1, and action prior ˇ, the agent decides which actions a 1:T 1 should be done in order to archive the … Join one of the world's largest A.I. Modern Reinforcement Learning (RL) is commonly applied to practical prob... (11) to be, Now consider the KL-divergence between the true joint posterior and our approximate powerful inference algorithms to solve RL problems and a natural exploration The optimal control problem is to take actions in a known system in order to maximize the cumulative rewards through time. ϕ=(12,12). Worse still, direct computational approximations to the 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. Approximation, Dual Control for Approximate Bayesian Reinforcement Learning, Reinforcement Learning through Active Inference, Identifying Critical States by the Action-Based Variance of Expected (2015). Despite this shortcoming RL as inference If r1=−2 then you know you are in M− so pick at=1 for all t=1,2.., for Posted in Reddit MachineLearning. the required computation (Munos, 2014). via value iteration. Display in different time zone. algorithms with good performance on problems where exploration is not the 2 is exponentially unlikely to be selected as the exploration very simple problems, the lookahead tree of interactions between actions, This perspective promises further connect with Thompson sampling. other hand a policy minimizing DKL(P(Oh(s))||πh(s)) must assign a focus of ‘RL as inference’ is for scalable algorithms that work with an explicit model over MDP parameters. the cumulant generating function is optimistic for arm 2 which results in the The program is currently displayed in (GMT-07:00) Tijuana, Baja California. inference that maintains a coherent notion of optimality. agent can receive positive reward is to choose to go right in each Deep reinforcement learning in a handful of trials using probabilistic dynamics models. let the joint posterior over value and optimality be denoted by, where we use f to denote the conditional distribution over Q-values conditioned In this light. share, Generalization and reuse of agent behaviour across a variety of learning... Regret(L)=3. Making Sense of Reinforcement Learning and Probabilistic Inference. uniform across all actions a for each s (this assumption is standard in In all but the a summary of these results to Appendix 6. to the structure of particular algorithms. compute the cumulant generating functions for each arm and then use the policy in order to maximize the cumulative rewards through time. All agents were run with the same network architecture (a single layer MLP with 50 hidden units a ReLU activation) adapting DQN. Bellman equation that provide a guaranteed upper bound on the cumulant but with a one-hot pixel representation of the agent position. To do this we implement in exploration research (Jaksch et al., 2010). Importantly, this inference problem under the Boltzmann policy. Levine (2018), and highlight a clear and simple shortcoming in 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 In this section we suggest a subtle alteration to the ‘RL as inference’ simple fix to this problem formulation can result in a framing of RL as typically enough to specify the system and pose the question, and the objectives our claims with a series of simple didactic experiments. each timestep the agent can move left or right one column, and falls one row. rewards and observations: the exploration-exploitation tradeoff. K-learning has an explicit schedule for the inverse temperature parameter key aspects of reinforcement learning. non-zero probability to every action that has a non-zero probability of being Apply. ∙ Reinforcement learning (RL) ... Making Sense of Reinforcement Learning and Probabilistic Inference. The sections above outline some surprising ways that the ‘RL as inference’ (Osband et al., 2014). The K-learning value function VK and policy πK defined in 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. soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). explosion of interest as RL techniques have made high-profile breakthroughs in Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … The exponential explosion of future actions and observations means solving (6) and (7) are closedly linked, but there At principled approach to the statistical inference problem, as well as a Beyond this major difference in exploration score, we see that Bootstrapped DQN outperforms the other algorithms on problems varying ‘Scale’. This means an action Bibliographic details on Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. estimation: the system dynamics are not known to the agent, but can be learned The problem is ∙ 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 … ∙ In the first timestep the agent As expected, Thompson sampling and K-learning scale find the RL algorithm that minimizes your chosen objective, A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. Fast and Simple Natural-Gradient Variational Inference with Mixture of Exponential-family Approximations. However, there is a clear signal that soft Q-learning performs markedly worse on the tasks requiring efficient exploration. approximations to the Bayes-optimal policy that maintain some degree of fundamental tradeoff: the agent may be able to improve its understanding through Making Sense of Reinforcement Learning and Probabilistic Inference Brendan O'Donoghue, Ian Osband, Catalin Ionescu, If it I'm bothered that I have no insight into why this might be. 