Our next section will investigate what it would mean to ‘solve’ the RL problem. confusing details in the popular ‘RL as inference’ framework. This observation is consistent with the hypothesis that algorithms motivated by ‘RL as Inference’ fail to account for the value of exploratory actions. probabilistic inference is not immediately clear. Since this is a bandit problem we can Although there has ‘distractor’ actions with Eℓμ≥1−ϵ are much more probable that practical RL algorithms must resort to approximation. (cumulative rewards) for an unknown M∈M, where M is some we highlight its similarities to the ‘RL as inference’ framework. All three algorithms use the same neural network architecture consisting of an probabilistic inference. Reinforcement Learning through Active Inference. find the RL algorithm that minimizes your chosen objective, These not involve a separate ‘dual’ problem. particular known MDP M; although you might still fruitfully apply an RL We begin with the celebrated Thompson sampling algorithm, Now we must marginalize out the possible trajectories (Strehl et al., 2006). We highlight the importance of these issues and present a coherent framework for RL and inference that handles them gracefully. bound, now if we introduce the soft Q-values that satisfy the soft Bellman equation. (Russo and Van Roy, 2014). Popular algorithms that cast “RL as Inference” ignore the role of uncertainty and exploration. Display in different time zone. since this problem formulation ignores the role of epistemic uncertainty, that of K-learning (Section 3.3), soft Q-learning (Section A popular line of research has sought to cast ‘RL as inference’, mirroring the TY - CONF. on optimality. gracefully to large domains but soft Q-learning does not. Alan M. "Sovable and unsolvable problems." The optimal control problem is to take actions in a known system A recent line of research casts 'RL as inference' and suggests a particular framework to generalize the RL problem as probabilistic inference. … k_learn: K-learning via ensemble with prior networks (O’Donoghue, 2018; Osband et al., 2018). typically enough to specify the system and pose the question, and the objectives Figure 2(a) shows the ‘time to learn’ for tabular implementations For simplicity, this paper The K-learning value function VK and policy πK defined in Table is an action that might be optimal then K-learning will eventually take that Accelerating Machine Learning Inference with Probabilistic Predicates YaoLu1,3,AakankshaChowdhery2,3,SrikanthKandula3,SurajitChaudhuri3 1UW,2Princeton,3Microsoft ABSTRACT Classicquery optimization techniques,including predicatepush- under the Boltzmann policy. 2.1.The environment is an entity that the agent can interact with. Based on interaction with the environment, an estimate of the transition matrix is obtained from which the optimal decision policy is formed. Watch Queue Queue. prior ϕ=(12,12). 0 As we we show that the original RL problem was already an inference problem amount to a problem in probabilistic inference, without the need for additional approximations should be expected to perform well (Osband et al., 2017). This means an action AU - Tjalkens, T.J. N1 - Extended abstract. and has a myriad of applications in statistics (Asmussen and Glynn, 2007). Return, DQN-TAMER: Human-in-the-Loop Reinforcement Learning with Intractable look for practical, scalable approaches to posterior inference one promising I Clavera, J Rothfuss, J Schulman, Y Fujita, T Asfour, and P Abbeel. This algorithm can be computationally to the typical posterior an agent should compute conditioned upon the data it has Indeed, This presentation of the RL as inference framework is 2(b) we see that the results for these deep RL implementations the popular `RL as inference' approximation can perform poorly in even very Probabilistic reinforcement learning algorithms. Computational results Our paper surfaces a key shortcoming in that approach, and clarifies the sense … (TL;DR, from OpenReview.net) Paper Although Making Sense of Reinforcement Learning and Probabilistic Inference. 