Patent Publication Number: US-2023143937-A1

Title: Reinforcement learning with inductive logic programming

Description:
BACKGROUND 
     The present invention generally relates to machine learning systems, and, more particularly, to reinforcement learning systems with safety constraints. 
     While reinforcement learning can be effectively used to train interactions within a predetermined environment, systems trained with reinforcement learning may have poor performance in environments that were not used for training. In applications where safety is a concern, such poor performance can translate into dangerous operating conditions. 
     SUMMARY 
     A method for training a model includes learning Markov decision processes using reinforcement learning in respective training environments. Logic rules are extracted from the Markov decision processes. T reward logic neural network (LNN) and a safety LNN are trained using the logic rules extracted from the Markov decision processes. The reward LNN and the safety LNN each take a state-action pair as an input and output a corresponding score for the state-action pair. 
     A method for automated motion includes determining a state of an environment using a sensor on a vehicle. A proposed action is determined, based on the state, using a reward LNN that generates a reward score based on a state-action pair. It is determined that the proposed action is safe, using a safety LNN that generates a safety score based on the state-action pair. The proposed action is automatically performed on the vehicle. 
     A system for automated motion includes a sensor that collects state information about an environment, a driving system that performs actions in a vehicle, a hardware processor, and a memory that stores a computer program. When executed by the hardware processor, the computer program causes the hardware processor to determine a proposed action, based on the state information, using a reward LNN that generates a reward score based on a state-action pair, to determine that the proposed action is safe, using a safety LNN that generates a safety score based on the state-action pair, and to automatically perform the proposed action using the driving system. 
     These and other features and advantages will become apparent from the following detailed description of illustrative embodiments thereof, which is to be read in connection with the accompanying drawings. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The following description will provide details of preferred embodiments with reference to the following figures wherein: 
         FIG.  1    is a diagram of a vehicle with an automated driving system, in accordance with an embodiment of the present invention; 
         FIG.  2    is a diagram of an exemplary training environment for an automated driving vehicle, in accordance with an embodiment of the present invention; 
         FIG.  3    is a block/flow diagram of a method for training an automated driving model using inductive logic programming, in accordance with an embodiment of the present invention; 
         FIG.  4    is a block/flow diagram of a method for performing automated actions using a constrained Markov decision process (CMDP) model, based on a reward logic neural network (LNN) and a safety LNN, in accordance with an embodiment of the present invention; 
         FIG.  5    is a block/flow diagram of a method for extracting logic rules from sub-CMDPs, in accordance with an embodiment of the present invention; 
         FIG.  6    is a block diagram of a computing device that can be used to perform model learning and automated driving, in accordance with an embodiment of the present invention; 
         FIG.  7    is a block diagram of reinforcement learning with inductive logic programming for learning a model, in accordance with an embodiment of the present invention; 
         FIG.  8    is a diagram of a neural network architecture, in accordance with an embodiment of the present invention; 
         FIG.  9    is a diagram of a deep neural network architecture, in accordance with an embodiment of the present invention; 
         FIG.  10    depicts a cloud computing environment according to an embodiment of the present invention; and 
         FIG.  11    depicts abstraction model layers according to an embodiment of the present invention. 
     
    
    
