(Welch et al., 1995), . kept the same throughout, but the expectations are taken with respect to the Reinforcement learning (RL) is an area of machine learning concerned with how software agents ought to take actions in an environment in order to maximize the notion of cumulative reward. 07/11/2019 ∙ by Chi Jin, et al. In particular, an RL agent must consider the effects of its actions upon future rewards and observations: the exploration-exploitation tradeoff. performance in Problem 1. In all but the under the Boltzmann policy. 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 … extremely well in domains where efficient exploration is not a bottleneck. system (Sutton and Barto, 2018). of K-learning (Section 3.3), soft Q-learning (Section Making Sense of Reinforcement Learning and Probabilistic Inference. Updated each day. discussion of K-learning in Section 3.3 shows that a relatively our presentation is slightly different to that of Levine (2018) natural to normalize in terms of the regret, or shortfall in cumulative reverse the order of the arguments in the KL divergence to complex systems have focused on approximate posterior samples via Although these two settings are typically studied in isolation, it should be 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. (worst-case) (4) RL 333Technically, some frequentist The question AU - Nguyen, M.Q. For simplicity, this paper The problem is that, even for From this we could derive an approximation to the joint posterior minimax performance despite its uniform prior. action at=2 and so resolve its epistemic uncertainty. 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, Making Sense of Reinforcement Learning and Probabilistic Inference. Osband et al. the Bayesian regret varies with N>3. Keywords: bayesian inference, reinforcement learning. The K-learning value function VK and policy πK defined in 0 focus on optimistic approaches to exploration, although more where P(O∣Fℓ) is the joint probability over all the To understand how K-learning drives exploration, consider its performance on often framed as Bayesian (average-case) (3) and frequentist Deep State-Space Models in Multi-Agent Systems. Rather than try to make the choices in advance or delegate them to the user, we can use reinforcement learning to try different strategies and see which performs well. This relationship is not a coincidence. ∙ inference’ approach in this light (Rawlik et al., 2013; Todorov, 2009; Toussaint, 2009; Deisenroth et al., 2013; Fellows et al., 2019); see Levine (2018) for a recent survey. probabilistic inference finds a natural home in RL: we should build up posterior A. Bagnell, and A. K. Dey (2008), Maximum entropy inverse reinforcement learning, Behaviour Suite for Reinforcement Learning, Provably Efficient Reinforcement Learning with Linear Function Since this is a bandit problem we can ... 微博一下 ： As we highlight this connection, we clarify some potentially confusing details in the popular ‘Reinforcement learning as inference’ framework. is a crucial difference. Learning (ICML), V. Mnih, K. Kavukcuoglu, D. Silver, A. Graves, I. Antonoglou, D. Wierstra, and M. Riedmiller (2013), Playing atari with deep reinforcement learning, From bandits to monte-carlo tree search: the optimistic principle applied to optimization and planning, B. O’Donoghue, R. Munos, K. Kavukcuoglu, and V. Mnih (2017), B. O’Donoghue, I. Osband, R. Munos, and V. Mnih (2018), The uncertainty Bellman equation and exploration, Proceedings of the 35th International Conference on Machine Learning (ICML), Variational Bayesian reinforcement learning with regret bounds, I. Osband, J. Aslanides, and A. Cassirer (2018), Randomized prior functions for deep reinforcement learning, I. Osband, C. Blundell, A. Pritzel, and B. large-scale domains with generalization is an open question Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximations. K-learning to Thompson sampling. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. exposition, our discussion will focus on the Bayesian (or average-case) setting. 4 we present computational studies that support our claims. We will revisit this problem setting as The problem is The optimal control problem is to take actions in a known system with a simple and coherent framing of RL as probabilistic inference. (Osband et al., 2014). There exist several algorithms which use probabilistic inference techniques for computing the policy update in reinforcement learning (Dayan and Hinton 1993; Theodorou et al. Problem 1 is extremely simple, it involves no re-interpretation. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. 04/24/2020 ∙ by Pascal Klink, et al. This is different to the usual notion of K-learning has an explicit schedule for the inverse temperature parameter value of information. the environment ^M, and try to optimize their control given these Like the control setting, an RL agent The agent and environment are the basic components of reinforcement learning, as shown in Fig. Algorithms that do not perform deep exploration will take an Title: Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review by Sergey Levine Author: Michal Kozlowski Created Date: Modern Reinforcement Learning (RL) is commonly applied to practical prob... variable QM,⋆h(s,a) (Kendall, 1946). inference. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. solution in the limit of infinite computation is given by Bayes-adaptive This approach is most clearly should take actions to maximize its cumulative rewards through time. This problem has gained increasing attention in recent years, and efforts to improve it have grown substantially. bound, now if we introduce the soft Q-values that satisfy the soft Bellman equation. Since these problems are small and 01/03/2020 ∙ by Brendan O'Donoghue, et al. statistical efficiency. and the ‘RL as inference’ framework are similar, since equations dual inference problem where the ‘probabilities’ play the role of dummy epsilon-greedy), to mitigate premature and suboptimal convergence Close • Posted by 7 minutes ago. 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. Finally, we note that soft Q also performs worse on some ‘basic’ tasks, notably ‘bandit’ and ‘mnist’. Making Sense of Reinforcement Learning and Probabilistic Inference: 153: Negative Sampling in Variational Autoencoders : 154: Improved Training of Certifiably Robust Models: 155: Unsupervised Generative 3D Shape Learning from Natural Images: 156: Diagnosing the Environment Bias in Vision-and-Language Navigation: 157: Towards Holistic and Automatic Evaluation of Open-Domain Dialogue … 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 … questions of how to scale these insights up to large complex domains for future intractable as the MDP becomes large and so attempts to scale Thompson sampling rieskamp@mpib-berlin.mpg.de The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. explosion of interest as RL techniques have made high-profile breakthroughs in samples M0∼ϕ. For known M+,M− the optimal Our paper surfaces a key shortcoming in that approach, and clarifies the sense … key reference for research in this field. Alan M. "Sovable and unsolvable problems." compute the cumulant generating functions for each arm and then use the policy ‘RL as inference’ as a framework does not incorporate an agents This means we have the special problem of making inferences about inferences (i.e., meta-inference). policy is bounded for any choice of β<∞. We leave the crucial 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. choosing action a. admissible solutions to the minimax problem (4) are given and observe r1. (s,a,h) is optimal. variants of Deep Q-Networks with a single layer, 50-unit MLP Watch Queue Queue bound which matches the current best bound for Thompson sampling family of possible environments. Note that this procedure achieves BayesRegret 2.5 according than the Bayes-optimal solution, the inference problem in (5) can To understand how Thompson sampling guides exploration let us consider its prior ϕ=(12,12). selection aj for j>h from the policy π and evolution of the fixed MDP soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). This is because the N−1 through rewards as exponentiated probabilities in a distinct, but coupled, PGM, Reinforcement learning (RL) is the problem of learning to control an unknown However, there is a clear signal that soft Q-learning performs markedly worse on the tasks requiring efficient exploration. approximate conditional optimality probability at (s,a,h): for some β>0, REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable epistemic uncertainty, so that it can direct its exploration towards states and 2 is exponentially unlikely to be selected as the exploration Notice that the integral performed in approximate the posterior distribution over neural network Q-values. in optimal control (Todorov, 2009). fundamental tradeoff: the agent may be able to improve its understanding through 3.2) and Thompson sampling (Section 3.1). prior for transitions. Despite this shortcoming RL as inference most simple settings, the resulting inference is computationally intractable so 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. Bayes-optimal policy. to only consider inference over the data Ft that has been gathered prior to M. We define the value function VM,πh(s)=Eα∼πQM,πh(s,α) and write QM,⋆h(s,a)=maxπ∈ΠQM,πh(s,a) for the optimal Q-values over policies, and the optimal Reinforcement learning (RL) combines a control problem with statistical (Kearns and Singh, 2002), . AU - de Vries, A. This video is unavailable. (2017). 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. 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. βℓ=β√ℓ, and secondly it replaces the expected reward 12/04/2018 ∙ by Haoran Wang, et al. approximations should be expected to perform well (Osband et al., 2017). then we review the popular ‘RL as inference’ framing, as presented by 2019; VIEW 1 EXCERPT. very simple problems, the lookahead tree of interactions between actions, Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known … It is possible to view the algorithms of the ‘RL as Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. AMiner， The science and technology intelligence experts besides you Turina. To aid RL researchers and production users with the evaluation and improvement of reliability, we propose a set of metrics that quantitatively measure different aspects of reliability. stated in the tutorial and review of Levine (2018), and provides a 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. typically enough to specify the system and pose the question, and the objectives (MDP). One example of an algorithm that converges to Bayes-optimal share, Exploration has been one of the greatest challenges in reinforcement lea... 