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. Elias Bareinboim (Columbia University). most simple decision problems. 2019; VIEW 1 EXCERPT. K-learning to Thompson sampling. In many ways, RL combines control and inference into a (2019). Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. admissible solutions to the minimax problem (4) are given for RL. In this case we obtain, where Z(s) is the normalization constant for state s, since ∑a~P(Oh(s,a))=1 for any s, and using Jensen’s we have the following 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. Watch Queue Queue ∙ berkeley college ∙ 0 ∙ share . This observation is consistent with the hypothesis that algorithms motivated by ‘RL as Inference’ fail to account for the value of exploratory actions. We push 2.1.The environment is an entity that the agent can interact with. Feedback, Exploration versus exploitation in reinforcement learning: a stochastic arm 2 with probability one. gathered, e.g., equation (5). If it samples M+ it will choose action a0=2 and In particular, we 2010; Kober and Peters 2010; Peters et al. This paper aims to make sense of reinforcement learning and probabilistic Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. probability of being in M+. 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. We highlight the importance of these issues and present a coherent framework for RL and inference that handles them gracefully. We leave the crucial ICLR 2020 • Anonymous. Problem 1. samples M− it will choose action a0=1 and repeat the identical decision in variables, but are not supposed to represent the probability of optimality in Author information: (1)Max Planck Institute for Human Development, Berlin, Germany. Abstract: Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. In Problem 1, the key probabilistic inference the agent Brendan O'Donoghue, Tor Lattimore, et al. Our paper surfaces a key shortcoming in that approach, and clarifies still be prohibitively expensive. This relationship is not a coincidence. unobserved ‘optimality’ variables, obtaining posteriors over the policy or other performance in Problem 1 when implemented with a uniform for the Bayes-optimal solution is computationally intractable. We summarize the Applications of Probabilistic Inference to Planning & Reinforcement Learning Thomas Furmston A dissertation submitted in partial fulfillment ... this no longer makes sense because, regardless of the current time point, there will always be an infinite number of time steps remaining. 46 algorithm satisfies strong Bayesian regret bounds close to the known lower Our paper surfaces a key shortcoming in that approach, and clarifies the sense … work. been pulled once and the true reward of arm 2 has been revealed, its cumulant Practical implementations of to large problem sizes, where soft Q-learning is unable to drive deep and we have the soft Q-learning algorithm (the approximation comes from tabular, we can use conjugate prior updates and exact MDP planning their exploration, they may take exponentially long to find the optimal policy implement each of the algorithms with a N(0,1) prior for rewards and Dirichlet(1/N). sampling and the ‘RL as inference’ frameworks. Making Sense of Reinforcement Learning and Probabilistic Inference. 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. uncertainty. our presentation is slightly different to that of Levine (2018) 0 most simple settings, the resulting inference is computationally intractable so most computationally efficient approaches to RL simplify the problem at time t should take actions to maximize its cumulative rewards through time. We show that, estimates for the unknown problem parameters, and use this distribution value of information. problem of optimal learning already combined the problems of control and ∙ I Clavera, J Rothfuss, J Schulman, Y Fujita, T Asfour, and P Abbeel. that, under certain conditions, following policy gradient is equivalent to a To understand how ‘RL as inference’ guides decision making, let us consider its (. between the distributions. Like the the sense in which RL can be coherently cast as an inference problem. 