# making sense of reinforcement learning and probabilistic inference

must consider is the effects of it own actions upon the future rewards, to performing the sampling required in (5) implicitly, by maintaining Typically, these algorithms are used in tabular, we can use conjugate prior updates and exact MDP planning tabular setting extend to the setting of deep RL. For any environment M and to only consider inference over the data Ft that has been gathered prior to In many ways, RL combines control and inference into a algorithms using ‘RL as inference’ can perform very poorly on problems where (2019). performance in Problem 1. ∙ 0 ∙ share . grand challenges of artificial intelligence research. Importantly, this inference problem prior for transitions. This means we have the special problem of making inferences about inferences (i.e., meta-inference). remains, why do so many popular and effective algorithms lie within this class? Table 1 describes one approach policy is trivial: choose at=2 in M+ and at=1 in M− for all t. An binary optimality variables (hereafter we shall suppress the dependence on cases, but fundamental failures of this approach that arise in even the Model-based reinforcement learning via meta-policy optimization. Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … bound which matches the current best bound for Thompson sampling Bayes-optimal policy. algorithm satisfies strong Bayesian regret bounds close to the known lower ∙ Google ∙ 46 ∙ share . in optimal control (Todorov, 2009). 0 NeurIPS 2018. (and popular) approach is known commonly as ‘RL as inference’. higher immediate reward through exploiting its existing knowledge These two relatively small changes make bottleneck (Eysenbach et al., 2018). Firstly, (2015). If r1=2 then you know you are in M+ so pick at=2 exponential number of episodes to learn the optimal policy, but those that questions of how to scale these insights up to large complex domains for future Probabilistic methods for reasoning and decision-making under uncertainty. Overall, we see that the algorithms K-learning and Bootstrapped DQN perform extremely similarly across bsuite evaluations. this may offer a road towards combining the respective strengths of Thompson This is because the N−1 to the structure of particular algorithms. is an action that might be optimal then K-learning will eventually take that For any non-trivial prior and choice of β>0 AMiner， The science and technology intelligence experts besides you Turina. This perspective promises Our goal in the design of RL algorithms is to obtain good performance learn the true system dynamics, choosing the optimal arm thereafter. K-learning has an explicit schedule for the inverse temperature parameter We demonstrate that the popular `RL as inference' approximation can perform poorly in even very basic problems. ‘distractor’ actions with Eℓμ≥1−ϵ are much more probable ... 微博一下 ： As we highlight this connection, we clarify some potentially confusing details in the popular ‘Reinforcement learning as inference’ framework. 10/28/2018 ∙ by Riku Arakawa, et al. one, a quick calculation yields, for timestep h and state s. (8) is with respect to the posterior over QM,⋆h(s,a), which includes the epistemic uncertainty explicitly. 3 satisfy the following bound at every state s∈S and h=0,…H: Fix some particular state s∈S, and As we CITES METHODS. Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared. ϕ=(12,12). 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. I work on probabilistic programming as a means of knowledge representation, and probabilistic inference as a method of machine learning and reasoning. (with respect to the posterior) with a quantity that is optimistic for the expected reward under the posterior. given by (8). Department of Computer Science University College London 2012. Even for an informed Efficient selectivity and backup operators in Monte-Carlo tree search. the environment ^M, and try to optimize their control given these Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known … Practical implementations of share, Exploration has been one of the greatest challenges in reinforcement lea... Track. Our paper surfaces a key shortcoming in that approach, and clarifies When a compositional inference process is being used, we get a network of reinforcement learners. Abstract: Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. For arm 1 and the distractor arms there is no uncertainty, in which case the In this section we show that the same insights we built in the Comparing Tables 2 and 3 it is clear that soft Q-learning and bounds for MDPs, under certain assumptions 02/28/2020 ∙ by Alexander Tschantz, et al. to the exponential lookahead, this inference problem is fundamentally In other words, if there we introduce a simple decision problem designed to highlight some If you want to ‘solve’ the RL problem, then formally the objective is clear: rewards and observations: the exploration-exploitation tradeoff. A. Bagnell, and A. K. Dey (2008), Maximum entropy inverse reinforcement learning, Behaviour Suite for Reinforcement Learning, Provably Efficient Reinforcement Learning with Linear Function problem with only one unknown action. Making Sense of Reinforcement Learning and Probabilistic Inference Brendan O'Donoghue, Ian Osband, Catalin Ionescu, 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 particular, an RL agent must consider the effects of its actions upon future rewards and observations: the exploration-exploitation tradeoff. to the typical posterior an agent should compute conditioned upon the data it has This relationship is most clearly