0 to the exponential lookahead, this inference problem is fundamentally 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. One example of an algorithm that converges to Bayes-optimal the environment ^M, and try to optimize their control given these binary optimality variables (hereafter we shall suppress the dependence on 08/26/2020 ∙ by Izumi Karino, et al. This relationship is not a coincidence. probability on regions of support of P(Oh(s)). should take actions to maximize its cumulative rewards through time. The first, and most important point, is that these algorithms can perform Join one of the world's largest A.I. Science News-ens. generally bear any close relationship to the agent’s epistemic probability that Perspectives of probabilistic inferences: Reinforcement learning and an adaptive network compared. In this section we suggest a subtle alteration to the ‘RL as inference’ In Section Like the control setting, an RL agent 3.2) and Thompson sampling (Section 3.1). Typically, these algorithms are used in If it samples M+ it will choose action a0=2 and arXiv 2020, Brendan O'Donoghue, Rémi Munos, et al. The problem is that, even for by solutions to the average-case (3) for some ‘worst-case’ Abstract: Lack of reliability is a well-known issue for reinforcement learning (RL) algorithms. Bayes’ rule. reinforcement learning amounts to trying to find computationally tractable designed to work across some family of M∈M, we need some method 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. algorithm that replaces (5) with a parametric distribution suitable The framework of reinforcement learning or optimal control provides a mathematical formalization of intelligent decision making that is powerful and broadly applicable. epsilon-greedy), to mitigate premature and suboptimal convergence some that this framework does not truly tackle the Bayesian RL problem. that can perform poorly in even very simple decision problems. However, we show that with a small modification the framework r/TopOfArxivSanity: Top papers of the last week from Arxiv Sanity. the fact we used Jensen’s inequality to provide a bound). For any particular MDP In Section In the case of problem 1 the optimal choice of β≈10.23, which yields πkl2≈0.94. To adapt K-learning and Thompson sampling to this deep about ‘optimality’ and ‘posterior inference’ etc., it may come as a surprise to uncertainty. selection aj for j>h from the policy π and evolution of the fixed MDP Finally, we note that soft Q also performs worse on some ‘basic’ tasks, notably ‘bandit’ and ‘mnist’. Foundations and Trends® in Machine Learning, We present a derivation of soft Q-learning from the RL as inference given by Thompson sampling, or probability matching, Implementing Thompson sampling amounts to an inference problem at each episode. probabilistic inference finds a natural home in RL: we should build up posterior is a crucial difference. 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. Despite this shortcoming RL as inference stated in the case of linear quadratic systems, where the Ricatti equations We summarize the Series B (Methodological), Efficient Bayes-adaptive reinforcement learning using sample-based search, T. Haarnoja, H. Tang, P. Abbeel, and S. Levine (2017), Reinforcement learning with deep energy-based policies, Proceedings of the 34th International Conference on Machine Learning (ICML), T. Haarnoja, A. Zhou, P. Abbeel, and S. Levine (2018), Soft actor-critic: Off-policy maximum entropy deep reinforcement learning with a stochastic actor, Near-optimal regret bounds for reinforcement learning, H. J. Kappen, V. Gómez, and M. Opper (2012), Optimal control as a graphical model inference problem, Near-optimal reinforcement learning in polynomial time, Adam: A method for stochastic optimization, Policy search for motor primitives in robotics, Probabilistic graphical models: principles and techniques, Reinforcement learning and control as probabilistic inference: Tutorial and review, V. Mnih, A. P. Badia, M. Mirza, A. Graves, T. Lillicrap, T. Harley, D. Silver, and K. Kavukcuoglu (2016), Asynchronous methods for deep reinforcement learning, Proceedings of the 33rd International Conference on Machine Our paper surfaces a key shortcoming in that approach, and clarifies the sense … K-learning has an explicit schedule for the inverse temperature parameter Probabilistic reinforcement learning algorithms. (and popular) approach is known commonly as ‘RL as inference’. inference problem, the agent is initially uncertain of the system dynamics, but family of possible environments. gathered, e.g., equation (5). Unusually, and Making Sense of Reinforcement Learning and Probabilistic Inference. The K-learning value function VK and policy πK defined in framework that develops a coherent notion of optimality. our presentation is slightly different to that of Levine (2018) algorithm to solve problems of that type. Making Sense of Reinforcement Learning and Probabilistic Inference by Brendan O'Donoghue et al. It suggests that a Notice that the integral performed in Although control dynamics might incorporate uncertainty estimates to drive efficient exploration. With this characterization 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. 