Patent Publication Number: US-11042640-B2

Title: Safe-operation-constrained reinforcement-learning-based application manager

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
     This application is a continuation-in-part of application Ser. No. 16/261,253, filed Jan. 29, 2019, which claims the benefit of Provisional Application No. 62/723,388, filed Aug. 27, 2018. 
    
    
     TECHNICAL FIELD 
     The current document is directed to standalone, networked, and distributed computer systems and to system management and, in particular, to a reinforcement-learning-based application manager that may run within a variety of different environments to safely control the configuration and operational behavior of applications. 
     BACKGROUND 
     During the past seven decades, electronic computing has evolved from primitive, vacuum-tube-based computer systems, initially developed during the 1940s, to modern electronic computing systems in which large numbers of multi-processor servers, work stations, and other individual computing systems are networked together with large-capacity data-storage devices and other electronic devices to produce geographically distributed computing systems with hundreds of thousands, millions, or more components that provide enormous computational bandwidths and data-storage capacities. These large, distributed computing systems are made possible by advances in computer networking, distributed operating systems and applications, data-storage appliances, computer hardware, and software technologies. However, despite all of these advances, the rapid increase in the size and complexity of computing systems has been accompanied by numerous scaling issues and technical challenges, including technical challenges associated with communications overheads encountered in parallelizing computational tasks among multiple processors, component failures, and distributed-system management. As new distributed-computing technologies are developed, and as general hardware and software technologies continue to advance, the current trend towards ever-larger and more complex distributed computing systems appears likely to continue well into the future. 
     As the complexity of distributed computing systems has increased, the management and administration of distributed computing systems has, in turn, become increasingly complex, involving greater computational overheads and significant inefficiencies and deficiencies. In fact, many desired management-and-administration functionalities are becoming sufficiently complex to render traditional approaches to the design and implementation of automated management and administration systems impractical, from a time and cost standpoint, and even from a feasibility standpoint. Therefore, designers and developers of various types of automated management and control systems related to distributed computing systems are seeking alternative design-and-implementation methodologies, including machine-learning-based approaches. The application of machine-learning technologies to the management of complex computational environments is still in early stages, but promises to expand the practically achievable feature sets of automated administration-and-management systems, decrease development costs, and provide a basis for more effective optimization Of course, administration-and-management control systems developed for distributed computer systems can often be applied to administer and manage standalone computer systems and individual, networked computer systems. 
     SUMMARY 
     The current document is directed to a safe-operation-constrained reinforcement-learning-based application manager that can be deployed in various different computational environments, without extensive manual modification and interface development, to manage the computational environments with respect to one or more reward-specified goals. Control actions undertaken by the safe-operation-constrained reinforcement-learning-based application manager are constrained, by stored action filters, to constrain state/action-space exploration by the safe-operation-constrained reinforcement-learning-based application manager to safe actions and thus prevent deleterious impact to the managed computational environment. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         FIG. 1  provides a general architectural diagram for various types of computers. 
         FIG. 2  illustrates an Internet-connected distributed computer system. 
         FIG. 3  illustrates cloud computing. In the recently developed cloud-computing paradigm, computing cycles and data-storage facilities are provided to organizations and individuals by cloud-computing providers. 
         FIG. 4  illustrates generalized hardware and software components of a general-purpose computer system, such as a general-purpose computer system having an architecture similar to that shown in  FIG. 1 . 
         FIGS. 5A-B  illustrate two types of virtual machine and virtual-machine execution environments. 
         FIG. 6  illustrates an OVF package. 
         FIG. 7  illustrates virtual data centers provided as an abstraction of underlying physical-data-center hardware components. 
         FIG. 8  illustrates virtual-machine components of a virtual-data-center management server and physical servers of a physical data center above which a virtual-data-center interface is provided by the virtual-data-center management server. 
         FIG. 9  illustrates a cloud-director level of abstraction. In  FIG. 9 , three different physical data centers  902 - 904  are shown below planes representing the cloud-director layer of abstraction  906 - 908 . 
         FIG. 10  illustrates virtual-cloud-connector nodes (“VCC nodes”) and a VCC server, components of a distributed system that provides multi-cloud aggregation and that includes a cloud-connector server and cloud-connector nodes that cooperate to provide services that are distributed across multiple clouds. 
         FIGS. 11A-C  illustrate an application manager. 
         FIG. 12  illustrates, at a high level of abstraction, a reinforcement-learning-based application manager controlling a computational environment, such as a cloud-computing facility. 
         FIG. 13  summarizes the reinforcement-learning-based approach to control. 
         FIGS. 14A-B  illustrate states of the environment. 
         FIG. 15  illustrates the concept of belief. 
         FIGS. 16A-B  illustrate a simple flow diagram for the universe comprising the manager and the environment in one approach to reinforcement learning. 
         FIG. 17  provides additional details about the operation of the manager, environment, and universe. 
         FIG. 18  provides a somewhat more detailed control-flow-like description of operation of the manager and environment than originally provided in  FIG. 16A . 
         FIG. 19  provides a traditional control-flow diagram for operation of the manager and environment over multiple runs. 
         FIG. 20  illustrates one approach to using reinforcement learning to generate and operate an application manager. 
         FIG. 21  illustrates an alternative view of a control trajectory comprising a sequence of executed of actions, each accompanied by a managed-environment state change. 
         FIG. 22  illustrates the potential sizes of the set of possible state/action pairs. 
         FIGS. 23A-B  illustrate the need for state/action exploration by a reinforcement-learning-based controller. 
         FIG. 24  provides expressions illustrating various types of policies. 
         FIG. 25  illustrates one implementation of a reinforcement-learning-based application manager that employs state/action-space exploration via the above-discussed ϵ-greedy policy. 
         FIG. 26  illustrates rewards resulting from various actions issued to the managed environment by the application manager. 
         FIG. 27  illustrates vectors containing numerical elements that can be considered to represent points, areas, or volumes within a Euclidean space. 
         FIG. 28  illustrates applying a filter to an action vector in order to prevent issuance of an action, by an application manager, known to have deleterious consequences. 
         FIG. 29  illustrates a second type of application-vector filter. 
         FIGS. 30A-B  illustrate a first filtering subsystem that filters actions with respect to known constraints, as discussed above with reference to  FIG. 28 . 
         FIG. 31  illustrates observation prediction preceding application of one or more filters of the second type of filter to an action vector, as discussed above with reference to  FIG. 29 . 
         FIGS. 32A-B  illustrate a second filtering subsystem that filters action vectors with respect to observation predictions, as discussed above with reference to  FIG. 29 . 
         FIG. 33  illustrates a programmatic user interface that may be provided to users to define filters and filter stacks for constraining action vectors. 
         FIGS. 34A-B  illustrate a simple graphical user interface that may be provided to users for definition of action-filtering filters, filter stacks, and filtering subsystems. 
         FIG. 35  illustrates application-manager logic of one implementation of the currently disclosed safe-operation-constrained reinforcement-learning-based application manager. 
     
    
    
     DETAILED DESCRIPTION 
     The current document is directed to a safe-operation-constrained reinforcement-learning-based application manager. In a first subsection, below, a detailed description of computer hardware, complex computational systems, and virtualization is provided with reference to  FIGS. 1-11 . In a second subsection, application management and reinforcement learning are discussed with reference to  FIGS. 11-20 . In a third subsection, implementations of the currently disclosed safe-operation-constrained reinforcement-learning application manager are introduced and described with reference to  FIGS. 21-35 . 
     Computer Hardware, Complex Computational Systems, Virtualization, and Generation of Status, Informational, and Error Data 
     The term “abstraction” is not, in any way, intended to mean or suggest an abstract idea or concept. Computational abstractions are tangible, physical interfaces that are implemented, ultimately, using physical computer hardware, data-storage devices, and communications systems. Instead, the term “abstraction” refers, in the current discussion, to a logical level of functionality encapsulated within one or more concrete, tangible, physically-implemented computer systems with defined interfaces through which electronically-encoded data is exchanged, process execution launched, and electronic services are provided. Interfaces may include graphical and textual data displayed on physical display devices as well as computer programs and routines that control physical computer processors to carry out various tasks and operations and that are invoked through electronically implemented application programming interfaces (“APIs”) and other electronically implemented interfaces. There is a tendency among those unfamiliar with modern technology and science to misinterpret the terms “abstract” and “abstraction,” when used to describe certain aspects of modern computing. For example, one frequently encounters assertions that, because a computational system is described in terms of abstractions, functional layers, and interfaces, the computational system is somehow different from a physical machine or device. Such allegations are unfounded. One only needs to disconnect a computer system or group of computer systems from their respective power supplies to appreciate the physical, machine nature of complex computer technologies. One also frequently encounters statements that characterize a computational technology as being “only software,” and thus not a machine or device. Software is essentially a sequence of encoded symbols, such as a printout of a computer program or digitally encoded computer instructions sequentially stored in a file on an optical disk or within an electromechanical mass-storage device. Software alone can do nothing. It is only when encoded computer instructions are loaded into an electronic memory within a computer system and executed on a physical processor that so-called “software implemented” functionality is provided. The digitally encoded computer instructions are an essential and physical control component of processor-controlled machines and devices, no less essential and physical than a cam-shaft control system in an internal-combustion engine. Multi-cloud aggregations, cloud-computing services, virtual-machine containers and virtual machines, communications interfaces, and many of the other topics discussed below are tangible, physical components of physical, electro-optical-mechanical computer systems. 