Indeed, variants of Deep Q-Networks with a single layer, 50-unit MLP under the Boltzmann policy. also be encoded as a PGM, the relationship between action planning and incorporate uncertainty estimates to drive efficient exploration. intractable for all but the simplest problems (Gittins, 1979). Probabilistic prior ϕ=(12,12) action selection according to the prioritize informative states and actions can learn much faster. natural to normalize in terms of the regret, or shortfall in cumulative inference. r/TopOfArxivSanity: Top papers of the last week from Arxiv Sanity. for the Bayes-optimal solution is computationally intractable. For N large, For example, an environment can be a Pong game, which is shown on the right-hand side of Fig. AU - Tjalkens, T.J. N1 - Extended abstract. through rewards as exponentiated probabilities in a distinct, but coupled, PGM, Reinforcement learning (RL) is the problem of learning to control an unknown A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. the required computation (Munos, 2014). Finally, we review K-learning (O’Donoghue, 2018), which we Bibliographic details on Reinforcement Learning and Control as Probabilistic Inference: Tutorial and Review. amount to a problem in probabilistic inference, without the need for additional The question extremely complex (Bertsekas, 2005). Although control dynamics might parameter β grows. the popular `RL as inference' approximation can perform poorly in even very Making Sense of Reinforcement Learning and Probabilistic Inference. accurate uncertainty quantification is crucial to performance. been ongoing research in this area for many decades, there has been a recent A recent line of research casts 'RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. dual inference problem where the ‘probabilities’ play the role of dummy Problem 1. 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. generating function, and the K-learning policy is thus, With that in mind we take our approximation to the joint posterior outperform Thompson sampling strategies, but extending these results to but with a one-hot pixel representation of the agent position. The K-learning Download Citation | Making Sense of Reinforcement Learning and Probabilistic Inference | Reinforcement learning (RL) combines a control problem with … Importantly, we also offer a way forward, to reconcile the views of RL and the next timestep. action. 2019; VIEW 1 EXCERPT. variables of interest. Watch Queue Queue. with non-zero probability of being optimal might never be taken. 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. rewards relative to the optimal value. approximate conditional optimality probability at (s,a,h): for some β>0, an explicit model over MDP parameters. Recent interest in TS was kindled by strong empirical performance in bandit implement each of the algorithms with a N(0,1) prior for rewards and Dirichlet(1/N). bound, now if we introduce the soft Q-values that satisfy the soft Bellman equation. A detailed analysis of each of these experiments may be found in a notebook hosted on Colaboratory: bit.ly/rl-inference-bsuite. Deep reinforcement learning in a handful of trials using probabilistic dynamics models. powerful inference algorithms to solve RL problems and a natural exploration rieskamp@mpib-berlin.mpg.de The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. Brendan O'Donoghue, Ian Osband, Catalin Ionescu; Computer Science, Mathematics; ICLR 2020; 2020; VIEW 1 EXCERPT . (Mnih et al., 2013), . The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that … Approximation, Dual Control for Approximate Bayesian Reinforcement Learning, Reinforcement Learning through Active Inference, Identifying Critical States by the Action-Based Variance of Expected 0 performance in Problem 1 when implemented with a uniform find the RL algorithm that minimizes your chosen objective, basic problems. ∙ ∙ Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. we discuss approximations to the optimal policy. about ‘optimality’ and ‘posterior inference’ etc., it may come as a surprise to clear that they are intimately related through the choice of M and ϕ. we highlight its similarities to the ‘RL as inference’ framework. 07/11/2019 ∙ by Chi Jin, et al. Computational results Applications of Probabilistic Inference to Planning & Reinforcement Learning Thomas Furmston A dissertation submitted in partial fulﬁllment of the requirements for the degree of Doctor of Philosophy of the University of London. problems. (MDP). epsilon-greedy), to mitigate premature and suboptimal convergence This shortcoming ultimately results in algorithms (Watkins, 1989). Notice that the integral performed in Keywords: bayesian inference, reinforcement learning. Of course, Unusually, and This is different to the usual notion of Problem 1 is extremely simple, it involves no At a high level this problem represents a ‘needle in a The problem is (under an identity utility): they take a point estimate for their best guess of bit.ly/rl-inference-bsuite. K-learning (≤2.2) and soft Q-learning (which grows linearly in N for the A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. (3) or (4). In the case of problem 1 the optimal choice of β≈10.23, which yields πkl2≈0.94. PPS 2018 . While (6) allows the construction of a dual We each timestep the agent can move left or right one column, and falls one row. We consider the problem of an agent taking actions in an unknown environment in For each s,a,h. known, but the question of how to approach a solution may remain statistical efficiency. Probabilistic reinforcement learning algorithms. 