     DETAILED DESCRIPTION 
     To help reinforcement learning systems generalize from the environments that they were trained into new environments, inductive logic programming can be used to extract rules from trained models. In addition, a safety constraint may be implemented that limits actions taken by the reinforcement learning system to those actions which are predicted to have a safe outcome. Two models may thus be trained using the inductive logic programming—one that maximizes a reward value and one that imposes a safety constraint. 
     Referring now to  FIG.  1   , a vehicle  100  with an automated driving system  102  is shown. The automated driving system  102  is used herein as a description of a potential application for a reinforcement learning system, but it should be understood that any appropriate system that operates within an environment can be used instead. 
     The automated driving system  102  interfaces with various systems in the vehicle  100 , including acceleration/throttle systems, braking systems, and steering systems. The automated driving system  102  can furthermore interface with other vehicle systems, for example engaging or disengaging systems such as traction control, four-wheel drive, global positioning satellite receiving, and any other systems relating to navigation and control for the vehicle  100 . The automated driving system  102  can be fully autonomous, accepting no driver input, or can be partially autonomous, where only some vehicle systems are controlled or where control can be overridden by a driver. 
     The systems of the vehicle  100  are limited in terms of their ability to change the vehicle&#39;s state. For example, the acceleration and braking systems are limited in the acceleration they can exert on the vehicle  100 , and the steering systems are limited in their turning radius and response speed. These different factors dictate how the vehicle  100  can move on the road within a given time period, providing the range of possible actions that the automated driving system  102  can take. 
     It should be understood that the term “vehicle” is used herein to refer to many different kinds of vehicles, including passenger vehicles and cargo vehicles. It should further be understood that the term “vehicle” is not limited to automobiles and other motorized conveyances, but can also include human-powered vehicles, such as bicycles. 
     As the vehicle  100  navigates on a roadway, it will encounter a variety of obstacles. Some of these obstacles are fixed in place, such as traffic control devices, while others may be in motion, such as road debris and other vehicles. The vehicle  100  includes one or more sensors  104  that sense the presence of obstacles on the road. The sensors  104  have a certain range, within which they are able to reliably detect the presence of an obstacle. The information from the sensors  104  may be provided as input to the automated driving system  102 , which uses them to identify the present state of the vehicle  100  and the environment that it operates within. 
     Referring now to  FIG.  2   , an example of reinforcement learning is shown. In this example, a vehicle  100  is given the task of navigating a course  200  along a path  202 . In this example, the vehicle  100  may be understood as a robot or a self-driving vehicle, but it should be understood that the present principles apply to any appropriate reinforcement learning application. The vehicle  100  can turn to the left or right to stay within the path  202 . The vehicle  100  succeeds at its task if it reaches the end of the path  202 , and fails at its task if it intersects with the borders of the path  202  before reaching the end. 
     In reinforcement learning, the success and failure of the task can be used to inform an automatic driving system  102  within the vehicle  100 . The automatic driving system  102  may update its policies to reflect the reward information, for example making the vehicle  100  less likely to perform actions that tend to result in failure, and more likely to perform actions that tend to result in success. In some cases, the reward value may be determined based on a time to reach the destination. 
     A variety of different trials  204  are shown as dotted lines. As can be seen many such trials  204  may result in failure. These trials  204  may represent unsafe driving conditions. A successful trial  206  is shown that reaches the end of the path  202  without an unsafe condition occurring. Thus, two different functions may be considered: a reward function that judges successful completion of the path and that may be used to compare successful paths  206  in accordance with some criteria (e.g., speed of completion), and a safety function that determines whether a given meets safety criteria. 
     During training of the automated driving system  102 , multiple such environments  100  may be used. Reinforcement learning will learn how to handle each of these environments in a safe and efficient way. However, when using the trained system in new environments, which may have unfamiliar arrangements of obstacles and hazards, the automated driving system  102  may not perform efficiently or safely. 
     Each training environment may be used to train a respective sub-constrained Markov decision process (CMDP), which may be combined into a general CMDP. A Markov decision process may be used as a reinforcement learning model, with a reward function Q r (s, a) that takes a present state s of the environment  200  and the vehicle  100  and an action a that the vehicle  100  may take within the environment  200 . A new state s′ is probabilistically generated, and a reward value is determined for the action. Multiple such actions a may be evaluated, and a best action may be selected in accordance with the reward and the new state s′. 
     In a CMDP, the Markov decision process is further constrained by a second function, in this case Q g (s, a), which represents a safety criterion. During operation, the highest-reward action a 1  may be determined using the reward function Q r (s, a 1 ). This action may then be evaluated using the safety function Q g (s, a 1 ) to determine a safety prediction. If this safety prediction falls below a threshold value, then the action a 1  is rejected, and a next-best action a 2  is evaluated for safety. This process may continue until an action a g  is found that can satisfy the safety threshold. The action a g  may then be performed by the automated driving system  102  to reach a new state s′. 
     The CMDP may be represented as: 
         =&lt; ,  ,  , r, g, b, γ, ρ&gt;
 
     where   is a set of states {s},   is a set of actions {a},  (s′|s, a) is a state transition function, r:  × →[0,1] is a bounded reward function, g:  × →[0,1] is a bounded safety function, b ∈   is a threshold for the safety constraint, γ ∈ [0,1) is a discount factor, and ρ ∈   is an initial state distribution. A CMDP with a logical representation may be expressed as: 
           + = ∪&lt; ,  &gt;
 
     In particular, the term p s :  →  is a state encoder that maps states s to a set of atoms  , and the term  :  →  is an action encoder that maps actions a to a set of atoms  . For all (s, a) ∈  × , the logical representation of a reward function  r : [0, 1] ×[0,1] →[0,1] and the safety function  g : [0,1] ×[0,1] →[0,1] can be respectively represented as: 
           g   ( ( s ),  ( a ))= g ( s, a ) 
         r ( ( s ),  ( a ))= r ( s, a ) 
     which include the following logical operations: ∧ (AND), ∨ (OR), ¬ (NOT), and → (IMPLY). 
     Each environment  200  that is used for training the automated driving system  102  may generate a respective sub-CMDP. The number of sub-CMDPs is L and subsets    i (i=1, 2, . . . , L) are the subsets of the states   that correspond to each respective sub-CMDP. The sub-CMDP may be expressed as    i   + =&lt;   i ,  ,    i , r i , g i , b, γ, ρ,  ,  &gt;, where    i , r i , and g i  are respectively the restrictions of the original  , r, g to the domain    i × . 
     The following optimization problem is used to determine actions in a target environment, which may not have been seen during training: 
     
