We swap either the top two or middle two blocks in this case, and also increase the total number of blocks. We place our work in the development of relational reinforcement learning (DÅ¾eroski etÂ al., 2001) that represent states, actions and policies in Markov Decision Processes (MDPs) using the first order logic where transitions and rewards structures of MDPs are unknown to the agent. Inductive logic programming (ILP) is a task to find a definition (set of clauses) of some intensional predicates, given some positive examples and negative examples (Getoor & Taskar, 2007). Some auxiliary predicates, for example, the predicates that count the number of blocks, are given to the agent. by minor modifications of the training environment. Ask: what can neuroscience do for me? Learning Algorithms via Neural Logic Networks. Montavon, G., Samek, W., and MÃ¼ller, K.-R. Methods for interpreting and understanding deep neural networks. The concept of relational reinforcement learning was first proposed by (DÅ¾eroski etÂ al., 2001) in which the first order logic was first used in reinforcement learning. Vinyals, O., and Battaglia, P. Programmatically Interpretable Reinforcement Learning, Sequential Triggers for Watermarking of Deep Reinforcement Learning Mnih, V., Badia, A.Â P., Mirza, M., Graves, A., Harley, T., Lillicrap, T.Â P., The interpretability is a critical capability of reinforcement learning algorithms for system evaluation and improvement. ((a,b,d,c)), ((a,b),(c,d)), ((a,b,c,d,e)), ((a,b,c,d,e,f)) and ((a,b,c,d,e,f,g)). 0 Extensive experiments con- We will train all the agents with vanilla policy gradient (Willia, 1992) in this work. M.Â G., Graves, A., Riedmiller, M., Fidjeland, A.Â K., Ostrovski, G., Petersen, Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday. Therefore, the initial states of all the generalization test of UNSTACK are: In all three tasks, the agent can only move the topmost block in a pile of blocks. Babuschkin, I., Tuyls, K., Reichert, D., Lillicrap, T., Lockhart, Wulfmeier, M., Posner, I., and Abbeel, P. Inductive policy selection for first-order mdps. where hn,j(e) implements one-step deduction using jth possible definition of nth clause.111Computational optimization is to replace â with typical + when combining valuations of two different predicates. address these two challenges, we propose a novel algorithm named Neural Logic 08/07/2019 â by Jorge A. Laval, et al. Hence, generalizability is a necessary condition for any algorithm to perform well. Performance on Train and Test Environments. LPAR-23: 23rd International Conference on Logic for Programming, Artificial Intelligence and Reasoning, vol 73, pages 230--248 Therefore, the algorithms cannot perform well in new domains. But the states and actions are represented as atoms and tuples. On the other side, thanks to the strong relational inductive bias, DILP shows superior interpretability and generalization ability than neural networks (Evans & Grefenstette, 2018). Therefore, the action atoms should be a subset of D. As for âILP, valuations of all the atoms will be deduced, i.e., D=G. Except that, the use of deep neural networks makes the learned policies hard to be interpretable. The overwhelming trend is, in varied environments, the neural networks perform even worse than a random player. on(X,Y) means the block X is on the entity Y (either blocks or floor). The first three columns demonstrate the return of the three agents. Get the latest machine learning methods with code. Extensive experiments conducted on cliff-walking and blocks manipulation The action predicate move(X,Y) simply move the top block in any column with more than 1 block to the floor. The book consists of three parts. The agent is also tested in the environments with more blocks stacking in one column. However, most DRL algorithms suffer a problem of generalizing the learned policy which makes the learning performance largely affected even by minor modifications of the training environment. The action is valid only if both Y and X are on the top of a pile or Y is floor and X is on the top of a pile. In the training environment of cliff-walking, the agent starts from the bottom left corner, labelled as S in FigureÂ 2. Reinforcement Learning with Deep Neural Networks in the last few years has shown great results with many different approaches. gÎ¸ can then be expressed as. There are four action atoms up(), down(), left(), right(). This problem can be modelled as a finite-horizon MDP. Hence, the solutions are not interpretable as they cannot be understood by humans as to how the answer was learned or achieved. Empirically, this design is crucial for inducing an interpretable and generalizable policy. The proposed methods show some level of generalization ability on the constructed block world problems and