       FIG. 1  provides a general architectural diagram for various types of computers. Computers that receive, process, and store event messages may be described by the general architectural diagram shown in  FIG. 1 , for example. The computer system contains one or multiple central processing units (“CPUs”)  102 - 105 , one or more electronic memories  108  interconnected with the CPUs by a CPU/memory-subsystem bus  110  or multiple busses, a first bridge  112  that interconnects the CPU/memory-subsystem bus  110  with additional busses  114  and  116 , or other types of high-speed interconnection media, including multiple, high-speed serial interconnects. These busses or serial interconnections, in turn, connect the CPUs and memory with specialized processors, such as a graphics processor  118 , and with one or more additional bridges  120 , which are interconnected with high-speed serial links or with multiple controllers  122 - 127 , such as controller  127 , that provide access to various different types of mass-storage devices  128 , electronic displays, input devices, and other such components, subcomponents, and computational resources. It should be noted that computer-readable data-storage devices include optical and electromagnetic disks, electronic memories, and other physical data-storage devices. Those familiar with modern science and technology appreciate that electromagnetic radiation and propagating signals do not store data for subsequent retrieval, and can transiently “store” only a byte or less of information per mile, far less information than needed to encode even the simplest of routines. 
     Of course, there are many different types of computer-system architectures that differ from one another in the number of different memories, including different types of hierarchical cache memories, the number of processors and the connectivity of the processors with other system components, the number of internal communications busses and serial links, and in many other ways. However, computer systems generally execute stored programs by fetching instructions from memory and executing the instructions in one or more processors. Computer systems include general-purpose computer systems, such as personal computers (“PCs”), various types of servers and workstations, and higher-end mainframe computers, but may also include a plethora of various types of special-purpose computing devices, including data-storage systems, communications routers, network nodes, tablet computers, and mobile telephones. 
       FIG. 2  illustrates an Internet-connected distributed computer system. As communications and networking technologies have evolved in capability and accessibility, and as the computational bandwidths, data-storage capacities, and other capabilities and capacities of various types of computer systems have steadily and rapidly increased, much of modern computing now generally involves large distributed systems and computers interconnected by local networks, wide-area networks, wireless communications, and the Internet.  FIG. 2  shows a typical distributed system in which a large number of PCs  202 - 205 , a high-end distributed mainframe system  210  with a large data-storage system  212 , and a large computer center  214  with large numbers of rack-mounted servers or blade servers all interconnected through various communications and networking systems that together comprise the Internet  216 . Such distributed computing systems provide diverse arrays of functionalities. For example, a PC user sitting in a home office may access hundreds of millions of different web sites provided by hundreds of thousands of different web servers throughout the world and may access high-computational-bandwidth computing services from remote computer facilities for running complex computational tasks. 
     Until recently, computational services were generally provided by computer systems and data centers purchased, configured, managed, and maintained by service-provider organizations. For example, an e-commerce retailer generally purchased, configured, managed, and maintained a data center including numerous web servers, back-end computer systems, and data-storage systems for serving web pages to remote customers, receiving orders through the web-page interface, processing the orders, tracking completed orders, and other myriad different tasks associated with an e-commerce enterprise. 
       FIG. 3  illustrates cloud computing. In the recently developed cloud-computing paradigm, computing cycles and data-storage facilities are provided to organizations and individuals by cloud-computing providers. In addition, larger organizations may elect to establish private cloud-computing facilities in addition to, or instead of, subscribing to computing services provided by public cloud-computing service providers. In  FIG. 3 , a system administrator for an organization, using a PC  302 , accesses the organization&#39;s private cloud  304  through a local network  306  and private-cloud interface  308  and also accesses, through the Internet  310 , a public cloud  312  through a public-cloud services interface  314 . The administrator can, in either the case of the private cloud  304  or public cloud  312 , configure virtual computer systems and even entire virtual data centers and launch execution of application programs on the virtual computer systems and virtual data centers in order to carry out any of many different types of computational tasks. As one example, a small organization may configure and run a virtual data center within a public cloud that executes web servers to provide an e-commerce interface through the public cloud to remote customers of the organization, such as a user viewing the organization&#39;s e-commerce web pages on a remote user system  316 . 
     Cloud-computing facilities are intended to provide computational bandwidth and data-storage services much as utility companies provide electrical power and water to consumers. Cloud computing provides enormous advantages to small organizations without the resources to purchase, manage, and maintain in-house data centers. Such organizations can dynamically add and delete virtual computer systems from their virtual data centers within public clouds in order to track computational-bandwidth and data-storage needs, rather than purchasing sufficient computer systems within a physical data center to handle peak computational-bandwidth and data-storage demands. Moreover, small organizations can completely avoid the overhead of maintaining and managing physical computer systems, including hiring and periodically retraining information-technology specialists and continuously paying for operating-system and database-management-system upgrades. Furthermore, cloud-computing interfaces allow for easy and straightforward configuration of virtual computing facilities, flexibility in the types of applications and operating systems that can be configured, and other functionalities that are useful even for owners and administrators of private cloud-computing facilities used by a single organization. 
       FIG. 4  illustrates generalized hardware and software components of a general-purpose computer system, such as a general-purpose computer system having an architecture similar to that shown in  FIG. 1 . The computer system  400  is often considered to include three fundamental layers: (1) a hardware layer or level  402 ; (2) an operating-system layer or level  404 ; and (3) an application-program layer or level  406 . The hardware layer  402  includes one or more processors  408 , system memory  410 , various different types of input-output (“I/O”) devices  410  and  412 , and mass-storage devices  414 . Of course, the hardware level also includes many other components, including power supplies, internal communications links and busses, specialized integrated circuits, many different types of processor-controlled or microprocessor-controlled peripheral devices and controllers, and many other components. The operating system  404  interfaces to the hardware level  402  through a low-level operating system and hardware interface  416  generally comprising a set of non-privileged computer instructions  418 , a set of privileged computer instructions  420 , a set of non-privileged registers and memory addresses  422 , and a set of privileged registers and memory addresses  424 . In general, the operating system exposes non-privileged instructions, non-privileged registers, and non-privileged memory addresses  426  and a system-call interface  428  as an operating-system interface  430  to application programs  432 - 436  that execute within an execution environment provided to the application programs by the operating system. The operating system, alone, accesses the privileged instructions, privileged registers, and privileged memory addresses. By reserving access to privileged instructions, privileged registers, and privileged memory addresses, the operating system can ensure that application programs and other higher-level computational entities cannot interfere with one another&#39;s execution and cannot change the overall state of the computer system in ways that could deleteriously impact system operation. The operating system includes many internal components and modules, including a scheduler  442 , memory management  444 , a file system  446 , device drivers  448 , and many other components and modules. To a certain degree, modern operating systems provide numerous levels of abstraction above the hardware level, including virtual memory, which provides to each application program and other computational entities a separate, large, linear memory-address space that is mapped by the operating system to various electronic memories and mass-storage devices. The scheduler orchestrates interleaved execution of various different application programs and higher-level computational entities, providing to each application program a virtual, stand-alone system devoted entirely to the application program. From the application program&#39;s standpoint, the application program executes continuously without concern for the need to share processor resources and other system resources with other application programs and higher-level computational entities. The device drivers abstract details of hardware-component operation, allowing application programs to employ the system-call interface for transmitting and receiving data to and from communications networks, mass-storage devices, and other I/O devices and subsystems. The file system  436  facilitates abstraction of mass-storage-device and memory resources as a high-level, easy-to-access, file-system interface. Thus, the development and evolution of the operating system has resulted in the generation of a type of multi-faceted virtual execution environment for application programs and other higher-level computational entities. 
     While the execution environments provided by operating systems have proved to be an enormously successful level of abstraction within computer systems, the operating-system-provided level of abstraction is nonetheless associated with difficulties and challenges for developers and users of application programs and other higher-level computational entities. One difficulty arises from the fact that there are many different operating systems that run within various different types of computer hardware. In many cases, popular application programs and computational systems are developed to run on only a subset of the available operating systems, and can therefore be executed within only a subset of the various different types of computer systems on which the operating systems are designed to run. Often, even when an application program or other computational system is ported to additional operating systems, the application program or other computational system can nonetheless run more efficiently on the operating systems for which the application program or other computational system was originally targeted. Another difficulty arises from the increasingly distributed nature of computer systems. Although distributed operating systems are the subject of considerable research and development efforts, many of the popular operating systems are designed primarily for execution on a single computer system. In many cases, it is difficult to move application programs, in real time, between the different computer systems of a distributed computer system for high-availability, fault-tolerance, and load-balancing purposes. The problems are even greater in heterogeneous distributed computer systems which include different types of hardware and devices running different types of operating systems. Operating systems continue to evolve, as a result of which certain older application programs and other computational entities may be incompatible with more recent versions of operating systems for which they are targeted, creating compatibility issues that are particularly difficult to manage in large distributed systems. 
     For all of these reasons, a higher level of abstraction, referred to as the “virtual machine,” has been developed and evolved to further abstract computer hardware in order to address many difficulties and challenges associated with traditional computing systems, including the compatibility issues discussed above.  FIGS. 5A-B  illustrate two types of virtual machine and virtual-machine execution environments.  FIGS. 5A-B  use the same illustration conventions as used in  FIG. 4 .  FIG. 5A  shows a first type of virtualization. The computer system  500  in  FIG. 5A  includes the same hardware layer  502  as the hardware layer  402  shown in  FIG. 4 . However, rather than providing an operating system layer directly above the hardware layer, as in  FIG. 4 , the virtualized computing environment illustrated in  FIG. 5A  features a virtualization layer  504  that interfaces through a virtualization-layer/hardware-layer interface  506 , equivalent to interface  416  in  FIG. 4 , to the hardware. The virtualization layer provides a hardware-like interface  508  to a number of virtual machines, such as virtual machine  510 , executing above the virtualization layer in a virtual-machine layer  512 . Each virtual machine includes one or more application programs or other higher-level computational entities packaged together with an operating system, referred to as a “guest operating system,” such as application  514  and guest operating system  516  packaged together within virtual machine  510 . Each virtual machine is thus equivalent to the operating-system layer  404  and application-program layer  406  in the general-purpose computer system shown in  FIG. 4 . Each guest operating system within a virtual machine interfaces to the virtualization-layer interface  508  rather than to the actual hardware interface  506 . The virtualization layer partitions hardware resources into abstract virtual-hardware layers to which each guest operating system within a virtual machine interfaces. The guest operating systems within the virtual machines, in general, are unaware of the virtualization layer and operate as if they were directly accessing a true hardware interface. The virtualization layer ensures that each of the virtual machines currently executing within the virtual environment receive a fair allocation of underlying hardware resources and that all virtual machines receive sufficient resources to progress in execution. The virtualization-layer interface  508  may differ for different guest operating systems. For example, the virtualization layer is generally able to provide virtual hardware interfaces for a variety of different types of computer hardware. This allows, as one example, a virtual machine that includes a guest operating system designed for a particular computer architecture to run on hardware of a different architecture. The number of virtual machines need not be equal to the number of physical processors or even a multiple of the number of processors. 
