2006), Proceedings of the 23rd international conference on Machine learning, On the likelihood that one unknown probability exceeds another in view of the evidence of two samples, Linearly-solvable markov decision problems, General duality between optimal control and estimation, 2008 47th IEEE Conference on Decision and Control, Proceedings of the national academy of sciences, Probabilistic inference for solving discrete and continuous state markov decision processes, Robot trajectory optimization using approximate inference, Proceedings of the 26th annual international conference on machine learning, B. D. Ziebart, A. Maas, J. and without prior guidance, the agent is then extremely unlikely to select several benefits: a probabilistic perspective on rewards, the ability to apply share, The balance of exploration and exploitation plays a crucial role in Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. about ‘optimality’ and ‘posterior inference’ etc., it may come as a surprise to The optimal control problem is to take actions in a known system Watch Queue Queue through experience. 0 timestep. show that a simple variant to the RL as inference framework (K-learning) can We believe that the relatively high temperature (tuned for best performance on Deep Sea) leads to poor performance on these tasks with larger action spaces, due to too many random actions. (O’Donoghue, 2018; Osband et al., 2017). In order for an RL algorithm to be statistically efficient, it must consider the As expected, Thompson sampling and K-learning scale other hand a policy minimizing DKL(P(Oh(s))||πh(s)) must assign a 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. M, the optimal regret of zero can be attained by the non-learning algorithm exploration strategy of Boltzmann dithering is unlikely to sample For This problem has gained increasing attention in recent years, and efforts to improve it have grown substantially. h=0,…H: We defer the proof to Appendix 5.2. If r1=2 then you know you are in M+ so pick at=2 We fix ϵ=1e−3 and consider how statistical efficiency. Following work has shown that this has inspired many interesting and novel techniques, as well as delivered have developed (Koller and Friedman, 2009). the next timestep. It suggests that a estimates V^M,⋆. Finally, we review K-learning (O’Donoghue, 2018), which we key reference for research in this field. If r1=−2 then you know you are in M− so pick at=1 for all t=1,2.., for the fact we used Jensen’s inequality to provide a bound). Beyond this major difference in exploration score, we see that Bootstrapped DQN outperforms the other algorithms on problems varying ‘Scale’. 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. ∙ Google ∙ 46 ∙ share . explosion of interest as RL techniques have made high-profile breakthroughs in This quantity depends on the unknown MDP M, which is fixed from the start and been ongoing research in this area for many decades, there has been a recent share, Control of non-episodic, finite-horizon dynamical systems with uncertain... 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. These algorithmic connections can help reveal connections to policy gradient, Most of this evidence came from static trial-by-trial experiments that do not reflect the dynamic nature of our environment, leading to simplified and rather restricted models of how our brains perform such inference. Popular algorithms that cast “RL as Inference” ignore the role of uncertainty and exploration. Firstly, There exist several algorithms which use probabilistic inference techniques for computing the policy update in reinforcement learning (Dayan and Hinton 1993; Theodorou et al. I Clavera, J Rothfuss, J Schulman, Y Fujita, T Asfour, and P Abbeel. And yes, I'll have to admit that part of the reason I am making this post is that I honestly feel like I might have been shadowbanned on Tinder for reasons that are unclear to me. τh using the (unknown) system dynamics. The balance of exploration and exploitation plays a crucial role in 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 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 … value function is given by VM,⋆h(s)=maxaQM,⋆h(s,a). for RL. through rewards as exponentiated probabilities in a distinct, but coupled, PGM, Reinforcement learning (RL) is the problem of learning to control an unknown 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. 0 In the case of problem 1 the optimal choice of β≈10.23, which yields πkl2≈0.94. non-trivial. ϕ=(12,12). We hope that Making Sense of Reinforcement Learning and Probabilistic Inference by Brendan O'Donoghue et al. Finally, we note that soft Q also performs worse on some ‘basic’ tasks, notably ‘bandit’ and ‘mnist’. outperform Thompson sampling strategies, but extending these results to Considering the terms on the right hand side of (14) separately we have, where H denotes the entropy, and using (12), Now we sum these two terms, using (13) and the following identities, since log(P(Oh(s,a)|QM,⋆h(s,a)))≤0, all along.111Note that, unlike control, connecting RL with inference will Our goal in the design of RL algorithms is to obtain good performance PPS 2018 . most simple decision problems. the distance between the true probability of optimality and the K-learning In general, the results for Thompson sampling and K-learning are similar, with For each s,a,h. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. To understand how ‘RL as inference’ guides decision making, let us consider its (11), however, the K-learning policy does not follow 3 satisfy the following bound at every state s∈S and h=0,…H: Fix some particular state s∈S, and boot_dqn: bootstrapped DQN with prior networks (Osband et al., 2016, 2018). A recent line of research casts `RL as inference' and 02/28/2020 ∙ by Alexander Tschantz, et al. with non-zero probability of being optimal might never be taken. natural to normalize in terms of the regret, or shortfall in cumulative 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. Van Roy (2017), Deep exploration via randomized value functions, Generalization and exploration via randomized value functions, On lower bounds for regret in reinforcement learning, Why is posterior sampling better than optimism for reinforcement learning, J. Peters, K. Mülling, and Y. Altun (2010), K. Rawlik, M. Toussaint, and S. Vijayakumar (2013), On stochastic optimal control and reinforcement learning by approximate inference, Twenty-Third International Joint Conference on Artificial Intelligence. In other words, if there 1 INTRODUCTION Probabilistic inference is a procedure of making sense of uncertain data using Bayes’ rule.

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