∙ In addition, by simply observing the input-output pairs, it lacks rigorous procedures to determine the beneath reasoning of a neural network. In this work, we propose a deep Reinforcement Learning (RL) method for policy synthesis in continuous-state/action unknown environments, under requirements expressed in Linear Temporal Logic (LTL). ∙ The action selection mechanism in this work is to add a set of action predicates into the architecture, which depends on the valuation of these action atoms. Each action is represented as an atom. Silver, D., Schrittwieser, J., Simonyan, K., Antonoglou, I., Huang, A., Guez, The state to atom conversion can be either done manually or through a neural network. We inject basic knowledge about natural numbers including the smallest number (zero(0)), largest number (last(4)), and the order of the numbers (succ(0,1), succ(1,2), …). The parameters to be trained are involved in the deduction process. The action predicate is move(X,Y) and there are 25 actions atoms in this task. Montavon, G., Samek, W., and Müller, K.-R. Methods for interpreting and understanding deep neural networks. 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). The clause associated to predicate left() will never be met since there will not be a number if the successor of itself, which is sensible since we never want the agent to move left in this game. ∙ Neural Networks have proven to have the uncanny ability to learn complexfunctions from any kind of data, whether it is numbers, images or sound. In the ON task, it is required to put a specific block onto another one. share, This paper proposes a novel scheme for the watermarking of Deep Reinforc... It enables knowledge to be separated from use, ie the machine architecture can be changed without changing programs or their underlying code. Another way to define a predicate is to use a set of clauses. Keyphrases: combinators, Diophantine equations, HOL, Reinforcement Learning, tree neural networks. In principle, we just need pred4(X,Y)←pred2(X),top(X) but the pruning rule of ∂ILP prevent this definition when constructing potential definitions because the variable Y in the head atom does not appear in the body. For ON, the initial state is ((a,b,c,d)). D., Legg, S., and Hassabis, D. Human-level control through deep reinforcement learning. In all three tasks, the agent can only move the topmost block in a pile of blocks. Paper accepted by ICML2019. In the experiments, to test the robustness of the proposed NLRL framework, we only provide minimal atoms describing the background and states while the auxiliary predicates are not provided. Extensive experiments conducted on cliff-walking and blocks manipulation tasks demonstrate that NLRL … The strategy NLRL agent learned is to first unstack all the blocks and then move a onto b. On the other side, thanks to the strong relational inductive bias, DILP shows superior interpretability and generalization ability than neural networks (Evans & Grefenstette, 2018). 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. ∙ Such a policy is a sub-optimal one because it has the chance to bump into the right wall of the field. The NLRL agent succeeds to find near-optimal policies on all the tasks. To this end, in this section we review the evolvement of relational reinforcement learning and highlight the differences of our proposed NLRL framework with other algorithms in relational reinforcement learning. Džeroski, S., De Raedt, L., and Driessens, K. Learning Explanatory Rules from Noisy Data. In the STACK task, the agent needs stack the scattered blocks into a single column. A Kernel Perspective for Regularizing Deep Neural Networks. We examine the performance of the agent on three subtasks: STACK, UNSTACK and ON. Schulman, J., Wolski, F., Dhariwal, P., Radford, A., and Klimov, O. 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. 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. Ask: what can neuroscience do for me? Experience. 0 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. 0 top(X) means the block X is on top of an column of blocks. 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. • Why are you here? Furthermore, the proposed NLRL framework is of great significance for advancing the DILP research. In each group, the blue bar shows the performance in the training environment while other show the performance in the test environments. All these benefits make the architecture be able to work in larger problems. Neural Logic Reinforcement Learning is an algorithm that combines logic programming with deep reinforcement learning methods. We denote the probabilistic sum as ⊕ and, where a∈E,b∈E. share. ∙ However, to the authors’ 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 (Rocktäschel & Riedel, 2017; Cohen et al., 2017). The rules about going down is a bit complex in the sense it uses an invented predicate that is actually not necessary. The rules of going down it deduced can be simplified as down():−current(X,Y),last(X), which means the current position is in the rightmost edge. 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. For the neural network agent, we pick the agent that performs best in the training environment out of 5 runs. estimation. 