       
         
           
             
               
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     where V r   π  is a value function for a policy π and s 0  is a state. 
     Referring now to  FIG.  3   , a method of training a machine learning system is shown. Block  302  begins by training sub-CMDPs on respective training environments. This training may be performed using any appropriate reinforcement learning implementation, and may generate respective policies for each training environment. Block  304  may form a target CMDP that can be used in a variety of different environments by connecting the sub-CMDPs into a single hierarchical structure that will select a most appropriate environment&#39;s policy when presented with a previously unseen target environment. 
     Block  306  extracts rules from the trained sub-CMDPs. As will be described in greater detail below, the rules may be extracted using inductive logic programming, such as by using logical neural network (LNN) models. The input to block  306  may include state-action pairs, e.g., ( (s),  (a)), and the output may be the functions Q r   i (s, a) and q g   i (s, a) for each environment i. The rules may optionally be inspected and modified by a human operator in block  308 . The rules from the various sub-CMDPs can be concatenated into a total inductive logic programming reward function, 
     
       
         
           
             
               
                 
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     that selects the minimum safety score from the various sub-CMDPs. At block  310 , the reward function Q r   ILP (s, a) may be combined with the target CMDP from block  304 , Q(a, s), to generate an action proposal: 
     
       
         
           
             
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     Referring now to  FIG.  4   , a method of using a trained machine learning system is shown. Block  402  determines the current state s of the agent and the environment. Following the vehicular example above, the state s may include information about the vehicle  100 , such as location, speed, and direction, and may further include information about the environment  200 , such as detected obstacles, pedestrians, and other vehicles, road conditions, and weather conditions. Block  404  then determines an action proposal 
     
       
         
           
             
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     using the machine learning model described above. This first action proposal will represent the action in   that generates the highest combined reward value. For example, this may be the action that covers the greatest distance toward a destination. 
     Block  406  then calculates a value for the safety function Q g   ILP (a 1 , s), using the action proposal. If this value is not above a predetermined threshold (e.g., Q g   ILP ≥b), then block  408  rejects the action proposal a 1 . Processing returns to block  404 , with a new action being proposed from the set of actions, excluding a 1 : 
     
       
         
           
             