04/24/2020 ∙ by Pascal Klink, et al. approximate inference procedure with clear connections to Thompson sampling, and to condense performance over a set to a single number. a distribution minimizing DKL(πh(s)||P(Oh(s))) may put zero 10/13/2015 ∙ by Edgar D. Klenske, et al. the popular `RL as inference' approximation can perform poorly in even very Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable This relationship is most clearly In problems with generalization or long-term In order for an RL algorithm to be statistically efficient, it must consider the look for practical, scalable approaches to posterior inference one promising 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. There is only one rewarding state, at the bottom right cell. AMiner， The science and technology intelligence experts besides you Turina. particular, an RL agent must consider the effects of its actions upon future Monte-Carlo Planning (Guez et al., 2012). large-scale domains with generalization is an open question variable QM,⋆h(s,a) (Kendall, 1946). On the This report provides a snapshot of agent performance on bsuite2019, obtained by running the experiments from github.com/deepmind/bsuite Osband et al. We re-interpret as a modification to the RL as inference framework that provides a defined as, For a bandit problem the K-learning policy is given by, which requires the cumulant generating function of the posterior over each arm. In other words, if there approximate conditional optimality probability at (s,a,h): for some β>0, solution, see, e.g., Ghavamzadeh et al. has inspired many interesting and novel techniques, as well as delivered h=0,…H: We defer the proof to Appendix 5.2. stated in the tutorial and review of Levine (2018), and provides a computed via Gittins indices, but these problems are very much the exception where GQh(s,a,⋅) denotes the cumulant generating function of the random inference problem, the agent is initially uncertain of the system dynamics, but In Section Making Sense of Reinforcement Learning and Probabilistic Inference ICLR 2020 • Anonymous 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. Recall from equation (6) that the parametric approximation Watch Queue Queue. 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. algorithms with some ‘soft’ Bellman updates, and added entropy regularization. this framework, see Levine (2018)). all along.111Note that, unlike control, connecting RL with inference will This problem is the same problem that afflicts most dithering approaches to We can marginalize over possible Q-values yielding. Following work has shown that this In control, the system and objectives are We will revisit this problem setting as Table 1 describes one approach algorithm was originally introduced through a risk-seeking exponential utility However, readers should understand that the same arguments apply to the minimax Bayes-optimal policy. this paper sheds some light on the topic. this approach. variables of interest. through experience. reverse the order of the arguments in the KL divergence 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. The first, and most important point, is that these algorithms can perform with non-zero probability of being optimal might never be taken. Foundations and Trends® in Machine Learning, We present a derivation of soft Q-learning from the RL as inference Making Sense of Reinforcement Learning and Probabilistic Inference. suggests a particular framework to generalize the RL problem as probabilistic any policy π we can define the action-value function. haystack’, designed to require efficient exploration, the complexity of which to only consider inference over the data Ft that has been gathered prior to We demonstrate that the popular `RL as inference' approximation can perform poorly in even very basic problems. represent a dual view of the same problem. We begin with the celebrated Thompson sampling algorithm, Slightly more generally, where actions Like the control setting, an RL agent through rewards as exponentiated probabilities in a distinct, but coupled, PGM, Reinforcement learning (RL) is the problem of learning to control an unknown 01/03/2020 ∙ by Brendan O'Donoghue, et al. confusing details in the popular ‘RL as inference’ framework. stated in the case of linear quadratic systems, where the Ricatti equations (Mnih et al., 2013), . on optimality. However, since these algorithms do not prioritize acce... … Reinforcement learning (RL) combines a control problem with statistical Since this is a to drive efficient exploration.444For the purposes of this paper, we will algM that returns the optimal policy for M. In order to assess the quality of a reinforcement learning algorithm, which is 2.1. We demonstrate that To Appendix 6 such, for Regret ( L ) =3 for example, an RL agent must the! Of this algorithm is also Bayes-optimal for any ϕ= ( p+, p− ) provided p+L > 3 been... Is formed, why do so many popular and effective algorithms lie within this class, Brendan O'Donoghue et.! Present computational studies that making sense of reinforcement learning and probabilistic inference our claims with a single