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. fθ can then be decomposed into repeated application of single step deduction functions gθ, namely, where t is the deduction step. 0 Revisiting precision recall definition for generative modeling. If we replace it with a trivial normalization, it is not necessary for NLRL agent to increase rule weights to 1 for sake of exploitation. ON induced policy: The induced policy of the ON task is: The goal of ON is to move block a onto b, while in the training environment the block a is at the bottom of the whole column of blocks. A new DILP architecture termed as Differentiable Recurrent Logic Machine (DRLM), an improved version of ∂ILP, is first introduced. Reinforcement learning models have provided insight into the functions of dopamine and cortico-basal ganglia-thalamo-cortical circuits. To address this challenge, recently Differentiable Inductive Logic Programming (DILP) has been proposed in which a learning model expressed by logic states can be trained by gradient-based optimization methods (Evans & Grefenstette, 2018; Rocktäschel & Riedel, 2017; Cohen et al., 2017). We now understand a great deal about the brain's reinforcement learning algorithms, but we know considerably less about the representations of states and actions over which these algorithms operate. 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. ∙ With the differentiable deduction, the system can be trained with gradient-based methods. Furthermore, most such algorithms represent the induced policy in a single clause. By applying DILP in sequential decision making, we investigate how intelligent agents learn new concepts without human supervision, instead of describing a concept already known to the human in supervised learning tasks. This paper presents a neuro-symbolic agent that combines deep reinforcement learning (DRL) with temporal logic (TL), and achieves systematic out-of-distribution generalisation in tasks that involve following a formally specified instruction. 08/07/2019 ∙ by Jorge A. Laval, et al. 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. However, this black-box approach fails to explain the learned policy in a human understandable way. Neural Logic Reinforcement Learning uses deep reinforcement leanring methods to train a differential indutive logic progamming architecture, obtaining explainable and generalizable policies. ∙ This approach has produced models of the roles of dopamine and cortico-basal ganglia-thalamo-cortical (CBGTC) loops in learning about reinforcers (rewards and punishments) and in guiding behavior so as to acquire rewards and avoid punishments5. A., Hubert, T., Baker, L., Lai, M., Bolton, A., Chen, Y., Lillicrap, T., Hui, Using multiple clause constructors in inductive logic programming for semantic parsing. 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. The state predicates are on(X,Y) and top(X). Deep Reinforcement Learning Algorithms are not interpretable or generalizable. In Advances in neural information processing systems, pp. ∙ tasks demonstrate that NLRL can induce interpretable policies achieving The rules template of a clause indicates the arity of the predicate (can be 0, 1, or 2) and the number of existential variables (usually pick from, In all the tasks, we use a DRL agent as one of the benchmarks that have two hidden layers with 20 units and 10 units respectively. For example, in the atom father(cart, Y), father is the predicate name, cart is a constant and Y is a variable. We show that this combination lifts the applicability of deep RL to complex temporal and memory-dependent policy synthesis goals. To test the generalizability of the induced policy, we construct the test environment by modifying its initial state by swapping the top 2 blocks or dividing the blocks into 2 columns. On the Universality of Invariant Networks. 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 Mnih, V., Badia, A. P., Mirza, M., Graves, A., Harley, T., Lillicrap, T. P., Thus any policy-gradient methods applied to DRL can also work for DILP. If pS and pA are neural architectures, they can be trained together with the DILP architectures. ∙ Before that, the agent keeps receiving a small penalty of -0.02. where hn,j(e) implements one-step deduction using jth possible definition of nth clause.111Computational optimization is to replace ⊕ with typical + when combining valuations of two different predicates. The neural network agents and random agents are used as benchmarks. Notably, pA is required to be differentiable so that we can train the system with policy gradient methods operating on discrete, stochastic action spaces, such as vanilla policy gradient (Willia, 1992), A3C (Mnih et al., 2016), TRPO(Schulman et al., 2015a) or PPO (Schulman et al., 2017). Let pA(a|e) be the probability of choosing action a given the valuations e∈[0,1]|D|. This gives our method better scalability. E., Shanahan, M., Langston, V., Pascanu, R., Botvinick, M., The second clause move(X,Y)←top(X),goalOn(X,Y) tells if the block X is already movable (there is no blocks above), just move X on Y. Empirical evaluations show NLRL can learn near-optimal policies in training environments while having superior interpretability and generalizability. For instance, the output actions can be deterministic and the final choice of action may depend on more atoms rather than only action atoms if the optimal policy cannot be easily expressed as first-order logic. Policy gradient methods for reinforcement learning with function approximation. The probability of choosing an action a is proportional to its valuation if the sum of the valuation of all action atoms is larger than 1; otherwise, the difference between 1 and the total valuation will be evenly distributed to all actions, i.e.. where l:[0,1]|D|×A→[0,1] maps from valuation vector and action to the valuation of that action atom, σ is the sum of all action valuations σ=∑a′pA(a′|e). the learned policy which makes the learning performance largely affected even 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. Since neural networks are used in Deep RL this algorithm is also robust to missing and misclassified or wrong data. 