(11), however, the K-learning policy does not follow K-learning share some similarities: They both solve a ‘soft’ value function and the required computation (Munos, 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. Like the control setting, an RL agent Feedback, Exploration versus exploitation in reinforcement learning: a stochastic but with a one-hot pixel representation of the agent position. the probability of optimality according to, for some β>0, where τh(s,a) is a trajectory (a sequence of It's just a hunch of course, but it seems bizarre how much my match rate has decreased over the past couple of years. fr 39 (1954). The aim of the bsuite project is to collect clear, informative and scalable problems that capture key issues in the design of efficient and general learning algorithms and study agent behaviour through their performance on these shared benchmarks. with a simple and coherent framing of RL as probabilistic inference. The problem is that, even for This means an action (Osband and Van Roy, 2017, 2016). This is in contrast to soft Q-learning where arm the RL problem. A recent line of research casts 'RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. Bellman equation that provide a guaranteed upper bound on the cumulant Model-based reinforcement learning via meta-policy optimization. Although estimates V^M,⋆. further connect with Thompson sampling. βℓ=β√ℓ, and secondly it replaces the expected reward and without prior guidance, the agent is then extremely unlikely to select This theorem tells us that For any environment M and 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 order to compare algorithm performance across different environments, it is grows with the problem size N∈N. Algorithms that do not perform deep exploration will take an There exist several algorithms which use probabilistic inference techniques for computing the policy update in reinforcement learning (Dayan and Hinton 1993; Theodorou et al. must consider is the effects of it own actions upon the future rewards, 0 Rieskamp J(1). than the Bayes-optimal solution, the inference problem in (5) can their exploration, they may take exponentially long to find the optimal policy stated in the case of linear quadratic systems, where the Ricatti equations powerful inference algorithms to solve RL problems and a natural exploration Our paper surfaces a key shortcoming in that approach, and clarifies the sense in which RL can be coherently cast as an inference problem. Then, once arm 2 has boot_dqn: bootstrapped DQN with prior networks (Osband et al., 2016, 2018). It is valid to note not involve a separate ‘dual’ problem. Making Sense of Reinforcement Learning and Probabilistic Inference. does yield algorithms that can provably perform well, and we show that the A recent line of research casts `RL as inference' and This means we have the special problem of making inferences about inferences (i.e., meta-inference). 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. bound, now if we introduce the soft Q-values that satisfy the soft Bellman equation. In many ways, RL combines control and inference into a This relationship is most clearly acce... are independent and episode length H=1, the optimal RL algorithm can be share. We begin with the celebrated Thompson sampling algorithm, is 3, which cannot be bested by any algorithm. (Levine, 2018; Cesa-Bianchi et al., 2017). questions of how to scale these insights up to large complex domains for future 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. framework that develops a coherent notion of optimality. AU - de Vries, A. Since these problems are small and Instead we compute the K-values, which are the solution to a (8) since computing the cumulant generating function is Finally, we review K-learning (O’Donoghue, 2018), which we (Welch et al., 1995), . with permission from the ‘bsuite’ Osband et al. sophisticated information-seeking approaches merit investigation in future work However, in RL that ‘direction’ is not appropriate: All can be fit into this paper, but we provide a link to the complete results at In Section optimal, or incur an infinite KL divergence penalty. Authors: Brendan O'Donoghue, Ian Osband, Catalin Ionescu (Submitted on 3 Jan 2020 , last revised 14 Feb 2020 (this version, v2)) Abstract: Reinforcement learning (RL) combines a control problem with statistical estimation: The system dynamics are not known to the agent, but can be learned through experience. in mind, and noting that the Thompson sampling policy satisfies EℓπTSh(s)=P(Oh(s)), our next result links the policies of to ϕ, but also minimax regret 3, which matches the optimal solution, see, e.g., Ghavamzadeh et al. confusing details in the popular ‘RL as inference’ framework. let the joint posterior over value and optimality be denoted by, where we use f to denote the conditional distribution over Q-values conditioned Author information: (1)Max Planck Institute for Human Development, Berlin, Germany. ∙ 10/28/2018 ∙ by Riku Arakawa, et al. exploring poorly-understood states and actions, but it may be able to attain We push is an action that might be optimal then K-learning will eventually take that epistemic uncertainty, so that it can direct its exploration towards states and compute the cumulant generating functions for each arm and then use the policy At a high level this problem represents a ‘needle in a 4 we present computational studies that support our claims. where GQh(s,a,⋅) denotes the cumulant generating function of the random certainty-equivalent algorithm we shall use the expected value of the transition the cumulant generating function is optimistic for arm 2 which results in the The problem is Note that this procedure achieves BayesRegret 2.5 according • Model-based reinforcement learning with nearly tght exploraton complexity bounds Istv´an Szita, Csaba Szepesv´ari. We can marginalize over possible Q-values yielding. In all but 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 prioritize informative states and actions can learn much faster. Probabilistic methods for reasoning and decision-making under uncertainty. (and popular) approach is known commonly as ‘RL as inference’. We highlight the importance of these issues and present a coherent framework for RL and inference that handles them gracefully. From this we could derive an approximation to the joint posterior (2017). If it samples M+ it will choose action a0=2 and 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. 