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     This process may be repeated any number of times, until an action proposal a n  passes the safety threshold test of block  406 . When this occurs, block  410  performs the action a n  within the environment. Processing may then return to block  402 , to determine the current state that resulted from the action a n . 
     Referring now to  FIG.  5   , additional information on extracting the rules in block  306  is shown. Block  502  collects state-action pairs from trained the sub-CMDPs. For example, a dataset may be generated as (s, a, Q r   i (s, a), Q g   i (s, a)) for all i. Block  504  then trains ILP models to learn the symbolic relations that can be extracted from these state-action pairs. It is specifically contemplated that the ILP models may be implemented as LNNs. 
     As noted above, the LNNs may include AND, OR, NOT, and IMPLY gates. Training of LNNs is done in a manner similar training any other neural network. A loss function for each LNN is defined as a logical contradiction. The following pseudo-code illustrates an exemplary process for training the LNNs: 
     for I=1, 2, . . . do 
     generate random sub-CMDPs by extracting internal state spaces    i    
       ←logical representation of state in    i  for sub-CMDP i 
     Reward LNN i ←input: ( ,  ), output: Q r    
     Safety LNN i ←input: ( , ), output: Q g    
     In general, an LNN may be implemented as a form of recurrent neural network with a one-to-one correspondence to logical formulae in a system of weighted, real-valued logic. Evaluation of the LNN performs a logical inference. When training the LNN, a loss function penalizes logical contradictions. The LNN training process therefore tends to generate a logically consistent system from a training dataset of logic propositions. 
     For example, the state-action pairs of the sub-CMDPs can be expressed as logical propositions, such as A ∧ B→C, with A and B representing features of a state s and with C representing an action a. In this example, when the state includes the conditions A and B at the same time (e.g., a speed above 50 mpg and a stopped car ahead), then the sub-CMDP would perform the action C (e.g., applying brakes with sufficient force to prevent a collision). Training the LNNs seeks to create a system that will evaluate an input state-action pair in accordance with a goal (e.g., maximizing reward or safety) while maintaining logical consistency of the system. 
       FIG.  6    is a block diagram showing an exemplary computing device  600 , in accordance with an embodiment of the present invention. The computing device  600  is configured to generalize from reinforcement learning models to perform a function, such as automated driving. 
     The computing device  600  may be embodied as any type of computation or computer device capable of performing the functions described herein, including, without limitation, a computer, a server, a rack based server, a blade server, a workstation, a desktop computer, a laptop computer, a notebook computer, a tablet computer, a mobile computing device, a wearable computing device, a network appliance, a web appliance, a distributed computing system, a processor-based system, and/or a consumer electronic device. Additionally or alternatively, the computing device  600  may be embodied as a one or more compute sleds, memory sleds, or other racks, sleds, computing chassis, or other components of a physically disaggregated computing device. 
     As shown in  FIG.  6   , the computing device  600  illustratively includes the processor  610 , an input/output subsystem  620 , a memory  630 , a data storage device  640 , and a communication subsystem  650 , and/or other components and devices commonly found in a server or similar computing device. The computing device  600  may include other or additional components, such as those commonly found in a server computer (e.g., various input/output devices), in other embodiments. Additionally, in some embodiments, one or more of the illustrative components may be incorporated in, or otherwise form a portion of, another component. For example, the memory  630 , or portions thereof, may be incorporated in the processor  610  in some embodiments. 
     The processor  610  may be embodied as any type of processor capable of performing the functions described herein. The processor  610  may be embodied as a single processor, multiple processors, a Central Processing Unit(s) (CPU(s)), a Graphics Processing Unit(s) (GPU(s)), a single or multi-core processor(s), a digital signal processor(s), a microcontroller(s), or other processor(s) or processing/controlling circuit(s). 
     The memory  630  may be embodied as any type of volatile or non-volatile memory or data storage capable of performing the functions described herein. In operation, the memory  630  may store various data and software used during operation of the computing device  600 , such as operating systems, applications, programs, libraries, and drivers. The memory  630  is communicatively coupled to the processor  610  via the I/O subsystem  620 , which may be embodied as circuitry and/or components to facilitate input/output operations with the processor  610 , the memory  630 , and other components of the computing device  600 . For example, the I/O subsystem  620  may be embodied as, or otherwise include, memory controller hubs, input/output control hubs, platform controller hubs, integrated control circuitry, firmware devices, communication links (e.g., point-to-point links, bus links, wires, cables, light guides, printed circuit board traces, etc.), and/or other components and subsystems to facilitate the input/output operations. In some embodiments, the I/O subsystem  620  may form a portion of a system-on-a-chip (SOC) and be incorporated, along with the processor  610 , the memory  630 , and other components of the computing device  600 , on a single integrated circuit chip. 
     The data storage device  640  may be embodied as any type of device or devices configured for short-term or long-term storage of data such as, for example, memory devices and circuits, memory cards, hard disk drives, solid state drives, or other data storage devices. The data storage device  640  can store program code  640 A for reinforcement learning with inductive logic programming and program code  640 B for automated driving. The communication subsystem  650  of the computing device  600  may be embodied as any network interface controller or other communication circuit, device, or collection thereof, capable of enabling communications between the computing device  600  and other remote devices over a network. The communication subsystem  650  may be configured to use any one or more communication technology (e.g., wired or wireless communications) and associated protocols (e.g., Ethernet, InfiniBand®, Bluetooth®, Wi-Fi®, WiMAX, etc.) to effect such communication. 
