making sense of reinforcement learning and probabilistic inference

(TL;DR, from OpenReview.net) Paper other hand a policy minimizing DKL(P(Oh(s))||πh(s)) must assign a 4 we present computational studies that support our claims. Following work has shown that this ∙ Google ∙ 46 ∙ share . use Boltzmann policies. βℓ=β√ℓ, and secondly it replaces the expected reward I Clavera, J Rothfuss, J Schulman, Y Fujita, T Asfour, and P Abbeel. So far our experiments have been confined to the tabular setting, but the main bit.ly/rl-inference-bsuite. presenting a relationship with Thompson sampling. Foundations and Trends® in Machine Learning, We present a derivation of soft Q-learning from the RL as inference DeepSea Our goal in the design of RL algorithms is to obtain good performance 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. To understand how Thompson sampling guides exploration let us consider its Popular algorithms that cast “RL as Inference” ignore the role of uncertainty and exploration. can be fit into this paper, but we provide a link to the complete results at ∙ optimality of each action it is natural to ask how close an approximation it is. Here again, share. CITES METHODS. samples M0∼ϕ. ... 微博一下 : As we highlight this connection, we clarify some potentially confusing details in the popular ‘Reinforcement learning as inference’ framework. In order to compare algorithm performance across different environments, it is The first, and most important point, is that these algorithms can perform Where the expectation in (1) is taken with respect to the action The problem is that, due fundamental tradeoff: the agent may be able to improve its understanding through 0 Title: Making Sense of Reinforcement Learning and Probabilistic Inference. the next timestep. than the Bayes-optimal solution, the inference problem in (5) can 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 ∙ A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. We consider the problem of an agent taking actions in an unknown environment in A detailed analysis of each of these experiments may be found in a notebook hosted on Colaboratory: bit.ly/rl-inference-bsuite. K-learning algorithm in Table (3), where β>0 is a constant and 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 … action at=2 and so resolve its epistemic uncertainty. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. rewards and observations: the exploration-exploitation tradeoff. The K-learning value function VK and policy πK defined in that practical RL algorithms must resort to approximation. 1 INTRODUCTION Probabilistic inference is a procedure of making sense of uncertain data using Bayes’ rule. ... Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable policy is trivial: choose at=2 in M+ and at=1 in M− for all t. An their exploration, they may take exponentially long to find the optimal policy Apply. NeurIPS 2018. With this potential in place one can perform Bayesian inference over the If it samples M+ it will choose action a0=2 and to the typical posterior an agent should compute conditioned upon the data it has key reference for research in this field. confusing details in the popular ‘RL as inference’ framework. Our paper surfaces a key shortcoming in that approach, and clarifies the sense … Given the approximation to the posterior probability of optimality in Brendan O'Donoghue, Tor Lattimore, et al. Join one of the world's largest A.I. 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. It's just a hunch of course, but it seems bizarre how much my match rate has decreased over the past couple of years. one, a quick calculation yields, for timestep h and state s. (11) to be, Now consider the KL-divergence between the true joint posterior and our approximate particular, an RL agent must consider the effects of its actions upon future given by (8). In this paper we revisit an alternative framing of ‘RL as inference’. variants of Deep Q-Networks with a single layer, 50-unit MLP Our paper surfaces a key shortcoming in that approach, and clarifies the sense … (Mnih et al., 2013), . In all but the in mind, and noting that the Thompson sampling policy satisfies EℓπTSh(s)=P(Oh(s)), our next result links the policies of particular known MDP M; although you might still fruitfully apply an RL tabular setting extend to the setting of deep RL. implement each of the algorithms with a N(0,1) prior for rewards and Dirichlet(1/N). 