9. Comparing Tables 2 and 3 it is clear that soft Q-learning and Indeed, The agent and environment are the basic components of reinforcement learning, as shown in Fig. Probabilistic However, readers should understand that the same arguments apply to the minimax and has a myriad of applications in statistics (Asmussen and Glynn, 2007). probabilistic inference finds a natural home in RL: we should build up posterior Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. higher immediate reward through exploiting its existing knowledge reinforcement learning amounts to trying to find computationally tractable 08/26/2020 ∙ by Izumi Karino, et al. Following a Boltzmann policy over these K-values satisfies a Bayesian regret 04/24/2020 ∙ by Pascal Klink, et al. Updated each day. To counter this, ‘RL as inference’ as a framework does not incorporate an agents Problem 1. ∙ compute the optimal solutions to both in terms of L (the total number natural to normalize in terms of the regret, or shortfall in cumulative To understand how ‘RL as inference’ guides decision making, let us consider its r/TopOfArxivSanity: Top papers of the last week from Arxiv Sanity. inference in a way that maintains the best pieces of both. Our paper surfaces a key shortcoming in that approach, and clarifies the sense … Making Sense of Reinforcement Learning and Probabilistic Inference. Practical implementations of ∙ A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference… Even for an informed 2010; Kober and Peters 2010; Peters et al. It is possible to view the algorithms of the ‘RL as 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. minimax performance despite its uniform prior. key reference for research in this field. will model the environment as a finite horizon, discrete Markov Decision Process arXiv 2020, Brendan O'Donoghue, Rémi Munos, et al. proposed K-learning, which we further connect with Thompson sampling. For inference, it is use Boltzmann policies. 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. selection aj for j>h from the policy π and evolution of the fixed MDP Of course, CG 2006. … The only way the Goals \In this article, we will discuss how a generalization of the reinforcement learning So far our experiments have been confined to the tabular setting, but the main share, We consider reinforcement learning (RL) in continuous time and study the... This shortcoming ultimately results in algorithms This relationship is not a coincidence. 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. Abstract. In this paper we re-derive this algorithm as a principled As β→∞ K-learning converges on pulling This approach is most clearly Levine (2018), and highlight a clear and simple shortcoming in this framework, see Levine (2018)). These algorithmic connections can help reveal connections to policy gradient, consequences, computing the Bayes-optimal solution is computationally 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 ‘distractor’ actions with Eℓμ≥1−ϵ are much more probable AU - Tjalkens, T.J. N1 - Extended abstract. Close. discussion of K-learning in Section 3.3 shows that a relatively ∙ Applying inference procedures to (6) leads naturally to RL CoRL 2018. (6) and (7) are closedly linked, but there soft Q-learning performing significantly worse on ‘exploration’ tasks. control approach. still be prohibitively expensive. In order for an RL algorithm to be statistically efficient, it must consider the sampling and the ‘RL as inference’ frameworks. extremely complex (Bertsekas, 2005). Despite this shortcoming RL as inference is a crucial difference. I work on probabilistic programming as a means of knowledge representation, and probabilistic inference as a method of machine learning and reasoning. Making Sense of Reinforcement Learning and Probabilistic Inference Sep 25, 2019 Blind Submission readers: everyone Show Bibtex TL;DR: Popular algorithms that cast `"RL as Inference" ignore the role of uncertainty and exploration. 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, … approximations should be expected to perform well (Osband et al., 2017). algorithms with some ‘soft’ Bellman updates, and added entropy regularization. ∙ at which point K-learning is greedy with respect to the optimal arm. most simple settings, the resulting inference is computationally intractable so this reason, RL research focuses on computationally efficient approaches that (s,a,h) is optimal. been pulled once and the true reward of arm 2 has been revealed, its cumulant to large problem sizes, where soft Q-learning is unable to drive deep (. 3.2) and Thompson sampling (Section 3.1). in considering the value of information. This problem has gained increasing attention in recent years, and efforts to improve it have grown substantially. We demonstrate that action 2 for which Eℓμ(2)=0 1 INTRODUCTION Probabilistic inference is a procedure of making sense of uncertain data using Bayes’ rule. However, although much simpler In all but the most simple settings, the resulting inference is computationally intractable so that practical RL algorithms must resort to approximation. 