     As shown, the computing device  600  may also include one or more peripheral devices  660 . The peripheral devices  660  may include any number of additional input/output devices, interface devices, and/or other peripheral devices. For example, in some embodiments, the peripheral devices  660  may include a display, touch screen, graphics circuitry, keyboard, mouse, speaker system, microphone, network interface, and/or other input/output devices, interface devices, and/or peripheral devices. 
     Of course, the computing device  600  may also include other elements (not shown), as readily contemplated by one of skill in the art, as well as omit certain elements. For example, various other sensors, input devices, and/or output devices can be included in computing device  600 , depending upon the particular implementation of the same, as readily understood by one of ordinary skill in the art. For example, various types of wireless and/or wired input and/or output devices can be used. Moreover, additional processors, controllers, memories, and so forth, in various configurations can also be utilized. Further, in another embodiment, a cloud configuration can be used (e.g., see  FIGS.  10 - 11   ). These and other variations of the processing system  600  are readily contemplated by one of ordinary skill in the art given the teachings of the present invention provided herein. 
     Referring now to  FIG.  7   , additional detail on the reinforcement learning with ILP  640 A is shown. Reinforcement learning  702  uses training environments  704  to generate sub-CMDPs  706 . For example, each sub-CMDP  706  may correspond to a different respective training environment  704 . LNN training  708  extracts state-action pairs from the sub-CMDPs  706  and uses them to train LNNs, including a reward LNN  710  and a safety LNN  712 . These LNNs may be used by other systems, such as automated driving  640 B, to inform the performance of actions in an automated system. As noted above, the LNNs may be implemented as a form of recurrent neural network (RNN), with a one-to-one correspondence to a set of logical formulae. 
     RNNs may be used to process sequences of information, such as an ordered series of feature vectors. This makes RNNs well suited to text processing and speech recognition, where information is naturally sequential. Each neuron in an RNN receives two inputs: a new input from a previous layer, and a previous input from the current layer. An RNN layer thereby maintains information about the state of the sequence from one input to the next. 
     In an LNN, neural activation functions may be constrained to the logical operations described above, and results may be expressed in terms of bounds on truth values, distinguishing between known states, approximately unknown states, unknown states, and contradictory states. An LNN may be expressed as a graph of syntax trees for all represented formulae, connected to one another via neurons for each proposition. Thus, there may be one neuron for each logical operation occurring in each formula, and one neuron for each unique proposition occurring in any formula. 
     Referring now to  FIG.  8   , an exemplary neural network architecture is shown. In layered neural networks, nodes are arranged in the form of layers. A simple neural network has an input layer  820  of source nodes  822 , a single computation layer  830  having one or more computation nodes  832  that also act as output nodes, where there is a single node  832  for each possible category into which the input example could be classified. An input layer  820  can have a number of source nodes  822  equal to the number of data values  812  in the input data  810 . The data values  812  in the input data  810  can be represented as a column vector. Each computational node  830  in the computation layer generates a linear combination of weighted values from the input data  810  fed into input nodes  820 , and applies a non-linear activation function that is differentiable to the sum. The simple neural network can perform classification on linearly separable examples (e.g., patterns). 
     Referring now to  FIG.  9   , a deep neural network architecture is shown. A deep neural network, also referred to as a multilayer perceptron, has an input layer  820  of source nodes  822 , one or more computation layer(s)  830  having one or more computation nodes  832 , and an output layer  840 , where there is a single output node  842  for each possible category into which the input example could be classified. An input layer  820  can have a number of source nodes  822  equal to the number of data values  812  in the input data  810 . The computation nodes  832  in the computation layer(s)  830  can also be referred to as hidden layers because they are between the source nodes  822  and output node(s)  842  and not directly observed. Each node  832 ,  842  in a computation layer generates a linear combination of weighted values from the values output from the nodes in a previous layer, and applies a non-linear activation function that is differentiable to the sum. The weights applied to the value from each previous node can be denoted, for example, by w 1 , w 2 , w n−1  w n . The output layer provides the overall response of the network to the inputted data. A deep neural network can be fully connected, where each node in a computational layer is connected to all other nodes in the previous layer. If links between nodes are missing the network is referred to as partially connected. 
     Training a deep neural network can involve two phases, a forward phase where the weights of each node are fixed and the input propagates through the network, and a backwards phase where an error value is propagated backwards through the network. 
     The computation nodes  832  in the one or more computation (hidden) layer(s)  830  perform a nonlinear transformation on the input data  812  that generates a feature space. The feature space the classes or categories may be more easily separated than in the original data space. 
     To train a neural network, training data can be divided into a training set and a testing set. The training data includes pairs of an input and a known output. During training, the inputs of the training set are fed into the neural network using feed-forward propagation. After each input, the output of the neural network is compared to the respective known output. Discrepancies between the output of the neural network and the known output that is associated with that particular input are used to generate an error value, which may be backpropagated through the neural network, after which the weight values of the neural network may be updated. This process continues until the pairs in the training set are exhausted. 