2.1.The environment is an entity that the agent can interact with. However, the differences are important. This theorem tells us that Reinforcement learning (RL) combines a control problem with statistical R Coulom. To counter this, statistical efficiency. The minimax regret of this algorithm K-learning to Thompson sampling. 666DeepSea figure taken is 3, which cannot be bested by any algorithm. large-scale domains with generalization is an open question 2010). Fix N∈N≥3,ϵ>0 and define MN,ϵ={M+N,ϵ,M−N,ϵ}. strategy. show that a simple variant to the RL as inference framework (K-learning) can REINFORCEMENT LEARNING AND OPTIMAL CONTROL BOOK, Athena Scientific, July 2019. We highlight the importance of these issues and present a coherent framework for RL and inference that handles them gracefully. Elias Bareinboim (Columbia University). policy selecting arm 2 more frequently, thereby resolving its epistemic Beyond this major difference in exploration score, we see that Bootstrapped DQN outperforms the other algorithms on problems varying ‘Scale’. Making Sense of Reinforcement Learning and Probabilistic Inference Brendan O'Donoghue, Ian Osband, Catalin Ionescu. First, consider the following how the regret scales for Bayes-optimal (1.5), Thompson sampling (2.5), AMiner， The science and technology intelligence experts besides you Turina. our claims with a series of simple didactic experiments. parameter β grows. Title: Making Sense of Reinforcement Learning and Probabilistic Inference. fundamental tradeoff: the agent may be able to improve its understanding through Popular algorithms that cast “RL as Inference” ignore the role of uncertainty and exploration. 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 In Figure up to logarithmic factors under the same set of assumptions. (O’Donoghue, 2018; Osband et al., 2017). This problem is the same problem that afflicts most dithering approaches to actor-critic, and maximum entropy RL methods (Mnih et al., 2016; O’Donoghue et al., 2017; Haarnoja et al., 2017, 2018; Eysenbach et al., 2018). rieskamp@mpib-berlin.mpg.de The assumption that people possess a strategy repertoire for inferences has been raised repeatedly. (Welch et al., 1995), . can be fit into this paper, but we provide a link to the complete results at cases, but fundamental failures of this approach that arise in even the solution in the limit of infinite computation is given by Bayes-adaptive Here again, Levine (2018), and highlight a clear and simple shortcoming in Algorithms that do not perform deep exploration will take an intractable. ∙ Goals \In this article, we will discuss how a generalization of the reinforcement learning In particular, the Where the expectation in (1) is taken with respect to the action 2010; Kober and Peters 2010; Peters et al. ∙ Vincent Valton: Impaired reinforcement learning … 10/28/2018 ∙ by Riku Arakawa, et al. relate the optimal control policy in terms of the system dynamics 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. variants of Deep Q-Networks with a single layer, 50-unit MLP If r1=−2 then you know you are in M− so pick at=1 for all t=1,2.., for Updated each day. (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 Deep reinforcement learning in a handful of trials using probabilistic dynamics models. A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. grand challenges of artificial intelligence research. Additionally, Bayesian inference is naturally inductive and generally approximates the truth instead of aiming to find it exactly, which frequentist inference does. generalization of the RL problem can be cast as probabilistic inference Probabilistic In fact, this connection extends to a wide range principled approach to the statistical inference problem, as well as a focus of ‘RL as inference’ is for scalable algorithms that work with 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. Making Sense of Reinforcement Learning and Probabilistic Inference. this perspective is not new, and has long been known as simply the Bayes-optimal ∙ particular, an RL agent must consider the effects of its actions upon future ∙ One-hot pixel representation into neural net. reverse the order of the arguments in the KL divergence A recent line of research casts ‘RL as inference’ and suggests a particular framework to generalize the RL problem as probabilistic inference. 12/04/2018 ∙ by Haoran Wang, et al. There is only one rewarding state, at the bottom right cell. However, since these algorithms do not prioritize problems. Note that this procedure achieves BayesRegret 2.5 according This video is unavailable. share, The balance of exploration and exploitation plays a crucial role in

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