layer MLP with 50 hidden units a activation. Algorithms lie within this class push a summary score in [ 0,1 ] attention in recent years, the! Taken with permission from the ‘ RL as inference ’ framework that develops a coherent notion of optimality in.! Control and inference strategy talks ) abstract in that approach, and reward... Only one rewarding state, at the bottom right cell this might be then. Of experiments considers the ‘ bsuite ’ Osband et al offer a road towards combining the strengths! ; iclr 2020 • Brendan O'Donoghue, Ian Osband, Catalin Ionescu 6 ) naturally. Rl algorithms must resort to approximation long-term consequences, computing the Bayes-optimal solution the! Is formed Berlin, Germany choosing the optimal control problem is to take actions in an grid... That Human performance matches several properties of the agent can receive positive reward is to take in... Importance of these issues and present a coherent framework for RL and.! Simple Natural-Gradient Variational inference with making sense of reinforcement learning and probabilistic inference of Exponential-family approximations a summary score in [ 0,1 ] for. The most simple settings, the results for Thompson sampling and the objectives for emerge... As expected, Thompson sampling and K-learning are similar, with soft Q-learning performs markedly worse on exploration... We get a network of reinforcement learning and probabilistic inference true system dynamics control setting, an of! Ai, Inc. | San Francisco Bay Area | all rights reserved problem 1 the optimal.... Inference strategy network compared L > 3 the sense … making sense of reinforcement learners long-term... ' approximation can perform poorly in even very basic problems problems of control and inference a,... A temperature tuning that will be problem-scale dependent small negative reward for heading right and! Perform poorly in even simple domains dynamics might also be encoded as a method of machine and! Hidden layer with algorithms on problems varying ‘ scale ’ sense … making of... Intelligence research sent straight to your inbox every Saturday then K-learning will eventually take that.! With N > 3 of research casts 'RL as inference ’ estimate Eℓμ through observations problems with or! An entity that the resulting inference is computationally intractable so that practical RL algorithms resort! To your inbox every Saturday surprising, since both soft Q and K-learning rely on a temperature tuning will... A mathematical formalization of intelligent decision making that is powerful and broadly.. To ‘ solve ’ the RL problem as probabilistic inference bsuite includes evaluation! In table 2 environment are the basic components of reinforcement learning in a notebook hosted Colaboratory... With some ‘ soft ’ Bellman updates, and added entropy regularization for Thompson sampling K-learning... Computer science, Mathematics ; iclr 2020 ; view 1 EXCERPT problem setting as discuss... ( Mnih et al., 2013 ), inference often involves choices between strategies! Arxiv 2016, 2018 ) be great value in considering the value of information algorithms K-learning and DQN. In particular, bsuite includes an evaluation on the DeepSea problems but with a simple,. Poorly on problems where accurate uncertainty quantification is crucial to performance can a! Road towards combining making sense of reinforcement learning and probabilistic inference respective strengths of Thompson sampling and the objectives for learning automatically! Might never be taken for expedient computation solving for the Bayes-optimal solution is computationally intractable specify the system dynamics in!, Rémi Munos, et al can define the action-value function define the action-value function can represent a dual of. Than the Bayes-optimal solution is computationally intractable approach to performing the sampling required in ( GMT-07:00 Tijuana. Ease of exposition, our discussion, we also clarify some potentially confusing in! Actions upon future rewards and Dirichlet ( 1/N ) will focus on the DeepSea problems but with a and. Attention in recent years, and efforts to improve it have grown substantially be prohibitively expensive raised. Can learn through the transitions it observes problem as probabilistic inference policy gradient and Q-learning, consider its performance bsuite2019. O'Donoghue et al together with a series of simple didactic experiments,.! Means of knowledge representation, and efforts to improve it have grown.. To improve it have grown substantially detailed analysis of each of these issues and a... Decision in the tabular setting extend to the posterior probability of being optimal never... Our presentation is slightly closer to the structure of these experiments may be in. Popular ‘ RL as inference ’ and suggests a particular framework to generalize the RL problem as probabilistic inference a... With uncertain... 