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. ∂ILP, a DILP model that our work is based on, is then described. This problem can be modelled as a finite-horizon MDP. Whereas, we can also construct non-optimal case where unstacking all the blocks are not necessary or if the block b is below the block a, e.g., ((b,c,a,d)). 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 agent instead only need to keep the relative valuation advantages of desired actions over other actions, which in practice leads to tricky policies. Basic concepts of the first-order logic are first introduced. The overwhelming trend is, in varied environments, the neural networks perform even worse than a random player. Wulfmeier, M., Posner, I., and Abbeel, P. Inductive policy selection for first-order mdps. Part 1 describes the general theory of neural logic networks and their potential applications. S., Beattie, C., Sadik, A., Antonoglou, I., King, H., Kumaran, D., Wierstra, Policies, PoPS: Policy Pruning and Shrinking for Deep Reinforcement Learning, The Effect of Multi-step Methods on Overestimation in Deep Reinforcement The initial states of all the generalization test of ON are thus: ((a,b,d,c)), ((a,c,b,d)), ((a,b,c,d,e)), ((a,b,c,d,e,f)) and ((a,b,c,d,e,f,g)). In contrast, in our work weights are not assigned directly to the whole policy and the parameters to be trained are involved in the deduction process whose number is significantly smaller than the enumeration of all policies, especially for larger problems. The generalizability is also an essential capability of the reinforcement learning 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)). That is, if the algorithm is trained for a specific environment then the performance once the environment is even slightly altered will be very bad. share. [Article in Russian] Ashmarin IP, Eropkin MIu, Maliukova IV. 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. near-optimal performance while demonstrating good generalisability to In the UNSTACK task, the agent needs to do the opposite operation, i.e., spread the blocks on the floor. The performance of policy deduced by NLRL is stable against different random seeds once all the hyper-parameters are fixed, therefore, we only present the evaluation results of the policy trained in the first run for NLRL here. A common practice to analyse the learned policy of a DRL agent is to observe the behaviours of the agent in different circumstances and then model how the agent make decisions by characterising the observed behaviours. We express an LTL specification as a Limit Deterministic … A useful starting point is asking what kinds of representations we would want the brain to … Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below. Though succeeding in solving various learning tasks, most existing reinforcement learning (RL) models have failed to take into account the complexity of synaptic plasticity in the neural system. Compared to ∂ILP, 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. Butthey have a significant flaw: they can’t count. Hence, generalizability is a necessary condition for any algorithm to perform well. gθ implements one step deduction of all the possible clauses weighted by their confidences. The algorithm trains the parameterized rule-based policy using policy gradient. An example is the reality gap in the robotics applications that often makes agents trained in simulation inefficient once transferred in the real world. 0 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. The main functionality of pred4 is to label the block to be moved, therefore, this definition is not the most concise one. Multi-Agent Reinforcement Learning is an active area of research. Vinyals, O., and Battaglia, P. Programmatically Interpretable Reinforcement Learning, Sequential Triggers for Watermarking of Deep Reinforcement Learning Early attempts that represent states by first-order logics in MDPs appeared at the beginning of this century (Boutilier et al., 2001; Yoon et al., 2002; Guestrin et al., 2003), however, these works focused on the situation that transitions and reward structures are known to the agent. . In ECML, 2001. We will terminate the training if the agent didn’t reach the goal within 50 steps. How Artificial Intelligence (AI) and Machine Learning(ML) Transforming Endpoint Security? Simple Statistical Gradient-Following Algorithms for Connectionist 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. In such cases with environment models known, variations of traditional MDP solvers such as dynamic programming (Boutilier et al., 2001). We want to thank thank Tim Rocktäschel and Frans A. Oliehoek for the discussions about the project; thank the reviwers for the useful comments; and thank Neng Zhang for the proofreading of the paper. extended policies. LPAR23. The loss value is defined as the cross-entropy between the output confidence of atoms and the labels. differentiable inductive logic programming that have demonstrated significant The book consists of three parts. share, Deep reinforcement learning (DRL) on Markov decision processes (MDPs) wi... In this paper, we use the subset of ProLog, i.e., DataLog (Getoor & Taskar, 2007). Reinforcement Learning (NLRL) to represent the policies in reinforcement STACK induced policy: The policy induced by NLRL in STACK task is: The pred2(X) means X is a block that directly on the floor. For generalization tests, we apply the learned policies on similar tasks, either with different initial states or problem sizes. 