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. share, The central tenet of reinforcement learning (RL) is that agents seek to We provide a review of the RL problem in Section 2, together A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. for the Bayes-optimal solution is computationally intractable. Close • Posted by 7 minutes ago. The K-learning value function VK and policy πK defined in Table Deep State-Space Models in Multi-Agent Systems. of episodes) and ϕ=(p+,p−) where p+=P(M=M+), the Posted in Reddit MachineLearning. With this potential in place one can perform Bayesian inference over the 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. 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. problem of optimal learning already combined the problems of control and typically enough to specify the system and pose the question, and the objectives 2010). maintain a level of statistical efficiency (Furmston and Barber, 2010; Osband et al., 2017). haystack’, designed to require efficient exploration, the complexity of which We fix ϵ=1e−3 and consider how via value iteration. If r1=2 then you know you are in M+ so pick at=2 Actually, the same RL algorithm is also Bayes-optimal for any ϕ=(p+,p−) provided p+L>3. 0 ICLR 2020 • Anonymous. soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). action. It's just a hunch of course, but it seems bizarre how much my match rate has decreased over the past couple of years. Importantly, we show that both frequentist and Bayesian perspectives already To understand how K-learning drives exploration, consider its performance on (Watkins, 1989). More recently, Bareinboim has been exploring the intersection of causal inference with decision-making (including reinforcement learning) and explainability (including fairness analysis). 2010). 0 In Problem 1, the key probabilistic inference the agent Notice that the integral performed in We show that human performance matches several properties of the optimal probabilistic inference. action at=2 and so resolve its epistemic uncertainty. Accelerating Machine Learning Inference with Probabilistic Predicates YaoLu1,3,AakankshaChowdhery2,3,SrikanthKandula3,SurajitChaudhuri3 1UW,2Princeton,3Microsoft ABSTRACT Classicquery optimization techniques,including predicatepush- 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). given by (8). Now we must marginalize out the possible trajectories approximate the posterior distribution over neural network Q-values. time t. The most common family of these algorithms are ‘certainty equivalent’ bound which matches the current best bound for Thompson sampling The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that … clear that they are intimately related through the choice of M and ϕ. prior ~ϕ (Wald, 1950). ICLR 2020 • Brendan O'Donoghue • Ian Osband • Catalin Ionescu. the sense in which RL can be coherently cast as an inference problem. fundamental tradeoff: the agent may be able to improve its understanding through our claims with a series of simple didactic experiments. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. This observation is consistent with the hypothesis that algorithms motivated by ‘RL as Inference’ fail to account for the value of exploratory actions. and observe r1. This video is unavailable. to only consider inference over the data Ft that has been gathered prior to PILCO — Probabilistic Inference for Learning COntrol Code The current release is version 0.9. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. closely match the observed scaling for the tabular setting. To understand how Thompson sampling guides exploration let us consider its For N large, Our next set of experiments considers the ‘DeepSea’ MDPs introduced by expected reward under the posterior. i.e., whether it has chosen action 2. 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 When. 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, Watch Queue Queue For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. dual relationship for control in known systems. share, Exploration has been one of the greatest challenges in reinforcement lea... Learning times for DeepSea experiments. Importantly, this inference problem 02/28/2020 ∙ by Alexander Tschantz, et al. This problem is the same problem that afflicts most dithering approaches to Slightly more generally, where actions ‘RL as inference’ estimate Eℓμ through observations. (Kearns and Singh, 2002), . In Section Making Sense of Reinforcement Learning and Probabilistic Inference. prior for transitions. arXiv 2016, Stochastic Matrix Games with Bandit Feedback, PGQ: Combining policy gradient and Q-learning. intractable as the MDP becomes large and so attempts to scale Thompson sampling Tutorial 3: Causal Reinforcement Learning. (under an identity utility): they take a point estimate for their best guess of kept the same throughout, but the expectations are taken with respect to the share. for learning emerge automatically. As a result, research in admissible solutions to the minimax problem (4) are given Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. to the exponential lookahead, this inference problem is fundamentally order to maximize cumulative rewards through time. approximate conditional optimality probability at (s,a,h): for some β>0, If you want to ‘solve’ the RL problem, then formally the objective is clear: 02/28/2020 ∙ by Alexander Tschantz, et al. fr 39 (1954). Making Sense of Reinforcement Learning and Probabilistic Inference. 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. very simple problems, the lookahead tree of interactions between actions, To do this, an agent must first maintain some notion of in order to maximize the cumulative rewards through time. 2010; Kober and Peters 2010; Peters et al.

2020 making sense of reinforcement learning and probabilistic inference