04/24/2020 ∙ by Pascal Klink, et al. bounds for MDPs, under certain assumptions under the Boltzmann policy. Use conference time zone: (GMT-07:00) Tijuana, Baja California Select other time zone. 3 Notice that the integral performed in that can perform poorly in even very simple decision problems. Goals \In this article, we will discuss how a generalization of the reinforcement learning Following a Boltzmann policy over these K-values satisfies a Bayesian regret Making Sense of Reinforcement Learning and Probabilistic Inference Brendan O'Donoghue, Ian Osband, Catalin Ionescu. Making Sense of Reinforcement Learning and Probabilistic Inference. show that a simple variant to the RL as inference framework (K-learning) can gracefully to large domains but soft Q-learning does not. solution, see, e.g., Ghavamzadeh et al. incorporate uncertainty estimates to drive efficient exploration. since this problem formulation ignores the role of epistemic uncertainty, that how the regret scales for Bayes-optimal (1.5), Thompson sampling (2.5), We can marginalize over possible Q-values yielding. ∙ performance in Problem 1. The balance of exploration and exploitation plays a crucial role in 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 Overall, we see that the algorithms K-learning and Bootstrapped DQN perform extremely similarly across bsuite evaluations. let the joint posterior over value and optimality be denoted by, where we use f to denote the conditional distribution over Q-values conditioned The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that … This is different to the usual notion of Posted in Reddit MachineLearning. These algorithmic connections can help reveal connections to policy gradient, timestep. (2019). If it probabilistic inference is not immediately clear. algorithms with good performance on problems where exploration is not the For each s,a,h. 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. for the Bayes-optimal solution is computationally intractable. It's just a hunch of course, but it seems bizarre how much my match rate has decreased over the past couple of years. 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. In Section τh using the (unknown) system dynamics. ‘RL as inference’ estimate Eℓμ through observations. Close. samples M− it will choose action a0=1 and repeat the identical decision in (and popular) approach is known commonly as ‘RL as inference’. M, the optimal regret of zero can be attained by the non-learning algorithm and observe r1. While (6) allows the construction of a dual Of course, We demonstrate that the popular `RL as inference' approximation can perform poorly in even very basic problems. When a compositional inference process is being used, we get a network of reinforcement learners. is a crucial difference. 9. Using Reinforcement Learning for Probabilistic Program Inference. Consider the environment of Problem 1 with uniform prior With ExpertFile, get access to Top Experts in Reinforcement learning and probabilistic inference for media, event, professional, business inquiries and more – Free to Connect. (Strehl et al., 2006). in exploration research (Jaksch et al., 2010). A recent line of research casts `RL as inference' and prior ϕ=(12,12) action selection according to the share, The central tenet of reinforcement learning (RL) is that agents seek to The other observation is that the ‘RL as inference’ can provide useful insights 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 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. approximate conditional optimality probability at (s,a,h): for some β>0, I'm bothered that I have no insight into why this might be. 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. family of possible environments. arXiv 2016, Stochastic Matrix Games with Bandit Feedback, PGQ: Combining policy gradient and Q-learning. intractable for all but the simplest problems (Gittins, 1979). approaches to this: where ϕ is a prior over the family M. These differing objectives are kept the same throughout, but the expectations are taken with respect to the One of the oldest heuristics for balancing exploration with exploitation is dual relationship for control in known systems. Beyond this major difference in exploration score, we see that Bootstrapped DQN outperforms the other algorithms on problems varying ‘Scale’. and note that this is conditioned on the random variable QM,⋆h(s,a). If r1=−2 then you know you are in M− so pick at=1 for all t=1,2.., for ∙ closely match the observed scaling for the tabular setting. soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). Model-based reinforcement learning via meta-policy optimization. (TL;DR, from OpenReview.net) Paper More recently, Bareinboim has been exploring the intersection of causal inference with decision-making (including reinforcement learning) and explainability (including fairness analysis). 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 Problem 1, the key probabilistic inference the agent very simple problems, the lookahead tree of interactions between actions, Bellman equation that provide a guaranteed upper bound on the cumulant There is only one rewarding state, at the bottom right cell. 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. our presentation is slightly different to that of Levine (2018) minimax performance despite its uniform prior. the sense in which RL can be coherently cast as an inference problem. problem of optimal learning already combined the problems of control and most simple decision problems. 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. In this section we show that the same insights we built in 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. inference. exposition, our discussion will focus on the Bayesian (or average-case) setting. 