     After the training has been completed, the neural network may be tested against the testing set, to ensure that the training has not resulted in overfitting. If the neural network can generalize to new inputs, beyond those which it was already trained on, then it is ready for use. If the neural network does not accurately reproduce the known outputs of the testing set, then additional training data may be needed, or hyperparameters of the neural network may need to be adjusted. 
     The present invention may be a system, a method, and/or a computer program product at any possible technical detail level of integration. The computer program product may include a computer readable storage medium (or media) having computer readable program instructions thereon for causing a processor to carry out aspects of the present invention. 
     The computer readable storage medium can be a tangible device that can retain and store instructions for use by an instruction execution device. The computer readable storage medium may be, for example, but is not limited to, an electronic storage device, a magnetic storage device, an optical storage device, an electromagnetic storage device, a semiconductor storage device, or any suitable combination of the foregoing. A non-exhaustive list of more specific examples of the computer readable storage medium includes the following: a portable computer diskette, a hard disk, a random access memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or Flash memory), a static random access memory (SRAM), a portable compact disc read-only memory (CD-ROM), a digital versatile disk (DVD), a memory stick, a floppy disk, a mechanically encoded device such as punch-cards or raised structures in a groove having instructions recorded thereon, and any suitable combination of the foregoing. A computer readable storage medium, as used herein, is not to be construed as being transitory signals per se, such as radio waves or other freely propagating electromagnetic waves, electromagnetic waves propagating through a waveguide or other transmission media (e.g., light pulses passing through a fiber-optic cable), or electrical signals transmitted through a wire. 
     Computer readable program instructions described herein can be downloaded to respective computing/processing devices from a computer readable storage medium or to an external computer or external storage device via a network, for example, the Internet, a local area network, a wide area network and/or a wireless network. The network may comprise copper transmission cables, optical transmission fibers, wireless transmission, routers, firewalls, switches, gateway computers and/or edge servers. A network adapter card or network interface in each computing/processing device receives computer readable program instructions from the network and forwards the computer readable program instructions for storage in a computer readable storage medium within the respective computing/processing device. 
     Computer readable program instructions for carrying out operations of the present invention may be assembler instructions, instruction-set-architecture (ISA) instructions, machine instructions, machine dependent instructions, microcode, firmware instructions, state-setting data, configuration data for integrated circuitry, or either source code or object code written in any combination of one or more programming languages, including an object oriented programming language such as Smalltalk, C++, or the like, and procedural programming languages, such as the “C” programming language or similar programming languages. The computer readable program instructions may execute entirely on the user&#39;s computer, partly on the user&#39;s computer, as a stand-alone software package, partly on the user&#39;s computer and partly on a remote computer or entirely on the remote computer or server. In the latter scenario, the remote computer may be connected to the user&#39;s computer through any type of network, including a local area network (LAN) or a wide area network (WAN), or the connection may be made to an external computer (for example, through the Internet using an Internet Service Provider). In some embodiments, electronic circuitry including, for example, programmable logic circuitry, field-programmable gate arrays (FPGA), or programmable logic arrays (PLA) may execute the computer readable program instructions by utilizing state information of the computer readable program instructions to personalize the electronic circuitry, in order to perform aspects of the present invention. 
     Aspects of the present invention are described herein with reference to flowchart illustrations and/or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and/or block diagrams, and combinations of blocks in the flowchart illustrations and/or block diagrams, can be implemented by computer readable program instructions. 
     These computer readable program instructions may be provided to a processor of a computer, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, create means for implementing the functions/acts specified in the flowchart and/or block diagram block or blocks. These computer readable program instructions may also be stored in a computer readable storage medium that can direct a computer, a programmable data processing apparatus, and/or other devices to function in a particular manner, such that the computer readable storage medium having instructions stored therein comprises an article of manufacture including instructions which implement aspects of the function/act specified in the flowchart and/or block diagram block or blocks. 
     The computer readable program instructions may also be loaded onto a computer, other programmable data processing apparatus, or other device to cause a series of operational steps to be performed on the computer, other programmable apparatus or other device to produce a computer implemented process, such that the instructions which execute on the computer, other programmable apparatus, or other device implement the functions/acts specified in the flowchart and/or block diagram block or blocks. 
     As employed herein, the term “hardware processor subsystem” or “hardware processor” can refer to a processor, memory, software or combinations thereof that cooperate to perform one or more specific tasks. In useful embodiments, the hardware processor subsystem can include one or more data processing elements (e.g., logic circuits, processing circuits, instruction execution devices, etc.). The one or more data processing elements can be included in a central processing unit, a graphics processing unit, and/or a separate processor- or computing element-based controller (e.g., logic gates, etc.). The hardware processor subsystem can include one or more on-board memories (e.g., caches, dedicated memory arrays, read only memory, etc.). In some embodiments, the hardware processor subsystem can include one or more memories that can be on or off board or that can be dedicated for use by the hardware processor subsystem (e.g., ROM, RAM, basic input/output system (BIOS), etc.). 