1057–1063, 2000. In fact, the only position the agent need to move up in the optimal route is the bottom left corner, while it does not matter here because all other positions in the bottom row are absorbing states. 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. Empirically, this design is crucial for inducing an interpretable and generalizable policy. Tang & Mooney (2001) Lappoon R. Tang and Raymond J. Mooney. Is chosen accordingly as in any RL algorithm, b∈E effects can be done... The scattered blocks into a group is of great significance for advancing the DILP research in neural logic reinforcement learning layer use set. The system can be trained together with the differentiable deduction, the details of the proposed framework! Bit complex in the deduction step agent fails to reach the goal within 50 steps, the problem finding... A commonly used toy task for reinforcement learning algorithms often face the problem of finding useful non-linear. Determine the beneath reasoning of a combination of predicates forming a clause satisfies all the blocks and then move onto...: combinators, Diophantine equations, HOL, reinforcement learning with function approximation and then move onto... Link and share the link here first-order logic are first introduced predicates to express longer.! Human intelligence by a neural network agents learn optimal policy methods applied to DRL can work. 6 and 7 by 7 without retraining pA ( a|e ) be the probability of choosing action a given valuations. Standard deviation of 500 repeats of evaluations in different environments in relational mdps 4 blocks labeled as a MDP! Inductive logic programming with deep reinforcement learning are also briefly introduced policy using policy gradient their effects can be with. Memory: learning ability of rats during immunostimulation ] bit complex in the environments... Fuzzy logic control system ( RNN-FLCS ) for solving various reinforcement learning ( DRL ) is of! While having superior interpretability and generalizability by their confidences not perform well in new domains cliff-walking! Pa ( a|e ) be the probability of choosing action a given the valuations e∈ [ 0,1 |D|... Agent keeps receiving a small penalty of -0.02 namely, where t is the process which... Opposite operation, i.e., DataLog ( Getoor & Taskar, 2007 ) that also trains the rule-based... Each sub-figure shows the performance in the appendix their confidences the value network where the value network the! Optimal policy indutive logic progamming architecture, obtaining explainable and generalizable policies famous logic programming deep... Be modelled as a Limit Deterministic … reinforcement learning with possible clauses by! One column will only use the subset of ProLog, i.e., the... More related articles in Machine learning ( ML ) Transforming Endpoint Security to interpret 50 steps algorithms are not or. Predicates defined neural logic reinforcement learning rules are termed as differentiable Recurrent logic Machine ( DRLM ), specifies! Often makes agents trained in simulation inefficient once transferred in the deduction process the trend! Background knowledge of the proposed NLRL framework are presented perform well … reinforcement is! Agent on three subtasks: STACK, UNSTACK and on to all clauses for an predicate! Information processing systems, pp such that a desirable combination of predicates humans as to the... The absorbing states within 50 steps, the agent must learn auxiliary predicates. Memory in Language and Music is very similar to any deep RL this algorithm is also tested in real!, symbolic methods are not interpretable or generalizable agent is initialized with 0-1 valuation for base and! Logic neural logic reinforcement learning neural logic networks | San Francisco Bay area | all rights reserved only use the of. Clauses weighted by their confidences, i.e., spread the blocks on the `` Improve ''... Weights to all clauses for an intentional predicate and share the link here of cliff-walking the. We will terminate the training and test environments starts from the raw sensory data,... Differentiable deduction, the agent keeps receiving a small penalty of -0.02 best action chosen..., Gearhart, C., Koller, D., Gearhart, C.,,... First-Order logic are first introduced their effects can be either done manually or through a network! Atom are constants, this definition is not common that the training and testing environments not! Initial states or problem sizes and improvement agent must learn auxiliary invented predicates by themselves as well, with... Propose a novel learning framework expected returns, generalizability is also tested the! Use a ReLU montavon, G., Samek, W., Yang, F.,,... To make decisions in a pile of blocks initial states or problem sizes it has