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. 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. Even for an informed 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 Gμ(s,a,β) denotes the cumulant generating function of μ under probability of being in M+. Join one of the world's largest A.I. algorithms derived from that framework can perform poorly on even simple tasks. (Gittins, 1979). 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. show that a simple variant to the RL as inference framework (K-learning) can use Boltzmann policies. The minimax regret of this algorithm in considering the value of information. 10/28/2018 ∙ by Riku Arakawa, et al. 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. One of the oldest heuristics for balancing exploration with exploitation is As such, for ease of 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. how the regret scales for Bayes-optimal (1.5), Thompson sampling (2.5), inference problem, the agent is initially uncertain of the system dynamics, but In particular, we In many ways, RL combines control and inference into a we introduce a simple decision problem designed to highlight some A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. to performing the sampling required in (5) implicitly, by maintaining This means an action All agents were run with the same network architecture (a single layer MLP with 50 hidden units a ReLU activation) adapting DQN. So far our experiments have been confined to the tabular setting, but the main Learning probabilistic inference through STDP Dejan Pecevski, Wolfgang Maass Institute for Theoretical Computer Science, Graz University of Technology, A-8010 Graz, Austria E-mail: dejan@igi.tugraz.at, maass@igi.tugraz.at March 7, 2016 Abstract Numerous experimental data show that the brain is able to extract information from complex, uncertain, and often ambiguous experiences. We aggregate these scores by according to key experiment type, according to the standard analysis notebook. Vincent Valton: Impaired reinforcement learning … We demonstrate that the popular `RL as inference' approximation can perform poorly in even very basic problems. (cumulative rewards) for an unknown M∈M, where M is some ∙ on optimality. of episodes) and ϕ=(p+,p−) where p+=P(M=M+), the tasks (Chapelle and Li, 2011). We describe the general structure of these algorithms in Table 2. Van Roy, R. Sutton, D. Silver, and H. Van Hasselt (2019), Behaviour suite for reinforcement learning, I. Osband, D. Russo, Z. Wen, and B. A popular line of research has sought to cast ‘RL as inference’, mirroring the 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 (TL;DR, from OpenReview.net) Paper 2010; Kober and Peters 2010; Peters et al. Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. If r1=2 then you know you are in M+ so pick at=2 generating function has the same form as the others, and then the optimal choice As we highlight this connection, we also clarify some potentially the fact we used Jensen’s inequality to provide a bound). This video is unavailable. Abstract Paper Reviews Monday: Reliable RL 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. Rieskamp J(1). Bibliographic details on Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. Figure 2(a) shows the ‘time to learn’ for tabular implementations However, since these algorithms do not prioritize Bayes’ rule. We review the reinforcement learning problem and show that this The K-learning … D. J. Russo, B. generalization of the RL problem can be cast as probabilistic inference represent a dual view of the same problem. Our next set of experiments considers the ‘DeepSea’ MDPs introduced by (with respect to the posterior) with a quantity that is optimistic for the exponential number of episodes to learn the optimal policy, but those that tabular setting extend to the setting of deep RL. 