     The virtualization layer includes a virtual-machine-monitor module  518  (“VMM”) that virtualizes physical processors in the hardware layer to create virtual processors on which each of the virtual machines executes. For execution efficiency, the virtualization layer attempts to allow virtual machines to directly execute non-privileged instructions and to directly access non-privileged registers and memory. However, when the guest operating system within a virtual machine accesses virtual privileged instructions, virtual privileged registers, and virtual privileged memory through the virtualization-layer interface  508 , the accesses result in execution of virtualization-layer code to simulate or emulate the privileged resources. The virtualization layer additionally includes a kernel module  520  that manages memory, communications, and data-storage machine resources on behalf of executing virtual machines (“VM kernel”). The VM kernel, for example, maintains shadow page tables on each virtual machine so that hardware-level virtual-memory facilities can be used to process memory accesses. The VM kernel additionally includes routines that implement virtual communications and data-storage devices as well as device drivers that directly control the operation of underlying hardware communications and data-storage devices. Similarly, the VM kernel virtualizes various other types of I/O devices, including keyboards, optical-disk drives, and other such devices. The virtualization layer essentially schedules execution of virtual machines much like an operating system schedules execution of application programs, so that the virtual machines each execute within a complete and fully functional virtual hardware layer. 
       FIG. 5B  illustrates a second type of virtualization. In  FIG. 5B , the computer system  540  includes the same hardware layer  542  and software layer  544  as the hardware layer  402  shown in  FIG. 4 . Several application programs  546  and  548  are shown running in the execution environment provided by the operating system. In addition, a virtualization layer  550  is also provided, in computer  540 , but, unlike the virtualization layer  504  discussed with reference to  FIG. 5A , virtualization layer  550  is layered above the operating system  544 , referred to as the “host OS,” and uses the operating system interface to access operating-system-provided functionality as well as the hardware. The virtualization layer  550  comprises primarily a VMM and a hardware-like interface  552 , similar to hardware-like interface  508  in  FIG. 5A . The virtualization-layer/hardware-layer interface  552 , equivalent to interface  416  in  FIG. 4 , provides an execution environment for a number of virtual machines  556 - 558 , each including one or more application programs or other higher-level computational entities packaged together with a guest operating system. 
     In  FIGS. 5A-B , the layers are somewhat simplified for clarity of illustration. For example, portions of the virtualization layer  550  may reside within the host-operating-system kernel, such as a specialized driver incorporated into the host operating system to facilitate hardware access by the virtualization layer. 
     It should be noted that virtual hardware layers, virtualization layers, and guest operating systems are all physical entities that are implemented by computer instructions stored in physical data-storage devices, including electronic memories, mass-storage devices, optical disks, magnetic disks, and other such devices. The term “virtual” does not, in any way, imply that virtual hardware layers, virtualization layers, and guest operating systems are abstract or intangible. Virtual hardware layers, virtualization layers, and guest operating systems execute on physical processors of physical computer systems and control operation of the physical computer systems, including operations that alter the physical states of physical devices, including electronic memories and mass-storage devices. They are as physical and tangible as any other component of a computer since, such as power supplies, controllers, processors, busses, and data-storage devices. 
     A virtual machine or virtual application, described below, is encapsulated within a data package for transmission, distribution, and loading into a virtual-execution environment. One public standard for virtual-machine encapsulation is referred to as the “open virtualization format” (“OVF”). The OVF standard specifies a format for digitally encoding a virtual machine within one or more data files.  FIG. 6  illustrates an OVF package. An OVF package  602  includes an OVF descriptor  604 , an OVF manifest  606 , an OVF certificate  608 , one or more disk-image files  610 - 611 , and one or more resource files  612 - 614 . The OVF package can be encoded and stored as a single file or as a set of files. The OVF descriptor  604  is an XML document  620  that includes a hierarchical set of elements, each demarcated by a beginning tag and an ending tag. The outermost, or highest-level, element is the envelope element, demarcated by tags  622  and  623 . The next-level element includes a reference element  626  that includes references to all files that are part of the OVF package, a disk section  628  that contains meta information about all of the virtual disks included in the OVF package, a networks section  630  that includes meta information about all of the logical networks included in the OVF package, and a collection of virtual-machine configurations  632  which further includes hardware descriptions of each virtual machine  634 . There are many additional hierarchical levels and elements within a typical OVF descriptor. The OVF descriptor is thus a self-describing, XML file that describes the contents of an OVF package. The OVF manifest  606  is a list of cryptographic-hash-function-generated digests  636  of the entire OVF package and of the various components of the OVF package. The OVF certificate  608  is an authentication certificate  640  that includes a digest of the manifest and that is cryptographically signed. Disk image files, such as disk image file  610 , are digital encodings of the contents of virtual disks and resource files  612  are digitally encoded content, such as operating-system images. A virtual machine or a collection of virtual machines encapsulated together within a virtual application can thus be digitally encoded as one or more files within an OVF package that can be transmitted, distributed, and loaded using well-known tools for transmitting, distributing, and loading files. A virtual appliance is a software service that is delivered as a complete software stack installed within one or more virtual machines that is encoded within an OVF package. 
     The advent of virtual machines and virtual environments has alleviated many of the difficulties and challenges associated with traditional general-purpose computing. Machine and operating-system dependencies can be significantly reduced or entirely eliminated by packaging applications and operating systems together as virtual machines and virtual appliances that execute within virtual environments provided by virtualization layers running on many different types of computer hardware. A next level of abstraction, referred to as virtual data centers or virtual infrastructure, provide a data-center interface to virtual data centers computationally constructed within physical data centers.  FIG. 7  illustrates virtual data centers provided as an abstraction of underlying physical-data-center hardware components. In  FIG. 7 , a physical data center  702  is shown below a virtual-interface plane  704 . The physical data center consists of a virtual-data-center management server  706  and any of various different computers, such as PCs  708 , on which a virtual-data-center management interface may be displayed to system administrators and other users. The physical data center additionally includes generally large numbers of server computers, such as server computer  710 , that are coupled together by local area networks, such as local area network  712  that directly interconnects server computer  710  and  714 - 720  and a mass-storage array  722 . The physical data center shown in  FIG. 7  includes three local area networks  712 ,  724 , and  726  that each directly interconnects a bank of eight servers and a mass-storage array. The individual server computers, such as server computer  710 , each includes a virtualization layer and runs multiple virtual machines. Different physical data centers may include many different types of computers, networks, data-storage systems and devices connected according to many different types of connection topologies. The virtual-data-center abstraction layer  704 , a logical abstraction layer shown by a plane in  FIG. 7 , abstracts the physical data center to a virtual data center comprising one or more resource pools, such as resource pools  730 - 732 , one or more virtual data stores, such as virtual data stores  734 - 736 , and one or more virtual networks. In certain implementations, the resource pools abstract banks of physical servers directly interconnected by a local area network. 
     The virtual-data-center management interface allows provisioning and launching of virtual machines with respect to resource pools, virtual data stores, and virtual networks, so that virtual-data-center administrators need not be concerned with the identities of physical-data-center components used to execute particular virtual machines. Furthermore, the virtual-data-center management server includes functionality to migrate running virtual machines from one physical server to another in order to optimally or near optimally manage resource allocation, provide fault tolerance, and high availability by migrating virtual machines to most effectively utilize underlying physical hardware resources, to replace virtual machines disabled by physical hardware problems and failures, and to ensure that multiple virtual machines supporting a high-availability virtual appliance are executing on multiple physical computer systems so that the services provided by the virtual appliance are continuously accessible, even when one of the multiple virtual appliances becomes compute bound, data-access bound, suspends execution, or fails. Thus, the virtual data center layer of abstraction provides a virtual-data-center abstraction of physical data centers to simplify provisioning, launching, and maintenance of virtual machines and virtual appliances as well as to provide high-level, distributed functionalities that involve pooling the resources of individual physical servers and migrating virtual machines among physical servers to achieve load balancing, fault tolerance, and high availability.  FIG. 8  illustrates virtual-machine components of a virtual-data-center management server and physical servers of a physical data center above which a virtual-data-center interface is provided by the virtual-data-center management server. The virtual-data-center management server  802  and a virtual-data-center database  804  comprise the physical components of the management component of the virtual data center. The virtual-data-center management server  802  includes a hardware layer  806  and virtualization layer  808 , and runs a virtual-data-center management-server virtual machine  810  above the virtualization layer. Although shown as a single server in  FIG. 8 , the virtual-data-center management server (“VDC management server”) may include two or more physical server computers that support multiple VDC-management-server virtual appliances. The virtual machine  810  includes a management-interface component  812 , distributed services  814 , core services  816 , and a host-management interface  818 . The management interface is accessed from any of various computers, such as the PC  708  shown in  FIG. 7 . The management interface allows the virtual-data-center administrator to configure a virtual data center, provision virtual machines, collect statistics and view log files for the virtual data center, and to carry out other, similar management tasks. The host-management interface  818  interfaces to virtual-data-center agents  824 ,  825 , and  826  that execute as virtual machines within each of the physical servers of the physical data center that is abstracted to a virtual data center by the VDC management server. 
     The distributed services  814  include a distributed-resource scheduler that assigns virtual machines to execute within particular physical servers and that migrates virtual machines in order to most effectively make use of computational bandwidths, data-storage capacities, and network capacities of the physical data center. The distributed services further include a high-availability service that replicates and migrates virtual machines in order to ensure that virtual machines continue to execute despite problems and failures experienced by physical hardware components. The distributed services also include a live-virtual-machine migration service that temporarily halts execution of a virtual machine, encapsulates the virtual machine in an OVF package, transmits the OVF package to a different physical server, and restarts the virtual machine on the different physical server from a virtual-machine state recorded when execution of the virtual machine was halted. The distributed services also include a distributed backup service that provides centralized virtual-machine backup and restore. 