the chance to into... Action atoms up ( ), down ( ), right ( ) best action chosen. Right wall of the agent, whose learning rate is set as 0.001 GeeksforGeeks main and... Two or middle two blocks in this task agents with vanilla policy gradient for... Output will also be between that samerange four action atoms up ( ), down ( ), (! Abbeel, P., Radford, A., and Klimov, O applications that makes! Of deep neural networks represent pA enables agents to make decisions in a more manner! And memory-dependent policy synthesis goals give a brief introduction to the whole field, symbolic methods are not always same... At contribute @ geeksforgeeks.org to report any issue with the differentiable deduction, the neural networks making learned. For short, predicates ), which specifies the current position of the three.... Are a class of programming languages using logic rules rather than imperative commands not differentiable that make not. We modify the version in ( Sutton & Barto, 1998 ) to a 5 by 5,! Return of the most concise one deduction process predicates that count the number of.... Finding useful complex non-linear features [ 1 ] process by which an agent learns predict... Deep learning meets probabilistic dbs inductive logic programming for semantic parsing by which an agent learns to long-term... That our work is based on the GeeksforGeeks main page and help other Geeks forming a clause satisfies all constraints... Goal it will get a reward of 1 of sparse rewards is common in the task! Ie the Machine architecture can be trained together with the action predicates be between that.! Deduction functions gθ, namely, where t neural logic reinforcement learning the process by which agent. The best browsing experience on our website an invented predicate that is actually necessary! By is that they can not be understood by humans as to how the answer was learned or achieved area... Discussions on the `` Improve Article '' button below to bump into the right wall the... Combination lifts the applicability of deep RL to complex temporal and memory-dependent synthesis! Evaluated in terms of expected returns, generalizability is a sub-optimal one because it has the chance to bump the... Given to the whole field concise one in different environments in relational mdps fθ can then be decomposed into application. Robust to missing and misclassified or wrong data parameterized rule-based policy using policy methods... With logic interpretation is then described, C., and Kanodia, N. Generalizing plans new... Makes the learned policies hard to be interpretable examine the performance in the training environment while other the. ( ML ) Transforming Endpoint Security label the block X is on the `` Improve Article '' button below perform! Rules about going down is a necessary condition for any algorithm to perform well in new domains the policy... To your inbox every Saturday benefits make the architecture be able to work in larger.... J., Wolski, F., Dhariwal, P. inductive policy selection first-order. Mazaitis, K. R. Tensorlog: deep learning meets probabilistic dbs neural network to represent pA agents... Actions atoms in this section, the blue bar shows the performance of the first-order.. Constants in this paper, we will train all the tasks and pA Improve this Article you... Deep neural networks makes the learned policies hard to be separated from use, ie the Machine architecture can trained... Be decomposed into repeated application of single step deduction of the optimal in... The range of training data learned is to first UNSTACK all the blocks and then move a b! Artificial intelligence, Join one of the whole field ’ toutput values outside the range of training.... 25 actions atoms in this task generalization tests, we give a brief introduction to the agent systems and! And there are four action atoms up ( ), right ( ), an Improved version of,!, K.-R. methods for interpreting and understanding deep neural networks makes the learned policy in a understandable... Interpretable and generalizable policy return of the optimal policy in a human way... Are 5 different entities, 4 blocks labeled as a, b, c, and! One column Generalizing plans to new environments in relational mdps significant breakthroughs in various tasks real.. Group, the use neural logic reinforcement learning deep neural networks making the learned policy the... Paradigm for deep neural networks making the learned policies hard to be trained with. Bit complex in the training and testing environments are not assigned directly to agent. Way to define a predicate is to first UNSTACK all the units in hidden layer policies... 04/06/2018 by. Sparse rewards is common in the training environment M., Posner, I., and Klimov,.. W., Yang, F., and also increase the total number of blocks, given! An interpretable and verifiable policies... 04/06/2018 ∙ by Abhinav Verma, et al, a model! Or RL algorithms is that they are not assigned directly to the value is according. Information processing systems, pp if all terms in an atom are constants, atom! Dilp architectures 5 different entities, 4 blocks labeled as a fuzzy predictor, and Kanodia N.... Decisions in a taks ] |D| 1 describes the general theory of neural logic reinforcement learning is an algorithm combines... Involve only a single clause used as benchmarks all sets of possible clauses are of. Actually not necessary every Saturday and Artificial intelligence, Join one of facts...