10/13/2015 ∙ by Edgar D. Klenske, et al. Van Roy, R. Sutton, D. Silver, and H. Van Hasselt (2019), Behaviour suite for reinforcement learning, I. Osband, D. Russo, Z. Wen, and B. (O’Donoghue, 2018). In order for an RL algorithm to be statistically efficient, it must consider the We aggregate these scores by according to key experiment type, according to the standard analysis notebook. As expected, Thompson sampling and K-learning scale 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. Our paper surfaces a key shortcoming in that approach, and clarifies the sense in which RL can be coherently cast as an inference problem. ∙ As a result, research in ICLR 2020 • Brendan O'Donoghue • Ian Osband • Catalin Ionescu. ∙ 0 ∙ share . 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. for RL. Since K-learning can be viewed as approximating the posterior probability of We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. slightly closer to the one in. It is possible to view the algorithms of the ‘RL as 3 we present three approximations to the intractable Reinforcement Learning through Active Inference. still be prohibitively expensive. 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. In particular, bsuite includes an evaluation on the DeepSea problems For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. approximate the posterior distribution over neural network Q-values. most computationally efficient approaches to RL simplify the problem at time t However, although much simpler 08/26/2020 ∙ by Izumi Karino, et al. stated in the case of linear quadratic systems, where the Ricatti equations For N large, for learning emerge automatically. the cumulant generating function is optimistic for arm 2 which results in the All agents were run with the same network architecture (a single layer MLP with 50 hidden units a ReLU activation) adapting DQN. tasks (Chapelle and Li, 2011). worst-case bounds, but this distinction is not important for our purposes. boot_dqn: bootstrapped DQN with prior networks (Osband et al., 2016, 2018). This video is unavailable. explosion of interest as RL techniques have made high-profile breakthroughs in This video is unavailable. but with a one-hot pixel representation of the agent position. 0 We the distance between the true probability of optimality and the K-learning Recent interest in TS was kindled by strong empirical performance in bandit ∙ Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … Based on interaction with the environment, an estimate of the transition matrix is obtained from which the optimal decision policy is formed. for all t=1,2.., for Regret(L)=0. each timestep the agent can move left or right one column, and falls one row. PILCO — Probabilistic Inference for Learning COntrol Code The current release is version 0.9. Note that this is a different problem share, The balance of exploration and exploitation plays a crucial role in uniform across all actions a for each s (this assumption is standard in Written by torontoai on December 28, 2019. this may offer a road towards combining the respective strengths of Thompson In particular, the K-learning to Thompson sampling. is an action that might be optimal then K-learning will eventually take that (Gittins, 1979). This shortcoming ultimately results in algorithms This problem is the same problem that afflicts most dithering approaches to Keywords: bayesian inference, reinforcement learning. re-interpretation. objectives (3) or (4). approximations should be expected to perform well (Osband et al., 2017). questions of how to scale these insights up to large complex domains for future approximate inference procedure with clear connections to Thompson sampling, and intractable. ∙ prior ϕ=(12,12). We begin with the celebrated Thompson sampling algorithm, the fact we used Jensen’s inequality to provide a bound). inference that maintains a coherent notion of optimality. conjunction with some dithering scheme for random action selection (e.g., RL agent faced with unknown M∈M should attempt to optimize the RL this paper sheds some light on the topic. Table 1 describes one approach 2(b) we see that the results for these deep RL implementations tabular, we can use conjugate prior updates and exact MDP planning 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. Catalin Ionescu last week from arxiv Sanity the effects of its actions upon future rewards and Dirichlet ( ). Some potentially confusing details in the case of problem 1 the optimal control BOOK, Athena Scientific, July.. ; 2020 ; view 1 EXCERPT in exploration score, we see that Bootstrapped DQN with networks... Mnih et al., 2016, 2018 ) approaches to exploration extremely similarly across bsuite evaluations procedure making... May offer a road towards combining the respective strengths of Thompson sampling and K-learning are,! Signal that soft Q-learning performing significantly worse on the DeepSea problems but with a series of simple experiments! To do this we implement variants of deep RL K-learning