     In some embodiments, the hardware processor subsystem can include and execute one or more software elements. The one or more software elements can include an operating system and/or one or more applications and/or specific code to achieve a specified result. 
     In other embodiments, the hardware processor subsystem can include dedicated, specialized circuitry that performs one or more electronic processing functions to achieve a specified result. Such circuitry can include one or more application-specific integrated circuits (ASICs), FPGAs, and/or PLAs. 
     These and other variations of a hardware processor subsystem are also contemplated in accordance with embodiments of the present invention. 
     It is to be understood that although this disclosure includes a detailed description on cloud computing, implementation of the teachings recited herein are not limited to a cloud computing environment. Rather, embodiments of the present invention are capable of being implemented in conjunction with any other type of computing environment now known or later developed. 
     Cloud computing is a model of service delivery for enabling convenient, on-demand network access to a shared pool of configurable computing resources (e.g., networks, network bandwidth, servers, processing, memory, storage, applications, virtual machines, and services) that can be rapidly provisioned and released with minimal management effort or interaction with a provider of the service. This cloud model may include at least five characteristics, at least three service models, and at least four deployment models. 
     Characteristics are as follows: 
     On-demand self-service: a cloud consumer can unilaterally provision computing capabilities, such as server time and network storage, as needed automatically without requiring human interaction with the service&#39;s provider. 
     Broad network access: capabilities are available over a network and accessed through standard mechanisms that promote use by heterogeneous thin or thick client platforms (e.g., mobile phones, laptops, and PDAs). 
     Resource pooling: the provider&#39;s computing resources are pooled to serve multiple consumers using a multi-tenant model, with different physical and virtual resources dynamically assigned and reassigned according to demand. There is a sense of location independence in that the consumer generally has no control or knowledge over the exact location of the provided resources but may be able to specify location at a higher level of abstraction (e.g., country, state, or datacenter). 
     Rapid elasticity: capabilities can be rapidly and elastically provisioned, in some cases automatically, to quickly scale out and rapidly released to quickly scale in. To the consumer, the capabilities available for provisioning often appear to be unlimited and can be purchased in any quantity at any time. 
     Measured service: cloud systems automatically control and optimize resource use by leveraging a metering capability at some level of abstraction appropriate to the type of service (e.g., storage, processing, bandwidth, and active user accounts). Resource usage can be monitored, controlled, and reported, providing transparency for both the provider and consumer of the utilized service. 
     Service Models are as follows: 
     Software as a Service (SaaS): the capability provided to the consumer is to use the provider&#39;s applications running on a cloud infrastructure. The applications are accessible from various client devices through a thin client interface such as a web browser (e.g., web-based e-mail). The consumer does not manage or control the underlying cloud infrastructure including network, servers, operating systems, storage, or even individual application capabilities, with the possible exception of limited user-specific application configuration settings. 
     Platform as a Service (PaaS): the capability provided to the consumer is to deploy onto the cloud infrastructure consumer-created or acquired applications created using programming languages and tools supported by the provider. The consumer does not manage or control the underlying cloud infrastructure including networks, servers, operating systems, or storage, but has control over the deployed applications and possibly application hosting environment configurations. 
     Infrastructure as a Service (IaaS): the capability provided to the consumer is to provision processing, storage, networks, and other fundamental computing resources where the consumer is able to deploy and run arbitrary software, which can include operating systems and applications. The consumer does not manage or control the underlying cloud infrastructure but has control over operating systems, storage, deployed applications, and possibly limited control of select networking components (e.g., host firewalls). 
     Deployment Models are as follows: 
     Private cloud: the cloud infrastructure is operated solely for an organization. It may be managed by the organization or a third party and may exist on-premises or off-premises. 
     Community cloud: the cloud infrastructure is shared by several organizations and supports a specific community that has shared concerns (e.g., mission, security requirements, policy, and compliance considerations). It may be managed by the organizations or a third party and may exist on-premises or off-premises. 
     Public cloud: the cloud infrastructure is made available to the general public or a large industry group and is owned by an organization selling cloud services. 
     Hybrid cloud: the cloud infrastructure is a composition of two or more clouds (private, community, or public) that remain unique entities but are bound together by standardized or proprietary technology that enables data and application portability (e.g., cloud bursting for load-balancing between clouds). 
     A cloud computing environment is service oriented with a focus on statelessness, low coupling, modularity, and semantic interoperability. At the heart of cloud computing is an infrastructure that includes a network of interconnected nodes. 