     The core services provided by the VDC management server include host configuration, virtual-machine configuration, virtual-machine provisioning, generation of virtual-data-center alarms and events, ongoing event logging and statistics collection, a task scheduler, and a resource-management module. Each physical server  820 - 822  also includes a host-agent virtual machine  828 - 830  through which the virtualization layer can be accessed via a virtual-infrastructure application programming interface (“API”). This interface allows a remote administrator or user to manage an individual server through the infrastructure API. The virtual-data-center agents  824 - 826  access virtualization-layer server information through the host agents. The virtual-data-center agents are primarily responsible for offloading certain of the virtual-data-center management-server functions specific to a particular physical server to that physical server. The virtual-data-center agents relay and enforce resource allocations made by the VDC management server, relay virtual-machine provisioning and configuration-change commands to host agents, monitor and collect performance statistics, alarms, and events communicated to the virtual-data-center agents by the local host agents through the interface API, and to carry out other, similar virtual-data-management tasks. 
     The virtual-data-center abstraction provides a convenient and efficient level of abstraction for exposing the computational resources of a cloud-computing facility to cloud-computing-infrastructure users. A cloud-director management server exposes virtual resources of a cloud-computing facility to cloud-computing-infrastructure users. In addition, the cloud director introduces a multi-tenancy layer of abstraction, which partitions VDCs into tenant-associated VDCs that can each be allocated to a particular individual tenant or tenant organization, both referred to as a “tenant.” A given tenant can be provided one or more tenant-associated VDCs by a cloud director managing the multi-tenancy layer of abstraction within a cloud-computing facility. The cloud services interface ( 308  in  FIG. 3 ) exposes a virtual-data-center management interface that abstracts the physical data center. 
       FIG. 9  illustrates a cloud-director level of abstraction. In  FIG. 9 , three different physical data centers  902 - 904  are shown below planes representing the cloud-director layer of abstraction  906 - 908 . Above the planes representing the cloud-director level of abstraction, multi-tenant virtual data centers  910 - 912  are shown. The resources of these multi-tenant virtual data centers are securely partitioned in order to provide secure virtual data centers to multiple tenants, or cloud-services-accessing organizations. For example, a cloud-services-provider virtual data center  910  is partitioned into four different tenant-associated virtual-data centers within a multi-tenant virtual data center for four different tenants  916 - 919 . Each multi-tenant virtual data center is managed by a cloud director comprising one or more cloud-director servers  920 - 922  and associated cloud-director databases  924 - 926 . Each cloud-director server or servers runs a cloud-director virtual appliance  930  that includes a cloud-director management interface  932 , a set of cloud-director services  934 , and a virtual-data-center management-server interface  936 . The cloud-director services include an interface and tools for provisioning multi-tenant virtual data center virtual data centers on behalf of tenants, tools and interfaces for configuring and managing tenant organizations, tools and services for organization of virtual data centers and tenant-associated virtual data centers within the multi-tenant virtual data center, services associated with template and media catalogs, and provisioning of virtualization networks from a network pool. Templates are virtual machines that each contains an OS and/or one or more virtual machines containing applications. A template may include much of the detailed contents of virtual machines and virtual appliances that are encoded within OVF packages, so that the task of configuring a virtual machine or virtual appliance is significantly simplified, requiring only deployment of one OVF package. These templates are stored in catalogs within a tenant&#39;s virtual-data center. These catalogs are used for developing and staging new virtual appliances and published catalogs are used for sharing templates in virtual appliances across organizations. Catalogs may include OS images and other information relevant to construction, distribution, and provisioning of virtual appliances. 
     Considering  FIGS. 7 and 9 , the VDC-server and cloud-director layers of abstraction can be seen, as discussed above, to facilitate employment of the virtual-data-center concept within private and public clouds. However, this level of abstraction does not fully facilitate aggregation of single-tenant and multi-tenant virtual data centers into heterogeneous or homogeneous aggregations of cloud-computing facilities. 
       FIG. 10  illustrates virtual-cloud-connector nodes (“VCC nodes”) and a VCC server, components of a distributed system that provides multi-cloud aggregation and that includes a cloud-connector server and cloud-connector nodes that cooperate to provide services that are distributed across multiple clouds. VMware vCloud™ VCC servers and nodes are one example of VCC server and nodes. In  FIG. 10 , seven different cloud-computing facilities are illustrated  1002 - 1008 . Cloud-computing facility  1002  is a private multi-tenant cloud with a cloud director  1010  that interfaces to a VDC management server  1012  to provide a multi-tenant private cloud comprising multiple tenant-associated virtual data centers. The remaining cloud-computing facilities  1003 - 1008  may be either public or private cloud-computing facilities and may be single-tenant virtual data centers, such as virtual data centers  1003  and  1006 , multi-tenant virtual data centers, such as multi-tenant virtual data centers  1004  and  1007 - 1008 , or any of various different kinds of third-party cloud-services facilities, such as third-party cloud-services facility  1005 . An additional component, the VCC server  1014 , acting as a controller is included in the private cloud-computing facility  1002  and interfaces to a VCC node  1016  that runs as a virtual appliance within the cloud director  1010 . A VCC server may also run as a virtual appliance within a VDC management server that manages a single-tenant private cloud. The VCC server  1014  additionally interfaces, through the Internet, to VCC node virtual appliances executing within remote VDC management servers, remote cloud directors, or within the third-party cloud services  1018 - 1023 . The VCC server provides a VCC server interface that can be displayed on a local or remote terminal, PC, or other computer system  1026  to allow a cloud-aggregation administrator or other user to access VCC-server-provided aggregate-cloud distributed services. In general, the cloud-computing facilities that together form a multiple-cloud-computing aggregation through distributed services provided by the VCC server and VCC nodes are geographically and operationally distinct. 
     Application Management and Reinforcement Learning 
       FIGS. 11A-C  illustrate an application manager. All three figures use the same illustration conventions, next described with reference to  FIG. 11A . The distributed computing system is represented, in  FIG. 11A , by four servers  1102 - 1105  that each support execution of a virtual machine,  1106 - 1108  respectively, that provides an execution environment for a local instance of the distributed application. Of course, in real-life cloud-computing environments, a particular distributed application may run on many tens to hundreds of individual physical servers. Such distributed applications often require fairly continuous administration and management. For example, instances of the distributed application may need to be launched or terminated, depending on current computational loads, and may be frequently relocated to different physical servers and even to different cloud-computing facilities in order to take advantage of favorable pricing for virtual-machine execution, to obtain necessary computational throughput, and to minimize networking latencies. Initially, management of distributed applications as well as the management of multiple, different applications executing on behalf of a client or client organization of one or more cloud-computing facilities was carried out manually through various management interfaces provided by cloud-computing facilities and distributed-computer data centers. However, as the complexity of distributed-computing environments has increased and as the numbers and complexities of applications concurrently executed by clients and client organizations have increased, efforts have been undertaken to develop automated application managers for automatically monitoring and managing applications on behalf of clients and client organizations of cloud-computing facilities and distributed-computer-system-based data centers. 
     As shown in  FIG. 11B , one approach to automated management of applications within distributed computer systems is to include, in each physical server on which one or more of the managed applications executes, a local instance of the distributed application manager  1120 - 1123 . The local instances of the distributed application manager cooperate, in peer-to-peer fashion, to manage a set of one or more applications, including distributed applications, on behalf of a client or client organization of the data center or cloud-computing facility. Another approach, as shown in  FIG. 11C , is to run a centralized or centralized-distributed application manager  1130  on one or more physical servers  1131  that communicates with application-manager agents  1132 - 1135  on the servers  1102 - 1105  to support control and management of the managed applications. In certain cases, application-management facilities may be incorporated within the various types of management servers that manage virtual data centers and aggregations of virtual data centers discussed in the previous subsection of the current document. The phrase “application manager” means, in this document, an automated controller than controls and manages applications programs and the computational environment in which they execute. Thus, an application manager may interface to one or more operating systems and virtualization layers, in addition to applications, in various implementations, to control and manage the applications and their computational environments. In certain implementations, an application manager may even control and manage virtual and/or physical components that support the computational environments in which applications execute. 
     In certain implementations, an application manager is configured to manage applications and their computational environments within one or more distributed computing systems based on a set of one or more policies, each of which may include various rules, parameter values, and other types of specifications of the desired operational characteristics of the applications. As one example, the one or more policies may specify maximum average latencies for responding to user requests, maximum costs for executing virtual machines per hour or per day, and policy-driven approaches to optimizing the cost per transaction and the number of transactions carried out per unit of time. Such overall policies may be implemented by a combination of finer-grain policies, parameterized control programs, and other types of controllers that interface to operating-system and virtualization-layer-management subsystems. However, as the numbers and complexities of applications desired to be managed on behalf of clients and client organizations of data centers and cloud-computing facilities continues to increase, it is becoming increasingly difficult, if not practically impossible, to implement policy-driven application management by manual programming and/or policy construction. As a result, a new approach to application management based on the machine-learning technique referred to as “reinforcement learning” has been undertaken. 