StarCraft mini-games, showing the potential of relation inductive bias in larger problems. In such cases with environment models known, variations of traditional MDP solvers such as dynamic programming (Boutilier etÂ al., 2001). A clause is a rule in the form Î±âÎ±1,...,Î±n, where Î± is the head atom and Î±1,...,Î±n are body atoms. Simple Statistical Gradient-Following Algorithms for Connectionist The main goal of the project is to model human intelligence by a special class of mathematical systems called neural logic networks. Before that, the agent keeps receiving a small penalty of -0.02. For the neural network agent, we pick the agent that performs best in the training environment out of 5 runs. Logic programming can be used to express knowledge in a way that does not depend on the implementation, making programs more flexible, compressed and understandable. LPAR23. If all terms in an atom are constants, this atom is called a ground atom. Reinforcement Learning. However, most DRL algorithms suffer a problem of generalizing Another direction is to use a hybrid architecture of DILP and neural networks, i.e., to replace pS with neural networks thus the agent can make decisions based on raw sensory data. The agent instead only need to keep the relative valuation advantages of desired actions over other actions, which in practice leads to tricky policies. 0 and for the ON task, there is one more background knowledge predicate goalOn(a,b), which indicates the target is to move block a onto the block b. It does not matter which activation function or wh… Then we increase the size of the whole field to 6 by 6 and 7 by 7 without retraining. Reinforcement Learning. NLRL is based on policy gradient methods and The Markov Decision Process (MDP) and reinforcement learning are also briefly introduced. Compared with traditional symbolic logic induction methods, with the use of gradients for optimising the learning model, DILP has significant advantages in dealing with stochasticity (caused by mislabeled data or ambiguous input) (Evans & Grefenstette, 2018). share, The recent success of deep neural networks (DNNs) for function approxima... The weights are updated through the forward chaining method. NLRL is based on policy gradient methods and differentiable inductive logic programming that have demonstrated significant advantages in terms of interpretability and generalisability in supervised … These algorithms learn solutions and not the path to find the solution. Furthermore, the proposed NLRL framework is of great significance for advancing the DILP research. In NLRL the agent must learn auxiliary invented predicates by themselves, together with the action predicates. â A Statistical Investigation of Long Memory in Language and Music. However, most DRL algorithms have the assumption that these two environments are identical, which makes the robustness of DRL remains a critical issue in real-world deployments. But in real-world problems, the training and testing environments are not always the same. In: Elvira Albert and Laura Kovács (editors). Zambaldi, V., Raposo, D., Santoro, A., Bapst, V., Li, Y., Tang & Mooney (2001) Lappoon R. Tang and Raymond J. Mooney. For example, if we have a training set with range from 0 to 100, the output will also be between that samerange. By using our site, you The predicates defined by rules are termed as intensional predicates. Deep Reinforcement Learning Algorithms are not interpretable or generalizable. Extensive experiments conducted on cliff-walking and blocks manipulation tasks demonstrate that NLRL … Predicates are composed of true statements based on the examples and environment given. Other required python packages specified by requirements.txt. What I mean by is that they can’toutput values outside the range of training data. The extensive experiments on block manipulation and cliff-walking have shown the great potential of the proposed NLRL algorithm in improving the interpretation and generalization of the reinforcement learning in decision making. 04/24/2019 â by Zhengyao Jiang, et al. However, the neural network agent seems only remembers the best routes in the training environment rather than learns the general approaches to solving the problems. Neural Logic Reinforcement Learning is an algorithm that combines logic programming with deep reinforcement learning methods. The generalized advantages (. In each group, the blue bar shows the performance in the training environment while other show the performance in the test environments. Symbolic dynamic programming for first-order mdps. 11/24/2019 â by Gang Chen, et al. The state predicates are on(X,Y) and top(X). In the UNSTACK task, the agent needs to do the opposite operation, i.e., spread the blocks on the floor. âILP, a DILP model that our work is based on, is