     Referring now to  FIG.  10   , illustrative cloud computing environment  1050  is depicted. As shown, cloud computing environment  1050  includes one or more cloud computing nodes  1010  with which local computing devices used by cloud consumers, such as, for example, personal digital assistant (PDA) or cellular telephone  1054 A, desktop computer  1054 B, laptop computer  1054 C, and/or automobile computer system  1054 N may communicate. Nodes  1010  may communicate with one another. They may be grouped (not shown) physically or virtually, in one or more networks, such as Private, Community, Public, or Hybrid clouds as described hereinabove, or a combination thereof. This allows cloud computing environment  1050  to offer infrastructure, platforms and/or software as services for which a cloud consumer does not need to maintain resources on a local computing device. It is understood that the types of computing devices  1054 A-N shown in  FIG.  10    are intended to be illustrative only and that computing nodes  1010  and cloud computing environment  1050  can communicate with any type of computerized device over any type of network and/or network addressable connection (e.g., using a web browser). 
     Referring now to  FIG.  11   , a set of functional abstraction layers provided by cloud computing environment  1150  ( FIG.  10   ) is shown. It should be understood in advance that the components, layers, and functions shown in  FIG.  11    are intended to be illustrative only and embodiments of the invention are not limited thereto. As depicted, the following layers and corresponding functions are provided: 
     Hardware and software layer  1160  includes hardware and software components. Examples of hardware components include: mainframes  1161 ; RISC (Reduced Instruction Set Computer) architecture based servers  1162 ; servers  1163 ; blade servers  1164 ; storage devices  1165 ; and networks and networking components  1166 . In some embodiments, software components include network application server software  1167  and database software  1168 . 
     Virtualization layer  1170  provides an abstraction layer from which the following examples of virtual entities may be provided: virtual servers  1171 ; virtual storage  1172 ; virtual networks  1173 , including virtual private networks; virtual applications and operating systems  1174 ; and virtual clients  1175 . 
     In one example, management layer  1180  may provide the functions described below. Resource provisioning  1181  provides dynamic procurement of computing resources and other resources that are utilized to perform tasks within the cloud computing environment. Metering and Pricing  1182  provide cost tracking as resources are utilized within the cloud computing environment, and billing or invoicing for consumption of these resources. In one example, these resources may include application software licenses. Security provides identity verification for cloud consumers and tasks, as well as protection for data and other resources. User portal  1183  provides access to the cloud computing environment for consumers and system administrators. Service level management  1184  provides cloud computing resource allocation and management such that required service levels are met. Service Level Agreement (SLA) planning and fulfillment  1185  provide pre-arrangement for, and procurement of, cloud computing resources for which a future requirement is anticipated in accordance with an SLA. 
     Workloads layer  1190  provides examples of functionality for which the cloud computing environment may be utilized. Examples of workloads and functions which may be provided from this layer include: mapping and navigation  1191 ; software development and lifecycle management  1192 ; virtual classroom education delivery  1193 ; data analytics processing  1194 ; transaction processing  1195 ; and reinforcement learning with ILP  1196 . 
     Reference in the specification to “one embodiment” or “an embodiment” of the present invention, as well as other variations thereof, means that a particular feature, structure, characteristic, and so forth described in connection with the embodiment is included in at least one embodiment of the present invention. Thus, the appearances of the phrase “in one embodiment” or “in an embodiment”, as well any other variations, appearing in various places throughout the specification are not necessarily all referring to the same embodiment. 
     It is to be appreciated that the use of any of the following “/”, “and/or”, and “at least one of”, for example, in the cases of “A/B”, “A and/or B” and “at least one of A and B”, is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of both options (A and B). As a further example, in the cases of “A, B, and/or C” and “at least one of A, B, and C”, such phrasing is intended to encompass the selection of the first listed option (A) only, or the selection of the second listed option (B) only, or the selection of the third listed option (C) only, or the selection of the first and the second listed options (A and B) only, or the selection of the first and third listed options (A and C) only, or the selection of the second and third listed options (B and C) only, or the selection of all three options (A and B and C). This may be extended, as readily apparent by one of ordinary skill in this and related arts, for as many items listed. 
     The flowchart and block diagrams in the Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of the present invention. In this regard, each block in the flowchart or block diagrams may represent a module, segment, or portion of instructions, which comprises one or more executable instructions for implementing the specified logical function(s). In some alternative implementations, the functions noted in the blocks may occur out of the order noted in the Figures. For example, two blocks shown in succession may, in fact, be accomplished as one step, executed concurrently, substantially concurrently, in a partially or wholly temporally overlapping manner, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustration, and combinations of blocks in the block diagrams and/or flowchart illustration, can be implemented by special purpose hardware-based systems that perform the specified functions or acts or carry out combinations of special purpose hardware and computer instructions. 
     Having described preferred embodiments of reinforcement learning with inductive logic programming (which are intended to be illustrative and not limiting), it is noted that modifications and variations can be made by persons skilled in the art in light of the above teachings. It is therefore to be understood that changes may be made in the particular embodiments disclosed which are within the scope of the invention as outlined by the appended claims. Having thus described aspects of the invention, with the details and particularity required by the patent laws, what is claimed and desired protected by Letters Patent is set forth in the appended claims.