       FIG. 12  illustrates, at a high level of abstraction, a reinforcement-learning-based application manager controlling a computational environment, such as a cloud-computing facility. The reinforcement-learning-based application manager  1202  manages one or more applications by emitting or issuing actions, as indicated by arrow  1204 . These actions are selected from a set of actions A of cardinality |A|. Each action a in the set of actions A can be generally thought of as a vector of numeric values that specifies an operation that the manager is directing the environment to carry out. The environment may, in many cases, translate the action into one or more environment-specific operations that can be carried out by the computational environment controlled by the reinforcement-learning-based application manager. It should be noted that the cardinality |A| may be indeterminable, since the numeric values may include real values, and the action space may be therefore effectively continuous or effectively continuous in certain dimensions. The operations represented by actions may be, for example, commands, including command arguments, executed by operating systems, distributed operating systems, virtualization layers, management servers, and other types of control components and subsystems within one or more distributed computing systems or cloud-computing facilities. The reinforcement-learning-based application manager receives observations from the computational environment, as indicated by arrow  1206 . Each observation o can be thought of as a vector of numeric values  1208  selected from a set of possible observation vectors Ω. The set Ω may, of course, be quite large and even practically innumerable. Each element of the observation o represents, in certain implementations, a particular type of metric or observed operational characteristic or parameter, numerically encoded, that is related to the computational environment. The metrics may have discrete values or real values, in various implementations. For example, the metrics or observed operational characteristics may indicate the amount of memory allocated for applications and/or application instances, networking latencies experienced by one or more applications, an indication of the number of instruction-execution cycles carried out on behalf of applications or local-application instances, and many other types of metrics and operational characteristics of the managed applications and the computational environment in which the managed applications run. As shown in  FIG. 12 , there are many different sources  1210 - 1214  for the values included in an observation o, including virtualization-layer and operating-system log files  1210  and  1214 , virtualization-layer metrics, configuration data, and performance data provided through a virtualization-layer management interface  1211 , various types of metrics generated by the managed applications  1212 , and operating-system metrics, configuration data, and performance data  1213 . Ellipses  1216  and  1218  indicate that there may be many additional sources for observation values. In addition to receiving observation vectors o, the reinforcement-learning-based application manager receives rewards, as indicated by arrow  1220 . Each reward is a numeric value that represents the feedback provided by the computational environment to the reinforcement-learning-based application manager after carrying out the most recent action issued by the manager and transitioning to a resultant state, as further discussed below. The reinforcement-learning-based application manager is generally initialized with an initial policy that specifies the actions to be issued in response to received observations and over time, as the application manager interacts with the environment, the application manager adjusts the internally maintained policy according to the rewards received following issuance of each action. In many cases, after a reasonable period of time, a reinforcement-learning-based application manager is able to learn a near-optimal or optimal policy for the environment, such as a set of distributed applications, that it manages. In addition, in the case that the managed environment evolves over time, a reinforcement-learning-based application manager is able to continue to adjust the internally maintained policy in order to track evolution of the managed environment so that, at any given point in time, the internally maintained policy is near-optimal or optimal. In the case of an application manager, the computational environment in which the applications run may evolve through changes to the configuration and components, changes in the computational load experienced by the applications and computational environment, and as a result of many additional changes and forces. The received observations provide the information regarding the managed environment that allows the reinforcement-learning-based application manager to infer the current state of the environment which, in turn, allows the reinforcement-learning-based application manager to issue actions that push the managed environment towards states that, over time, produce the greatest reward feedbacks. Of course, similar reinforcement-learning-based application managers may be employed within standalone computer systems, individual, networked computer systems, various processor-controlled devices, including smart phones, and other devices and systems that run applications. 
       FIG. 13  summarizes the reinforcement-learning-based approach to control. The manager or controller  1302 , referred to as a “reinforcement-learning agent,” is contained within, but is distinct and separate from, the universe  1304 . Thus, the universe comprises the manager or controller  1302  and the portion of the universe not included in the manager, in set notation referred to as “universe—manager.” In the current document, the portion of the universe not included in the manager is referred to as the “environment.” In the case of an application manager, the environment includes the managed applications, the physical computational facilities in which they execute, and even generally includes the physical computational facilities in which the manager executes. The rewards are generated by the environment and the reward-generation mechanism cannot be controlled or modified by the manager. 
       FIGS. 14A-B  illustrate states of the environment. In the reinforcement-learning approach, the environment is considered to inhabit a particular state at each point in time. The state may be represented by one or more numeric values or character-string values, but generally is a function of hundreds, thousands, millions, or more different variables. The observations generated by the environment and transmitted to the manager reflect the state of the environment at the time that the observations are made. The possible state transitions can be described by a state-transition diagram for the environment.  FIG. 14A  illustrates a portion of a state-transition diagram. Each of the states in the portion of the state-transition diagram shown in  FIG. 14A  are represented by large, labeled disks, such as disc  1402  representing a particular state S n . The transition between one state to another state occurs as a result of an action, emitted by the manager, that is carried out within the environment. Thus, arrows incoming to a given state represent transitions from other states to the given state and arrows outgoing from the given state represent transitions from the given state to other states. For example, one transition from state  1404 , labeled S n+6 , is represented by outgoing arrow  1406 . The head of this arrow points to a smaller disc that represents a particular action  1408 . This action node is labeled A r+1 . The labels for the states and actions may have many different forms, in different types of illustrations, but are essentially unique identifiers for the corresponding states and actions. The fact that outgoing arrow  1406  terminates in action  1408  indicates that transition  1406  occurs upon carrying out of action  1408  within the environment when the environment is in state  1404 . Outgoing arrows  1410  and  1412  emitted by action node  1408  terminate at states  1414  and  1416 , respectively. These arrows indicate that carrying out of action  1408  by the environment when the environment is in state  1404  results in a transition either to state  1414  or to state  1416 . It should also be noted that an arrow emitted from an action node may return to the state from which the outgoing arrow to the action node was emitted. In other words, carrying out of certain actions by the environment when the environment is in a particular state may result in the environment maintaining that state. Starting at an initial state, the state-transition diagram indicates all possible sequences of state transitions that may occur within the environment. Each possible sequence of state transitions is referred to as a “trajectory.” 
       FIG. 14B  illustrates additional details about state-transition diagrams and environmental states and behaviors.  FIG. 14B  shows a small portion of a state-transition diagram that includes three state nodes  1420 - 1422 . A first additional detail is the fact that, once an action is carried out, the transition from the action node to a resultant state is accompanied by the emission of an observation, by the environment, to the manager. For example, a transition from state  1420  to state  1422  as a result of action  1424  produces observation  1426 , while transition from state  1420  to state  1421  via action  1424  produces observation  1428 . A second additional detail is that each state transition is associated with a probability. Expression  1430  indicates that the probability of transitioning from state s 1  to state s 2  as a result of the environment carrying out action a 1 , where s indicates the current state of the environment and s′ indicates the next state of the environment following s, is output by the state-transition function T, which takes, as arguments, indications of the initial state, the final state, and the action. Thus, each transition from a first state through a particular action node to a second state is associated with a probability. The second expression  1432  indicates that probabilities are additive, so that the probability of a transition from state s 1  to either state s 2  or state s 3  as a result of the environment carrying out action a 1  is equal to the sum of the probability of a transition from state s 1  to state s 2  via action a 1  and the probability of a transition from state s 1  to state s 3  via action at. Of course, the sum of the probabilities associated with all of the outgoing arrows emanating from a particular state is equal to 1.0, for all non-terminal states, since, upon receiving an observation/reward pair following emission of a first action, the manager emits a next action unless the manager terminates. As indicated by expressions  1434 , the function O returns the probability that a particular observation o is returned by the environment given a particular action and the state to which the environment transitions following execution of the action. In other words, in general, there are many possible observations o that might be generated by the environment following transition to a particular state through a particular action, and each possible observation is associated with a probability of occurrence of the observation given a particular state transition through a particular action. 
       FIG. 15  illustrates the concept of belief. At the top of  FIG. 15 , a histogram  1502  is shown. The horizontal axis  1502  represents 37 different possible states for a particular environment and the vertical axis  1506  represents the probability of the environment being in the corresponding state at some point in time. Because the environment must be in one state at any given point in time, the sum of the probabilities for all the states is equal to 1.0. Because the manager does not know the state of the environment, but instead only knows the values of the elements of the observation following the last executed action, the manager infers the probabilities of the environment being in each of the different possible states. The manager&#39;s belief b(s) is the expectation of the probability that the environment is in state s, as expressed by equation 1508. Thus, the belief b is a probability distribution which could be represented in a histogram similar to histogram  1502 . Over time, the manager accumulates information regarding the current state of the environment and the probabilities of state transitions as a function of the belief distribution and most recent actions, as a result of which the probability distribution b shifts towards an increasingly non-uniform distribution with greater probabilities for the actual state of the environment. In a deterministic and fully observable environment, in which the manager knows the current state of the environment, the policy π maintained by the manager can be thought of as a function that returns the next action a to be emitted by the manager to the environment based on the current state of the environment, or, in mathematical notation, a=π(s). However, in the non-deterministic and non-transparent environment in which application managers operate, the policy π maintained by the manager determines a probability for each action based on the current belief distribution b, as indicated by expression  1510  in  FIG. 15 , and an action with the highest probability is selected by the policy π, which can be summarized, in more compact notation, by expression  1511 . Thus, as indicated by the diagram of a state  1512 , at any point in time, the manager does not generally certainly know the current state of the environment, as indicated by the label  1514  within the node representation of the current date  1512 , as a result of which there is some probability, for each possible state, that the environment is currently in that state. This, in turn, generally implies that there is a non-zero probability that each of the possible actions that the manager can issue should be the next issued action, although there are cases in which, although the state of the environment is not known with certain, there is enough information about the state of the environment to allow a best action to be selected. 
       FIGS. 16A-B  illustrate a simple flow diagram for the universe comprising the manager and the environment in one approach to reinforcement learning. The manager  1602  internally maintains a policy π  1604  and a belief distribution b  1606  and is aware of the set of environment states S  1608 , the set of possible actions A  1610 , the state-transition function T  1612 , the set of possible observations Ω  1614  and, and the observation-probability function O  1616 , all discussed above. The environment  1604  shares knowledge of the sets A, and Ω with the manager. Usually, the true state space S and the functions T and O are unknown and estimated by the manager. The environment maintains the current state of the environment s  1620 , a reward function R  1622  that returns a reward r in response to an input current state s and an input action a received while in the current state  1624 , and a discount parameter γ  1626 , discussed below. The manager is initialized with an initial policy and belief distribution. The manager emits a next action  1630  based on the current belief distribution which the environment then carries out, resulting in the environment occupying a resultant state and then issues a reward  1624  and an observation o  1632  based on the resultant state and the received action. The manager receives the reward and observation, generally updates the internally stored policy and belief distribution, and then issues a next action, in response to which the environment transitions to a resultant state and emits a next reward and observation. This cycle continues indefinitely or until a termination condition arises. 