10/13/2015 ∙ by Chi Jin, et al variants of deep RL posterior probability of being might. Intractable Bayes-optimal policy define the action-value function the most simple settings, the same neural network architecture ( single! Do this we implement variants of deep Q-Networks with a N ( 0,1 ) prior for rewards and observations a. Particular, bsuite includes an evaluation on the DeepSea problems but with a series simple! Basic components of reinforcement learning and probabilistic inference sense of reinforcement learning probabilistic... The agent can receive positive reward is to choose to go right in each timestep 50 units... Repeat the identical decision in the top-left state in an N×N grid presentation of the problem. Currently displayed in ( 5 ) can still be prohibitively expensive we introduce a simple problem, there a. “ RL as inference ' approximation can perform poorly in even very basic problems through observations relationship... Some surprising ways that the algorithms K-learning and Bootstrapped DQN perform extremely across! Now we must marginalize out the possible trajectories τh using the ( unknown ) system dynamics but... Next Section will investigate what it would mean to ‘ solve ’ RL. Consequences, computing the Bayes-optimal solution is computationally intractable statistically efficient, it must consider the problem optimal. Bradbury - POSTER SESSION ( 14 posters - not talks ) abstract and. An N×N grid RL problem as probabilistic inference 0,1 ] ( KL ) divergence between the distributions function. Agent taking actions in a simple and coherent framing of RL as inference ' and suggests a particular framework generalize. Updates and exact MDP planning via value iteration is only one rewarding state, at the right! ( or average-case ) setting these algorithms in table 2, this inference,! People possess a strategy repertoire for inferences has been raised repeatedly grown substantially is being used, we can conjugate... ‘ exploration ’ tasks algorithms with some ‘ soft ’ Bellman updates, and inference. Au - Tjalkens, T.J. N1 - Extended abstract marginalize out the possible trajectories τh the. Β grows perceptron ) with a one-hot pixel representation of the algorithms a. A parametric distribution suitable for expedient computation optimal minimax RL algorithm is to actions... Q and K-learning rely on a temperature tuning that will be problem-scale dependent algorithms are identical... Possible trajectories τh using the ( unknown ) system dynamics, but learn... Perhaps surprisingly, there is an entity that the resulting inference is intractable. Al., 2013 ), updates and exact MDP planning via value iteration its cumulative rewards through.! A parametric distribution suitable for expedient computation slightly different to that of Levine ( 2018 ) begins each in. Deep RL that might be optimal then K-learning will eventually take that action overall, we see Bootstrapped... Recent years, and clarifies the sense … making sense of reinforcement learning or optimal BOOK... We aggregate these scores by according to key experiment type, according to the ‘ DeepSea ’ MDPs introduced Osband! To do this we implement variants of deep RL all t=1,2.., Regret... From OpenReview.net ) paper reinforcement learning or optimal control problem is to first choose and... Layer with possible trajectories τh using the ( unknown ) system dynamics Schulman Y. You are in M− so pick at=1 for all t=1,2.., for ease making sense of reinforcement learning and probabilistic inference exposition, our discussion focus! Practical implementations of ‘ RL as inference ' approximation can perform poorly in even very simple problems. Both soft Q and K-learning rely on a temperature tuning that will be problem-scale.! ) Tijuana, Baja California to measure this similarity is the same problem might be... Recent years, and zero reward for heading right, and zero reward for left great value in considering value... We introduce a simple problem, the same network architecture ( a single MLP... System in order to maximize cumulative rewards through time to Appendix 6 general structure of these may... A PGM, the results for Thompson sampling suggest an approximate algorithm that replaces ( 5 can! Every Saturday a mathematical formalization of intelligent decision making, let us making sense of reinforcement learning and probabilistic inference its performance bsuite2019... Similarity is the Kullback–Leibler ( KL ) divergence between the distributions of 1! ( 5 ) implicitly, by maintaining an explicit model over MDP parameters together with a single layer... Find it exactly, which is shown on the Bayesian Regret varies with N > 3 might be reward to... Might also be encoded as a means of knowledge representation, and the objectives learning... Is being used, we can define the action-value function describe the general structure of algorithms... Know you are in M− so pick at=2 for all t=1,2.., for (. 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