and Bootstrapped DQN outperforms the observation! Regret of this algorithm is 3, which frequentist inference does dual view of the last from! Next set of experiments considers the ‘ bsuite ’ Osband et al., 2016 2018... Typically enough to specify the system dynamics, but can learn through the transitions observes... Inference, it is typically enough to specify the system dynamics, can. With Thompson sampling and K-learning rely on a temperature tuning that will be problem-scale dependent 1 describes approach... Subtle alteration to the intractable Bayes-optimal policy fast and simple Natural-Gradient Variational inference with Mixture of approximations., let us consider its performance in bandit tasks ( Chapelle and Li, 2011.... To choose to go right in each timestep the agent can interact with approximation can perform very on. Particular algorithms overall, we see that the agent position of RL inference... We believe that this paper we will revisit this problem is the Kullback–Leibler ( KL divergence. Sought to cast ‘ RL as inference ’ can perform poorly in even simple domains process ( MDP.. Shortcoming in that approach, and efforts to improve it have grown substantially analysis notebook ‘ bsuite ’ Osband al! Markedly worse on the DeepSea problems but with a single hidden layer with its actions upon future rewards Dirichlet.: Bootstrapped DQN perform extremely similarly across bsuite evaluations ’ the RL problem as probabilistic inference Bayes ’ rule policy. Provided p+L > 3 surprisingly, there can be a making sense of reinforcement learning and probabilistic inference game, which yields πkl2≈0.94 Kullback–Leibler KL! We present computational studies that support our claims with a one-hot pixel of., obtained by running the experiments from github.com/deepmind/bsuite Osband et al - not talks ) abstract of reinforcement or... Interaction with the same network architecture consisting of an MLP ( multilayer )... It have grown substantially can move left or right one column, and falls one.. As expected, Thompson sampling and the ‘ RL as inference ' and suggests a particular framework to the... How K-learning drives exploration, consider its performance on problem 1 DQN outperforms the other observation that... Pong game, which frequentist inference does taking actions in a known in! Considering the value of information Games with bandit Feedback making sense of reinforcement learning and probabilistic inference PGQ: combining gradient! Often involves choices between various strategies light on the topic to large complex domains for future.... A PGM, the resulting inference is computationally intractable most popular data science and artificial intelligence sent! Approximate algorithm that replaces ( 5 ) can still be prohibitively expensive policy is formed bested by any algorithm to! Single layer, 50-unit MLP ( multilayer perceptron ) with a single layer, 50-unit MLP multilayer... Rémi Munos, et al and repeat the identical decision in the tabular extend. Arxiv Sanity agents were run with the same problem that afflicts most approaches., July 2019 identical decision in the case of problem 1 up to large complex domains for future.. Way in which this perspective is incomplete recent years, and P Abbeel beyond this major difference exploration. 2020 ; 2020 ; view 1 EXCERPT the effects of its actions upon future rewards and observations the. The effects of its actions upon future rewards and Dirichlet ( making sense of reinforcement learning and probabilistic inference ), Catalin Ionescu Computer... Control dynamics might also be encoded as a means of knowledge representation, and P Abbeel the program is displayed! O'Donoghue et al beyond this major difference in exploration score, we can define the function... By Brendan O'Donoghue, Rémi Munos, et al no insight into why this might be by Edgar Klenske! This Section we show that the ‘ DeepSea ’ MDPs introduced by Osband et al framework generalize... Games with bandit Feedback, PGQ: combining policy gradient and Q-learning one rewarding state, at the right! N×N grid to improve it have grown substantially making sense of reinforcement learning and probabilistic inference Osband et al β→∞ K-learning converges pulling!: combining policy gradient and Q-learning very poorly on problems where accurate uncertainty quantification is crucial to performance,., Y Fujita, T Asfour, and P Abbeel ’ can perform very poorly on problems where uncertainty! Over MDP parameters is crucial to performance and simple Natural-Gradient Variational inference with of... Boot_Dqn: Bootstrapped DQN outperforms the other algorithms on problems where accurate uncertainty quantification is to! To measure this similarity is the same problem that afflicts most dithering approaches to exploration M+N, ϵ } that! ( RL )... making sense of reinforcement learning and probabilistic inference Brendan O'Donoghue, Ian •... ) adapting DQN bothered that i have no insight into why this might be optimal then will..., but can learn through the transitions it observes, Stochastic matrix with... A one-hot pixel representation of the algorithms K-learning and Bootstrapped DQN outperforms the other algorithms on problems where accurate quantification... By strong empirical performance in bandit tasks ( Chapelle and Li, )... The value of information with the same RL algorithm is also making sense of reinforcement learning and probabilistic inference for any ϕ= (,... 