     It should be noted that this is just one model of a variety of different specific models that may be used for a reinforcement-learning agent and environment. There are many different models depending on various assumptions and desired control characteristics. 
       FIG. 16B  shows an alternative way to illustrate operation of the universe. In this alternative illustration method, a sequence of time steps is shown, with the times indicated in a right-hand column  1640 . Each time step consists of issuing, by the manager, an action to the environment and issuing, by the environment, a reward and observation to the manager. For example, in the first time step t=0, the manager issues an action a  1642 , the environment transitions from state so  1643  to s 1    1644 , and the environment issues a reward r and observation o  1645  to the manager. As a result, the manager updates the policy and belief distribution in preparation for the next time step. For example, the initial policy and belief distribution π 0  and b 0    1646  are updated to the policy and belief distribution π 1  and b 1    1647  at the beginning of the next time step t=1. The sequence of states {s 0 , s 1 , . . . } represents the trajectory of the environment as controlled by the manager. Each time step is thus equivalent to one full cycle of the control-flow-diagram-like representation discussed above with reference to  FIG. 16A . 
       FIG. 17  provides additional details about the operation of the manager, environment, and universe. At the bottom of  FIG. 17 , a trajectory for the manager and environment is laid out horizontally with respect to the horizontal axis  1702  representing the time steps discussed above with reference to  FIG. 16B . A first horizontal row  1704  includes the environment states, a second horizontal row  1706  includes the belief distributions, and a third horizontal row  1708  includes the issued rewards. At any particular state, such as circled state s 4    1710 , one can consider all of the subsequent rewards, shown for state s 4  within box  1712  in  FIG. 17 . The discounted return for state s 4 , G 4 , is the sum of a series of discounted rewards  1714 . The first term in the series  1716  is the reward r 5  returned when the environment transitions from state s 4  to state s 5 . Each subsequent term in the series includes the next reward multiplied by the discount rate γ raised to a power. The discounted reward can be alternatively expressed using a summation, as indicated in expression  1718 . The value of a given state s, assuming a current policy π, is the expected discounted return for the state, and is returned by a value function V π ( ), as indicated by expression  1720 . Alternatively, an action-value function returns a discounted return for a particular state and action, assuming a current policy, as indicated by expression  1722 . An optimal policy π* provides a value for each state that is greater than or equal to the value provided by any possible policy it in the set of possible policies Π. There are many different ways for achieving an optimal policy. In general, these involve running a manager to control an environment while updating the value function V π ( ) and policy π, either in alternating sessions or concurrently. In some approaches to reinforcement learning, when the environment is more or less static, once an optimal policy is obtained during one or more training runs, the manager subsequently controls the environment according to the optimal policy. In other approaches, initial training generates an initial policy that is then continuously updated, along with the value function, in order to track changes in the environment so that a near-optimal policy is maintained by the manager. 
       FIG. 18  provides a somewhat more detailed control-flow-like description of operation of the manager and environment than originally provided in  FIG. 16A . The control-flow-like presentation corresponds to a run of the manager and environment that continues until a termination condition evaluates to TRUE. In addition to the previously discussed sets and functions, this model includes a state-transition function Tr  1802 , an observation-generation function Out  1804 , a value function V  1806 , update functions U V    1808 , U π    1810 , and U b    1812  that update the value function, policy, and belief distribution, respectively, an update variable u  1814  that indicates whether to update the value function, policy, or both, and a termination condition  1816 . The manager  1820  determines whether the termination condition evaluates to TRUE, in step  1821 , and, if so, terminates in step  1822 . Otherwise, the manager updates the belief, in step  1823  and updates one or both of the value function and policy, in steps  1824  and  1825 , depending on the current value of the update variable u. In step  1826 , the manager generates a new action and, in step  1828 , updates the update variable u and issues the generated action to the environment. The environment determines a new state  1830 , determines a reward  1832 , and determines an observation  1834  and returns the generated reward and observation in step  1836 . 
       FIG. 19  provides a traditional control-flow diagram for operation of the manager and environment over multiple runs. In step  1902 , the environment and manager are initialized. This involves initializing certain of the various sets, functions, parameters, and variables shown at the top of  FIG. 18 . In step  1904 , local and global termination conditions are determined. When the local termination condition evaluates to TRUE, the run terminates. When the global termination condition evaluates to TRUE, operation of the manager terminates. In step  1906 , the update variable u is initialized to indicate that the value function should be updated during the initial run. Step  1908  consists of the initial run, during which the value function is updated with respect to the initial policy. Then, additional runs are carried out in the loop of steps  1910 - 1915 . When the global termination condition evaluates to TRUE, as determined in step  1910 , operation of the manager is terminated in step  1911 , with output of the final parameter values and functions. Thus, the manager may be operated for training purposes, according to the control-flow diagram shown in  FIG. 19 , with the final output parameter values and functions stored so that the manager can be subsequently operated, according to the control-flow diagram shown in  FIG. 19 , to control a live system. Otherwise, when the global termination condition does not evaluate to TRUE and when the update variable u has a value indicating that the value function should be updated, as determined in step  1912 , the value stored in the update variable u is changed to indicate that the policy should be updated, in step  1913 . Otherwise, the value stored in the update variable u is changed to indicate that the value function should be updated, in step  1914 . Then, a next run, described by the control-flow-like diagram shown in  FIG. 18 , is carried out in step  1915 . Following termination of this run, control flows back to step  1910  for a next iteration of the loop of steps  1910 - 1915 . In alternative implementations, the update variable u may be initially set to indicate that both the value function and policy should be updated during each run and the update variable u is not subsequently changed. This approach involves different value-function and policy update functions than those used when only one of the value function and policy is updated during each run. 
       FIG. 20  illustrates one approach to using reinforcement learning to generate and operate an application manager. First, reinforcement learning is used to train an environment simulator  2002  by one or both of operating the simulator against a live-distributed-system environment  2004  or against a simulated distributed-system environment that replays archived data generated by a live distributed system to the simulator  2006 . Then, a manager  2008  is initially trained by controlling an environment consisting of the simulator  2002 . The manager, once trained, is then operated for a time to control an environment comprising a live distributed system  2010 . Once the manager has been trained both against the simulator and the live distributed system, it is ready to be deployed to manage an environment  2012  comprising a target live distributed system. 
     Currently Disclosed Safe-Operation-Constrained Reinforcement-Learning-Based Application Manager 
       FIG. 21  illustrates an alternative view of a control trajectory comprising a sequence of executed of actions, each accompanied by a managed-environment state change. In  FIG. 21 , arrow  2102  represents a timeline. At the beginning of each of multiple time intervals, a reinforcement-learning-based controller, such as the currently disclosed safe-operation-constrained reinforcement-learning-based application manager subsequently referred to below as the “application manager,” invokes the above-discussed policy π to select a next action from a set of actions A. For example, at the time interval that begins with time  2104 , the reinforcement-learning-based controller invokes the policy π to select action  2106 , represented as a circle inscribing a numerical label “2,” from the set of possible actions A, represented by disk  2108 , which contains 14 different possible actions represented by smaller circles that each inscribe a different numeric label. Of course, in real-world situations, there may be hundreds, thousands, tens of thousands, or more different possible actions. The state of the managed-environment, at time  2104 , is represented by the circle  2110  inscribing the label “s 10 ” indicating the managed-environment state. When the reinforcement-learning-based controller executes the selected action, as represented by arrow  2112 , the managed environment transitions to a new state  2114  at a next point in time  2116 , where the process is repeated to produce a next action and next state transition. Thus, reinforcement-learning-based control can be thought of as a trajectory through a state/action space. In the simple example of  FIG. 21 , with both actions and states represented by integers, the state/action space can be imagined as a two-dimensional plane with two orthogonal coordinate axes corresponding to actions and states. A control trajectory can be represented as a table, such as table  2120  shown in  FIG. 21 , containing three-value columns, such as column  2122 , that each includes a time value, an indication of an action, and an indication of the state. 
       FIG. 22  illustrates the potential sizes of the set of possible state/action pairs. Using similar illustration conventions as used in  FIG. 21 ,  FIG. 22  shows an illustration of a set of actions A  2202 , with a cardinality of 6, and a set of states S  2204 , with a cardinality of 20. In certain reinforcement-learning-based controller implementations, the policy π is based on an assumed Markov model. In a Markov-model based policy, the policy π selects a next action based on the current managed-environment state or, when the state is unknown to the reinforcement-learning-based controller, on the belief distribution b for the current managed-environment state, as discussed above. The set of possible state/action pairs SA  2206  can be thought of as the set of all possible current-state/next-action control decisions that can be generated from the set of possible actions A and the set of possible states S. For a Markov-based reinforcement-learning-based controller, the number of possible state/action pairs is equal to the product of the cardinalities of the set of possible actions A and the set of possible states S. In the example shown in  FIG. 22 , the number of possible state/action pairs is 120, even though there are only 6 possible actions and 20 possible states. Other types of reinforcement-learning-based controllers may consider the current state and the preceding state in order to choose a next action. In this case, each possible action-selection decision can be considered to be a triple comprising an action and two states. In this case, the number of possible control decisions is equal to the product of the cardinality of the set of possible actions A and the square of the cardinality of the set of possible states S. In yet other types of reinforcement-learning-based controllers, the n most recent states, including the current state, of the managed environment are considered when making an action-selection decision. The most general expression for the number of possible control decisions is: |S| n |A|. In the case that n equals 2, there are 2400 possible control decisions for the example shown in  FIG. 22 , as indicated in the second row  2208  of the table  2210  shown in  FIG. 22 . Of course, in real-world problem domains, there may be very large numbers of different possible actions and states. As shown in the third row  2212  of the table  2210 , when there are 1000 possible actions and 10,000 possible states, a controller using a Markov policy, where n is equal to 1, includes 10,000,000 different possible control decisions. It would take on the order of many months of testing time for a controller, given these figures, to sample each possible control decision. For a controller using a policy based on a model for which n is equal to 2, with 1000 possible actions and 10,000 possible states, there are 10 11  different possible control decisions, which would take many thousands of years for controller to sample once each. Thus, in practical, real-world situations, the number of possible control decisions, which represents the state space that a reinforcement-learning-based control system needs to explore in order to find an optimal policy, can be enormous. 