then described. Although such a flaw is not serious in the training environment, shifting the initial position of the agent to the top left or top right makes it deviate from the optimal obviously. In addition, in (Gretton, 2007), expert domain knowledge is needed to specify the potential rules for the exact task that the agent is dealing with. To address these two challenges, we propose a novel algorithm named Neural Logic Reinforcement Learning (NLRL) to represent the policies in reinforcement learning by first-order logic. Reinforcement learning models have provided insight into the functions of dopamine and cortico-basal ganglia-thalamo-cortical circuits. memory requirement Time requirement Necessary to visit all state spaces to learn how to play game • Uses approximation function • Using neural nets as an approximation function in reinforcement learning See your article appearing on the GeeksforGeeks main page and help other Geeks. Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. Neural Logic Reinforcement Learning. Detailed discussions on the modifications and their effects can be found in the appendix. Reinforcement learning with non-linear function approximators like backpropagation networks attempt to address this problem, but in many cases have been demonstrated to be non-convergent [2]. We will use the following schema to represent the pA in all experiments. Compared to âILP, in DRLM the number of clauses used to define a predicate is more flexible; it needs less memory to construct a model (less than 10 GB in all our experiments); it also enables learning longer logic chaining of different intensional predicates. The action predicate is move(X,Y) and there are 25 actions atoms in this task. These weights are updated based on the true values of the clauses, hence reaching the best clause possible with best weight and highest truth value. D., Legg, S., and Hassabis, D. Human-level control through deep reinforcement learning. Just like the architecture design of the neural network, the rules templates are important hyperparameters for the DILP algorithms. â Compared with traditional inductive logic programming methods, âILP has advantages in terms of robustness against noise/uncertainty and ability to deal with fuzzy data (Evans & Grefenstette, 2018). 04/06/2018 â by Abhinav Verma, et al. If pS and pA are neural architectures, they can be trained together with the DILP architectures. Predicate names (or for short, predicates), constants and variables are three primitives in DataLog. Notably, top(X) cannot be expressed using on here as in DataLog there is no expression of negation, i.e., it cannot have âtop(X) means there is no on(Y,X) for all Yâ. The pred3(X) has the same meaning of pred in UNSTACK task, as it labels the top block in a column that is at least two blocks in height, which in this tasks tells where the block on the floor should be moved to. Such a practice of induction-based interpretation is straightforward but the obtained decisions made by the agent in such systems might just be caused by coincidence. UNSTACK induced policy: The policy induced by NLRL in UNSTACK task is: We only show the invented predicates that are used by the action predicate and the definition clause with high confidence (larger than 0.3) here. To ∙ 0 ∙ share . The pred4(X,Y) means X is a block that directly on the floor and there is no other blocks above it, and Y is a block. Bias-Variance Tradeoff for Effective Deep Reinforcement Learning, Large-scale traffic signal control using machine learning: some traffic Deep reinforcement learning (DRL) has achieved significant breakthroughs in various tasks. We denote the probabilistic sum as â and, where aâE,bâE. For the STACK task, the initial state is ((a),(b),(c),(d)) in training environment. In the generalization test, we first move the initial position to the top right, top left and centre of the field, labelled as S1,S2,S3 respectively. Similar to the UNSTACK task, we swap the right two blocks, divide them into 2 columns and increase the number of blocks as generalization tests. Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. The interpretable reinforcement learning, e.g., relational reinforcement learning (DÅ¾eroski etÂ al., 2001), has the potential to improve the interpretability of the decisions made by the reinforcement learning algorithms and the entire learning process. Neural Networks have proven to have the uncanny ability to learn complexfunctions from any kind of data, whether it is numbers, images or sound. Weights are not assigned directly to the whole policy. Let pA(a|e) be the probability of choosing action a given the valuations eâ[0,1]|D|. We modify the version in (Sutton & Barto, 1998) to a 5 by 5 field, as shown in Figure 2. the learned policy which makes the learning performance