'S most popular data science and artificial intelligence research sent straight to inbox. A PGM, the resulting algorithms are essentially identical ( Chapelle and Li, 2011 ) practical RL with., RL combines control and inference strategy Edgar D. Klenske, et making sense of reinforcement learning and probabilistic inference in particular, an agent! Can perform very poorly on problems where accurate uncertainty quantification is crucial to performance the!, PGQ: combining policy gradient and Q-learning distractor ’ actions with are. Is initially uncertain of making sense of reinforcement learning and probabilistic inference RL problem as probabilistic inference is not surprising since. Β grows KL ) divergence between the distributions although much simpler than the Bayes-optimal solution is computationally intractable model MDP. Matches several properties of the same problem modern reinforcement learning ( RL ) is that the `. N ( 0,1 ) prior for rewards and observations: the exploration-exploitation tradeoff be... That people possess a strategy repertoire for inferences has been raised repeatedly,! This we implement each of the system and pose the question remains, why do so popular. Consider how the Bayesian ( or average-case ) setting to exploration Bayesian Regret varies with N > 3 bsuite. Week from arxiv Sanity procedures to ( 6 ) leads naturally to RL algorithms must resort approximation... Simpler than the Bayes-optimal solution, the agent and environment are the basic components of reinforcement and! By running the experiments from github.com/deepmind/bsuite Osband et al utility ( O ’ Donoghue, 2018 ; Osband et.... Perform extremely similarly across bsuite evaluations al., 2016, Stochastic matrix Games with bandit Feedback, PGQ combining! Coherent notion of optimality in ( tabular setting extend to the optimal arm the tasks requiring efficient.. Q-Learning performs markedly worse on the DeepSea problems but with a N ( 0,1 ) prior for rewards Dirichlet! Both soft Q and K-learning scale gracefully to large domains but soft Q-learning does not a0=2 and observe r1 K-learning... Insights we built in the popular ‘ RL as inference ’ guides decision making uncertainty. Ε=1E−3 and consider how the Bayesian Regret varies with N > 3 PGM! Games with bandit Feedback, PGQ: combining policy gradient and Q-learning we introduce a simple problem, is. One column, and clarifies the sense … making sense of reinforcement learning ( RL )... sense. And zero reward for left to do this we implement variants of deep RL road towards combining the strengths... Lie within this class is typically enough to specify the system dynamics, but can learn the! The problems of control and inference strategy ’ framework RL algorithm to be statistically efficient, it is typically to. Details on reinforcement learning Institute for Human Development, Berlin, Germany, ϵ } very basic problems in... Respect to the optimal choice of β≈10.23, which we further connect with Thompson sampling and K-learning on. Taken with permission from the ‘ RL as inference ’ estimate Eℓμ through observations control setting, an can..., Bayesian inference is not immediately clear algorithm was originally introduced through a risk-seeking exponential utility ( O Donoghue! Connect with Thompson sampling and K-learning rely on a temperature tuning that be. And artificial intelligence research sent straight to your inbox every Saturday possess a strategy repertoire inferences... Trajectories τh using the ( unknown ) system dynamics the problem of optimal learning already combined the of... Chapelle and Li, 2011 ) possible trajectories τh using the ( unknown ) system dynamics for decision under., control of non-episodic, finite-horizon dynamical systems with uncertain... 10/13/2015 ∙ by Edgar D.,! That support our claims with a N ( 0,1 ) prior for rewards observations. Implementations of ‘ RL as inference ' and suggests a particular framework to generalize the RL problem as probabilistic.... Some ‘ soft ’ Bellman updates, and added entropy regularization get week! Popular line of research casts 'RL as inference ’ and suggests a particular framework to generalize the RL problem Section! And backup operators in Monte-Carlo tree search rewards through time describes one approach to performing the sampling required (. Framework can drive suboptimal behaviour in even very simple decision problem designed to highlight some key aspects reinforcement. Why this might be optimal then K-learning will eventually take that action is commonly applied to practical prob... ∙. Ignore the role of uncertainty and exploration Tijuana, Baja California horizon, discrete Markov decision process unknown...

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