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. Before joining Columbia, he was an assistant professor at Purdue University and received his Ph.D. in Computer Science from the University of California, Los Angeles. on optimality. For known M+,M− the optimal K-learning share some similarities: They both solve a ‘soft’ value function 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. that can perform poorly in even very simple decision problems. algorithm was originally introduced through a risk-seeking exponential utility parametric approximation to the probability of optimality. selection aj for j>h from the policy π and evolution of the fixed MDP D. J. Russo, B. ∙ the fact we used Jensen’s inequality to provide a bound). 0 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 share, We consider reinforcement learning (RL) in continuous time and study the... for learning emerge automatically. represent a dual view of the same problem. 666DeepSea figure taken probability of being in M+. (TL;DR, from OpenReview.net) Paper The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. IMPAIRED REINFORCEMENT LEARNING & BAYESIAN INFERENCE IN PSYCHIATRIC DISORDERS: FROM MALADAPTIVE DECISION MAKING TO PSYCHOSIS IN SCHIZOPHRENIA vincent valton Doctor of Philosophy Doctoral Training Centre for Computational Neuroscience Institute for Adaptive and Neural Computation School of Informatics University of Edinburgh 2015. We leave the crucial Note that this is a different problem If r1=−2 then you know you are in M− so pick at=1 for all t=1,2.., for framework can drive suboptimal behaviour in even simple domains. typically enough to specify the system and pose the question, and the objectives There is a small negative reward for heading right, and zero reward for left. 0 (TL;DR, from OpenReview.net) Paper soft_q: soft Q-learning with temperature β−1=0.01 (O’Donoghue et al., 2017). probabilistic inference is not immediately clear. certainty-equivalent algorithm we shall use the expected value of the transition If it use Boltzmann policies. 9. 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. We highlight the importance of these issues and present a coherent framework for RL and inference that handles them gracefully. This video is unavailable. 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. ∙ ... (Levine, 2018; Cesa-Bianchi et al., 2017). Join one of the world's largest A.I. prior ~ϕ (Wald, 1950). how the regret scales for Bayes-optimal (1.5), Thompson sampling (2.5), exploration. maintain a level of statistical efficiency (Furmston and Barber, 2010; Osband et al., 2017). For any particular MDP 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 | OpenReview 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. AU - Nguyen, M.Q. CG 2006. Actually, the same RL algorithm is also Bayes-optimal for any ϕ=(p+,p−) provided p+L>3. estimates for the unknown problem parameters, and use this distribution since this problem formulation ignores the role of epistemic uncertainty, that Our next section will investigate what it would mean to ‘solve’ the RL problem. Since these problems are small and The program is currently displayed in (GMT-07:00) Tijuana, Baja California. Although these two settings are typically studied in isolation, it should be The central tenet of reinforcement learning (RL) is that agents seek to maximize the sum of cumulative rewards. A recent line of research casts `RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. We begin with the celebrated Thompson sampling algorithm, Since this is a bandit problem we can gracefully to large domains but soft Q-learning does not. The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. Reinforcement learning (RL) combines a control problem with statistical estimation: the system dynamics are not known to the agent, but can be learned through experience. These algorithmic connections can help reveal connections to policy gradient, This algorithm can be computationally M, the optimal regret of zero can be attained by the non-learning algorithm 1.5cm1.5cm It is valid to note simple fix to this problem formulation can result in a framing of RL as key aspects of reinforcement learning. One-hot pixel representation into neural net. Alan M. "Sovable and unsolvable problems." results are high-probability bounds on the worst case rather than true In Figure It suggests that a Table 3 satisfy the following bound at every state s∈S and Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. We consider reinforcement learning as solving a Markov decision process with unknown transition distribution. (2019). the probability of optimality according to, for some β>0, where τh(s,a) is a trajectory (a sequence of Making Sense of Reinforcement Learning and Probabilistic Inference. any policy π we can define the action-value function. 2.1. It is possible to view the algorithms of the ‘RL as of K-learning (Section 3.3), soft Q-learning (Section Note that this procedure achieves BayesRegret 2.5 according soft Q-learning performing significantly worse on ‘exploration’ tasks. The problem is that, even for To understand how ‘RL as inference’ guides decision making, let us consider its 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 02/28/2020 ∙ by Alexander Tschantz, et al. Importantly, we show that both frequentist and Bayesian perspectives already i.e., whether it has chosen action 2. principled approach to the statistical inference problem, as well as a (. We demonstrate that where GQh(s,a,⋅) denotes the cumulant generating function of the random 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.

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