largely affected even The symbolic representation of the state is current(X,Y), which specifies the current position of the agent. The agent is initialized with 0-1 valuation for base predicates and random weights to all clauses for an intentional predicate. â The neural network agents learn optimal policy in the training environment of 3 block manipulation tasks and learn near-optimal policy in cliff-walking. The proposed RNN-FLCS is constructed by integrating two neural-network-based fuzzy logic controllers (NN-FLC's), each of which is a connectionist model with a feedforward multilayered network developed for the realization of a fuzzy logic controller. NLRL is based on policy gradient methods and differentiable inductive logic programming that have demonstrated signiﬁcant advantages in terms of interpretability and generalisability in supervised tasks. The algorithm trains the parameterized rule-based policy using policy gradient. environments of different initial states and problem sizes. One of the most famous logic programming languages is ProLog, which expresses rules using the first-order logic. For further details on the computation of hn,j(e) (Fc in the original paper), readers are referred to Section 4.5 in (Evans & Grefenstette, 2018). However, this black-box approach fails to explain the learned policy in a human understandable way. DÅ¾eroski, S., DeÂ Raedt, L., and Driessens, K. Learning Explanatory Rules from Noisy Data. Random Matrix Improved Covariance Estimation for a Large Class of Metrics . However, to the authorsâ best knowledge, all current DILP algorithms are only tested in supervised tasks such as hand-crafted concept learning (Evans & Grefenstette, 2018) and knowledge base completion (RocktÃ¤schel & Riedel, 2017; Cohen etÂ al., 2017). • Why are you here? In this section, we present a formulation of MDPs with logic interpretation and show how to solve the MDP with the combination of policy gradient and DILP. The second clause move(X,Y)âtop(X),goalOn(X,Y) tells if the block X is already movable (there is no blocks above), just move X on Y. Writing code in comment? Logic programming languages are a class of programming languages using logic rules rather than imperative commands. 06/23/2020 â by Lingheng Meng, et al. An MDP with logic interpretation is a triple (M,pS,pA): pS:Sâ2G is the state interpretation that maps each state to a set of atoms including both information of the current state and background knowledge; pA:[0,1]|D|â[0,1]|A| is the action interpretation that maps the valuation (or score) of a set of atoms D. For a DILP system fÎ¸:2Gâ[0,1]|D|, the policy Ï:Sâ[0,1]|D| can be expressed as Ï(s)=pA(fÎ¸(pS(s))). The NLRL algorithm’s basic structure is very similar to any deep RL algorithm. The initial states of all the generalization test of STACK are: ((a),(b),(d),(c)), ((a,b),(d,c)), ((a),(b),(c),(d),(e)), ((a),(b),(c),(d),(e),(f)), ((a),(b),(c),(d),(e),(f),(g)). It enables knowledge to be separated from use, ie the machine architecture can be changed without changing programs or their underlying code. In the real world, it is not common that the training and test environments are exactly the same. To make a step further, in this work we propose a novel framework named as Neural Logic Reinforcement Learning (NLRL) to enable the DILP work on sequential decision-making tasks. Neural Logic Reinforcement Learning uses deep reinforcement leanring methods to train a differential indutive logic progamming architecture, obtaining explainable and generalizable policies. This a huge drawback of DRL algorithms. Thus any policy-gradient methods applied to DRL can also work for DILP. NLRL is based on policy gradient methods and differentiable inductive logic programming that have demonstrated significant advantages in terms of interpretability and generalisability in supervised tasks. When the agent reaches the cliff position it gets a reward of -1, and if the agent arrives the goal position, it gets a reward of 1. Reinforcement learning is the process by which an agent learns to predict long-term future reward. various tasks. For each step in forwarding chaining, we first get the value of all the clauses for all combinations of constants using the deduction matrix. The first clause of move move(X,Y)âtop(X),pred(X,Y) implements the unstack procedures, where the logics are similar to the UNSTACK task. 04/02/2019 ∙ by Ali Payani, et al. Therefore, values of all actions are obtained and the best action is chosen accordingly as in any RL algorithm. In addition, the problem of sparse rewards is common in the agent systems. Deep reinforcement learning (DRL) has achieved significant breakthroughs in share, Deep reinforcement learning (DRL) on Markov decision processes (MDPs) wi...

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