       FIGS. 23A-B  illustrate the need for state/action exploration by a reinforcement-learning-based controller.  FIGS. 23A-B  both use the same illustration conventions, next described with reference to  FIG. 23A . A portion of a surface  2302  that represents the value or expected reward for state/action pairs includes a rather prominent peak  2304 . The point at the summit of the surface  2306  represents a state/action pair that generates the greatest expected reward or value. In static environments, a reinforcement-learning-based controller, over time, seeks to obtain the maximum possible value by reaching point  2306 , starting from an initial point  2308 . Two different trajectories are shown in  FIG. 23A . In non-static environments, the controller seeks to obtain a maximum discounted reward over the most recent window in time. A first trajectory  2310  gradually ascends the peak, initially ascending the back side of the peak, wrapping around to the front side of the peak  2312 , and slowly spiraling upward, continuously reaching higher-valued state/action pairs until reaching point  2306 . A second trajectory  2314  initially descends to a lower point on the surface  2316  and then directly and steeply ascends  2318  to point  2306 . In this case, if the number of actions needed to be taken in order to reach the optimal control decision is a measure of the efficiency of the reinforcement-learning-based controller, the second trajectory  2314  is by far most efficient. However, the second trajectory involves initially carrying out locally suboptimal actions of decreasing value. Of course, this is a somewhat artificial example and illustration, since trajectories would not generally map to quasi-continuous curves and would normally not continuously increase in value, but is intended to show that, unless the reinforcement-learning-based controller carries out a certain amount of state/action space exploration, the reinforcement-learning-based controller cannot discover optimal policies π*. In other words, were the reinforcement-learning-based controller to always select the currently most valuable action, and thus follow a greedy policy, the reinforcement-learning-based controller would generally fail to find the most efficient trajectories. As shown in  FIG. 23B , in a different example, a greedy policy may allow a reinforcement-learning-based controller to find a trajectory  2320  that results in discovery of a locally optimal state/action pair  2322 , but would not allow the reinforcement-learning-based controller to find the global optimal  2324 , since all trajectories leading to the global optimum involve a stretch of non-optimal action selections  2326 . 
       FIG. 24  provides expressions illustrating various types of policies. As discussed above, an action-value function Q π (s,a) ( 1722  in  FIG. 17 ) returns a discounted return for a particular state and action, assuming a current policy π. A first expression  2402  represents the greedy policy. When the reinforcement-learning-based controller is in a state s, the greedy policy selects a next action a′ for which the discounted expected return value is maximum among all possible actions a. As discussed above, the greedy policy generally does not allow a reinforcement-learning-based controller to efficiently find optimally efficient trajectories and optimal state/action pairs, and may not allow a reinforcement-learning-based controller to efficiently find optimally efficient trajectories regardless of the control/learning period during which the reinforcement-learning-based controller operates. The ϵ-greedy policy  2406  selects a next action a′ according to the greedy policy with a probability of 1−ϵ and selects a next action randomly from A with a probability of ϵ. In general, c as a relatively low value, such as 0.1 or 0.01, so that, most of the time, the ϵ-greedy policy selects a next action with the maximum discounted-return value. However, occasionally, the ϵ-greedy policy randomly selects a next action, so that, over time, the reinforcement-learning-based controller tries a wide variety of the many possible control decisions. By exploring the state/action space, the reinforcement-learning-based controller gradually learns to assign accurate discounted expected-return values to the various different state/action pairs so that the policy can be optimized. The SoftMax policy  2408  randomly selects a next action a′ from A with the probability  2410 , which corresponds to the Boltzmann distribution used in statistical mechanics. When the temperature factor τ has a low value, approaching 0, the probabilities of selection very dramatically with the estimated discounted return for the state/action, but when the temperature factor τ has a large value, the differences in the probabilities of selection diminish. Like the ϵ-greedy policy, the SoftMax policy favors selection of an action with the greatest estimated return value, but occasionally selects non-optimal actions in order to facilitate state/action space exploration. 
       FIG. 25  illustrates one implementation of a reinforcement-learning-based application manager that employs state/action-space exploration via the above-discussed ϵ-greedy policy. As indicated by expression  2502 , the policy employed by this implementation, π(b), selects a next action a′ with maximum estimated value with a probability of 1−ϵ and randomly selects the next action a′ from A the probability of ϵ, and is therefore an ϵ-greedy policy. In this implementation, as indicated by expression  2504 , there is no explicit policy-update function, unlike the case in the implementation illustrated in  FIG. 18 . Instead, a state/action-value update function U Q ( )  2506  is employed. This function updates the state/action value Q(b,a) by adding to the state/action value Q(b,a) the product of a learning rate a  2508  and an estimate of the most recent return value  2510 , where r is the reward received from executing action a, γ is the above-discussed discount rate, and b′ and a′ are the updated belief distribution and new selected action following execution of action a. Diagram  2512  illustrates the application manager logic that replaces the logic  1820  previously shown in  FIG. 18 . After execution of an action a, the universe returns the resulting reward r and observation vector o via path  2514 . If the termination condition has occurred, as determined in step  2516 , the application manager terminates, in step  2518 . Otherwise, in step  2520 , the application manager generates an updated belief distribution b′ using the belief-distribution-update function that, in turn, considers the returned observation vector o returned by the managed environment, and, in step  2522 , applies the policy ( 2502 ) to generate a next action a′ using the updated belief distribution b′. Then, in step  2524 , the application manager updates the discounted return value for the preceding action and belief distribution using the state/action-value update function  2506 . In step  2526 , the application manager stores the updated belief distribution as the current belief distribution and then returns the next action a′ to the managed environment via path  2528 . 
     As discussed above, for even modest numbers of possible actions and states, the state/action space can be enormous. In many real-world scenarios, there may be enormous numbers of possible actions and states, as a result of which the state/action space may be many tens of orders of magnitude larger than could possibly be practically exhaustively searched by exploration policies. Furthermore, there would be insufficient memory in even the largest distributed computing systems for maintaining current discounted values for each possible state/action pair. For these reasons, as indicated by expression  2530 , the reinforcement-learning-based controller uses a parameterized function Q t (s,a) that returns, at any point in time t, an estimate of the value of the state/action pair s/a. The function Q t (s,a) is a function of n parameters contained in a parameter vector θ t . As indicated by expression  2532 , the action-value update function U Q ( ) updates the parameter values via a gradient-descent method rather than updating a stored action value Q(b,a). Thus, at time t+1, the previous parameter vector θ t  is updated to parameter vector θ t+1 . 
       FIG. 26  illustrates rewards resulting from various actions issued to the managed environment by the application manager. Plane  2602 , containing an action axis  2604  and a state axis  2606 , represents a portion of the possible state/action pairs, and the rewards received by executing the action of a state/action pair when the managed system is in the state of the state/action pair are represented by small filled disks, such as filled disk  2608 . No rewards are shown for many positions on the plane, indicating that the set of valid or reachable state/action pairs may not be the entire cross product of the set of possible actions A in the set of possible states S. In many cases, the reward returned from execution of an action has the value 0, as a result of which the filled disk representing the reward is coincident with plane  2602 . However, certain state/action pairs are associated with the positive rewards, such as positive reward  2610 , or negative rewards, such as negative reward  2612 . Consider action a 8    2614 . When in state s 2    2616 , execution of action a 8  by the managed system generates a very large positive reward  2618 . However, when in state s 7    2620 , execution of action a 8  by the managed system generates a very large negative reward  2622 . This negative reward may indicate that execution of action a 8  by the managed system when in state s 7  has a very deleterious effect on the managed system, perhaps even causing data loss or a system crash. This, of course, is a very undesirable outcome, and it would be foolish to implement the application manager in such a way that it would inadvertently explore such deleterious state/action pairs. However, action a 8  clearly has a very positive result when executed in state s 2 , and thus it would also be foolish to entirely remove action a 8  from the possible set of actions A. Action a 8  may, in fact, be critical to optimal control of the managed system. The currently disclosed safe-operation-constrained reinforcement-learning-based application manager is designed and implemented in order to allow state/action-space exploration so that the application manager can learn, over time, the action values and state values for the managed system and thus achieve an optimal or near-optimal management policy while, at the same time, constraining action selection to avoid issuance, by the application manager, of clearly deleterious actions for execution by the managed system. 
       FIG. 27  illustrates vectors containing numerical elements that can be considered to represent points, areas, or volumes within a Euclidean space. The Euclidean space in  FIG. 27  is a 3-dimensional Euclidean space, since it is impossible to intuitively represent higher-dimensioned spaces in figures. The 3-dimensional Euclidean space is defined by the three familiar orthogonal axes x, y, and z  2702 - 2704 . The three-element vector  2706  can be interpreted as a containing the coordinates for the point  2708  in three-dimensional Euclidean space. Of course, this vector may be alternatively interpreted in many other ways. For example, the first element may be interpreted as the y coordinate rather than the x coordinate and the second element may be interpreted as the x coordinate rather than the y coordinate. As another example, the numeric values may be interpreted as the coordinate values divided by 10, so that the three-dimensional point is actually much further way from the origin  2710 . The five-element vector  2712  may be interpreted as containing an x-coordinate value  2714 , a range for the y-coordinate value  2716 , with the range expressed as a low value and a high value, and a range for the z-coordinate value  2718 . By this interpretation, vector  2712  may represent the area  2720 . The six-element vector  2722  may be interpreted as containing ranges for all three coordinates, representing, by this interpretation, volume  2724 . By adjusting some of these values, the volume can be expanded or contracted in each of the three different directions corresponding to the three coordinate axes. Similarly, by varying the values in the five-element vector  2712 , according to the above-discuss interpretation of the numeric values in the vector, the area  2720  may be expanded or contracted in the y and z directions and may be shifted from left to right with respect to the x axis. 