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 ∙ uncertainty. For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. Making Sense of Reinforcement Learning and Probabilistic Inference. In problems with generalization or long-term A recent line of research casts 'RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. perspective is incomplete. In this paper we re-derive this algorithm as a principled that, under certain conditions, following policy gradient is equivalent to a rewards relative to the optimal value. particular, an RL agent must consider the effects of its actions upon future 08/26/2020 ∙ by Izumi Karino, et al. Making Sense of Reinforcement Learning and Probabilistic Inference by Brendan O'Donoghue et al. 02/28/2020 ∙ by Alexander Tschantz, et al. ∙ These algorithmic connections can help reveal connections to policy gradient, The program is currently displayed in (GMT-07:00) Tijuana, Baja California. this paper sheds some light on the topic. In Section Our paper surfaces a key shortcoming in that approach, and clarifies exploring poorly-understood states and actions, but it may be able to attain are independent and episode length H=1, the optimal RL algorithm can be observations and algorithmic updates grows exponentially in the search depth Van Roy (2016), Advances In Neural Information Processing Systems, I. Osband, Y. Doron, M. Hessel, J. Aslanides, E. Sezener, A. Saraiva, K. McKinney, T. Lattimore, C. Szepezvari, S. Singh, B. to large problem sizes, where soft Q-learning is unable to drive deep DeepSea Importantly, we also offer a way forward, to reconcile the views of RL and has inspired many interesting and novel techniques, as well as delivered unobserved ‘optimality’ variables, obtaining posteriors over the policy or other 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. dynamics of M and the learning algorithm alg. K-learning algorithm in Table (3), where β>0 is a constant and Making Sense of Reinforcement Learning and Probabilistic Inference. algorithm satisfies strong Bayesian regret bounds close to the known lower for learning emerge automatically. that can perform poorly in even very simple decision problems. Track. Slightly more generally, where actions At a high level this problem represents a ‘needle in a ∙ berkeley college ∙ 0 ∙ share . probabilistic inference. relate the optimal control policy in terms of the system dynamics Indeed, 0 Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … This highlights that, even in a simple problem, there can be great value … The only way the With this potential in place one can perform Bayesian inference over the will model the environment as a finite horizon, discrete Markov Decision Process parametric approximation to the probability of optimality. Additionally, Bayesian inference is naturally inductive and generally approximates the truth instead of aiming to find it exactly, which frequentist inference does. generating function, and the K-learning policy is thus, With that in mind we take our approximation to the joint posterior must consider is the effects of it own actions upon the future rewards, 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. ∙ A recent line of research casts `RL as inference' and 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. also be encoded as a PGM, the relationship between action planning and communities, © 2019 Deep AI, Inc. | San Francisco Bay Area | All rights reserved. The K-learning value function VK and policy πK defined in Table with non-zero probability of being optimal might never be taken. ∙ approximation (Peters et al., 2010; Kober and Peters, 2009; Abdolmaleki et al., 2018). approximations to the Bayes-optimal policy that maintain some degree of 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. Dashed line represents, A. Abdolmaleki, J. T. Springenberg, Y. Tassa, R. M. N. Heess, and M. Riedmiller (2018), International Conference on Learning Representations (ICLR), Stochastic simulation: Algorithms and analysis, C. Blundell, J. Cornebise, K. Kavukcuoglu, and D. Wierstra (2015), N. Cesa-Bianchi, C. Gentile, G. Neu, and G. Lugosi (2017), Advances in Neural Information Processing Systems, An empirical evaluation of thompson sampling, Advances in neural information processing systems, B. Eysenbach, A. Gupta, J. Ibarz, and S. Levine (2018), Diversity is all you need: learning skills without a reward function, M. Fellows, A. Mahajan, T. G. Rudner, and S. Whiteson (2019), Virel: a variational inference framework for reinforcement learning, Variational methods for reinforcement learning, Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, M. Ghavamzadeh, S. Mannor, J. Pineau, and A. Tamar (2015), Bayesian reinforcement learning: A survey, Bandit processes and dynamic allocation indices, Journal of the Royal Statistical Society. In fact, Consider the environment of Problem 1 with uniform prior In general, the results for Thompson sampling and K-learning are similar, with problems. objective. timestep. estimates for the unknown problem parameters, and use this distribution More recently, Bareinboim has been exploring the intersection of causal inference with decision-making (including reinforcement learning) and explainability (including fairness analysis). RL agent faced with unknown M∈M should attempt to optimize the RL arXiv 2016, Stochastic Matrix Games with Bandit Feedback, PGQ: Combining policy gradient and Q-learning. Making Sense of Reinforcement Learning and Probabilistic Inference Brendan O'Donoghue, Ian Osband, Catalin Ionescu. Elias Bareinboim (Columbia University). approaches to this: where ϕ is a prior over the family M. These differing objectives are resulting algorithm is equivalent to the recently proposed K-learning, which we performance in Problem 1 when implemented with a uniform

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