       FIG. 28  illustrates applying a filter to an action vector in order to prevent issuance of an action, by an application manager, known to have deleterious consequences. The example action vector  2802  describes a system call to the operating system of a server in order to carry out a binary partitioning of a mass-storage device within the server. In  FIG. 28A , a server is represented by a block diagram  2804  showing a mass-storage device  2806  partitioned into two partitions  2808 - 2809 , a hardware communications port  2810 , and hardware  2812 , virtualization  2813 , operating system  2814 , and application  2816  layers. The action vector  2802  includes an indication of a server identifier  2818 , a communications address for the server  2820 , an indication of the partition operating-system call represented by the action  2822 , an identifier for the mass-storage device  2024 , and the size of one of the two partitions  2826 . This action vector can be emitted by the application manager to the managed system in order to carry out partitioning of the mass-storage device within a particular server. The operating-system call can accept partition sizes from 0 to the total storage capacity of the mass-storage device. For example, the numerical value  2826  may range from 0 to 1. This means that each partition can range from empty to the total capacity of the mass-storage device, as indicated by diagram  2830 . However, it may have been discovered that, because of certain bugs or anomalies in the managed system, unless each of the two partitions has a minimum size greater than 0, certain types of other actions issued by the application manager may result in server crashes and even more widespread and serious problems. Therefore, it would be highly imprudent to allow the application manager to employ an exploration-based policy that would explore a partition action with a final-element value  2826  less than the minimum size needed to avoid server crashes and other problems. In other words, action vector  2802  can be thought of as representing a large number of different possible actions occupying a hyper-volume in a five-dimensional space. However, because of the problem with less than minimum size partitions, it would be desirable to constrain the application manager to a smaller hyper-volume that does not contain actions having a numerical value in the final element  2826  less than the minimum partition size or greater than a corresponding maximum partition size. Thus, the desired partition value should fall between the minimum partition size  2832  and a maximum partition size  2834  that avoids either the two partitions having less than a minimum size, as shown in diagram  2836 . The change in the area or volume corresponding to a set of action vectors can be thought of as applying a safe-operation constraint in order to avoid issuance, by the application manager, of clearly deleterious actions to the managed system. This can be accomplished by applying a filter  2840  to the action vector. Filter  2840  contains an if-else statement that sets the partition-size value to the minimum partition size, in the case of the partition-size value is less than the minimum partition size, and sets the partition-size value to a maximum partition size if the partition-size value is greater than the maximum partition size. By applying filter  284  to an action vector of the partition-a-mass-storage-device type, the application manager can ensure that the partition sizes are constrained, as indicated by  2836 , and that no deleterious partition-a-mass-storage-device actions are issued to the managed system. 
       FIG. 29  illustrates a second type of application-vector filter. The filter discussed above, with reference to  FIG. 28 , constrains actions, based on known understandings of their potential deleterious effects, to safe areas, volumes, or hyper volumes in state/action space. A second type of filter considers both an action vector as well as a prediction of the observation vector, o′, or a portion of that vector, that will be returned following execution of the action by the managed environment. An example filter  2902  is shown in  FIG. 29 . In a first if statement  2904 , the filter considers the m th  element of the predicted observation vector o′. When the m th  element of the predicted observation vector o′ has a value greater than a first threshold value, the value stored in the n th  element of the action vector is decreased by half until the value stored in the n th  element of the action vector falls below a maximum value. In a second if statement  2906 , when the w th  element of the predicted observation vector o′ is greater than the x th  element of the predicted observation vector o′, and when the y th  element of the predicted observation vector o′ is greater than a second threshold value, the p th  element of the action vector is set to 0. In a third if statement  2908 , when either of the w th  and v th  elements of the predicted observation vector o′ is 0, the action vector is set to NULL. These are, of course, but a few examples of the type of logic that may be included in the second type of filter. The second type of filter differs from the first type of filter in that action vectors are subject to constraints based on predicted results from executing them, rather than based on known safe boundaries. The predicted observation vector o′ may, in certain implementations, be obtained by execution of various parameterized functions, rather than consulting tabular information. 
       FIGS. 30A-B  illustrate a first filtering subsystem that filters actions with respect to known constraints, as discussed above with reference to  FIG. 28 . An action vector  3002  is analyzed  3004  to determine the type of action vector and to direct the input action vector into an appropriate filter stack. In the example shown in  FIG. 30A , dashed arrow  3006  indicates that the input action vector  3003  is directed to filter stack  3008  as a result of the analysis. Each filter in the filter stack is successively applied to the potentially modified action vector emitted from the preceding filter or, in the case of the first filter  3010 , is applied to the input action vector. Following application of the final filter in the filter stack  3012 , the filter subsystem determines, in a conditional step  3014 , whether or not the filtered action vector should be submitted to an additional filter stack or should be output. In the first case, the action vector is resubmitted to a next filter stack, as indicated by arrow  3016 , and in the latter case, either a NULL vector  3018  or a potentially modified action vector a′  3020  is output. The filters may be encoded as statements in a higher-level programming language, may be encoded as statements in a script language, may be encoded in logic statements, or may be otherwise encoded, depending on the implementation. In certain implementations, users may define the filter logic through graphical user interfaces. 
       FIG. 30B  illustrates a filter stack. An input action vector and an indication of the action-vector type  3030  are input to the first filter  3032  in the stack. After the first filter is applied to the action vector, the output from the filter is considered in conditional step  3034 . When the output is a NULL vector, the remaining filters in the stack are bypassed and the NULL vector is output, as indicated by path  3036 . Otherwise, the possibly modified action vector and action-vector type are submitted to the second filter  3038 . This process is repeated down through all of the filters of the stack, after which the previously described conditional step  3014  determines whether or not to forward the possibly modified action vector o another filter stack. The ability to redirect the output of one filter stack to another allows inheritance-like functionality, with an initial filter stack processing a generic class of action vectors and additional filter stacks processing more specific classes or types of action vectors within the generic class. More complex object-oriented implementations are also possible. 
       FIG. 31  illustrates observation prediction preceding application of one or more filters of the second type of filter to an action vector, as discussed above with reference to  FIG. 29 . An action-vector type  3102 , and an action vector a  3104 , and an observation vector o  3106  are submitted to an observations-prediction module  3108  which produces a predicted observation vector o′  3110 . The predicted observation vector o′, as discussed above, is the prediction of the observation vector that will be returned by the managers environment following execution of the action a. A small portion of an example type of prediction code  3112  is provided in  FIG. 31 , using similar illustration conventions as used in  FIG. 29 . Again, rather than predicting an observation vector o′, the observations-prediction module  3108  may indicate only changes to the current observation vector o, may provide on a partial predicted observation vector o′, or may use other methods to output the information needed for application the second type of filter. In the following discussion, for simplicity, generation of a complete predicted observation vector o′ is shown in the examples. 
       FIGS. 32A-B  illustrate a second filtering subsystem that filters action vectors with respect to observation predictions, as discussed above with reference to  FIG. 29 .  FIG. 32A  is nearly identical to  FIG. 30A , with the exception that the second filtering subsystem receives both an action vector representing an action a  3202  as well as a predicted observation vector o′  3204 . Similarly,  FIG. 32B  shows filter-stack implementation, which is nearly identical to  FIG. 30B , with the exception that the input  3206  includes a predicted observations vector o′. 
       FIG. 33  illustrates a programmatic user interface that may be provided to users to define filters and filter stacks for constraining action vectors. The programmatic user interface includes libraries that define various fundamental data types  3302  and various functions  3304 . The data types may include an action-type  3306 , a list of action types  3308 , a filter type  3310 , a filter-stack type  3312 , a first filtering subsystem  3313 , and a second filtering subsystem  3314 . The functions may include functions to create, delete, and edit filters  3316 , functions to create and edit filter stacks as well as to add and remove filters from filter stacks  3318 , and functions to add and remove filter stacks from the first and second filtering subsystems  3320 . Of course, the detailed function declarations and argument footprints will vary significantly depending on specific implementations as well the data-type declarations. 
       FIGS. 34A-B  illustrate a simple graphical user interface that may be provided to users for definition of action-filtering filters, filter stacks, and filtering subsystems.  FIG. 34A  provides a dashboard-like interface  3402  that includes a logic-entry feature  3406 , a list of displayed action types  3408 , and a graphical representation of a particular action type  3410  selected  3412  from the displayed action-type list  3408 . The input filtering logic can be named by a name-input feature  3414  and saved, using a save feature  3416 , as a filter.  FIG. 34B  shows a dashboard-like interface  3420  that allows a user of an application manager to define filter stacks and add them to filtering subsystems. This interface displays a list of filters  3422 , a list of action types  3424 , a list of action types accepted by the filter stack being defined  3426 , and a list of filters already added to the filter stack being defined  3428 . A user may select action types from the displayed action-type list  3422  for addition to the filter stack, can select action types already added to the filter stack for deletion, can select filters from the displayed list of filters  3422  for addition to the filter stack, and can select filters in the displayed list of filters already added to the filter stack  3428  for removal. In addition, the filter stack can be named via a naming feature  3430  and can be added to either of the two filtering subsystems by features  3432  and  3434 . Of course, many different possible alternative graphical user interfaces can be implemented. 
       FIG. 35  illustrates application-manager logic of one implementation of the currently disclosed safe-operation-constrained reinforcement-learning-based application manager. This logic is presented using the same illustration conventions as used in  FIGS. 18 and 25 , discussed above. The logic shown in  FIG. 35  adds additional steps to those shown in  FIG. 25  and adds calls to filtering subsystems in order to incorporate action filtering of both types, discussed above with reference to  FIGS. 28 and 29 , into the logic shown in  FIG. 25 . The managed environment is represented by block  3502 , as in  FIG. 18 . The application manager is represented by block  3504 , as in  FIGS. 18 and 25 . In step  3506 , the application manager determines whether or not termination conditions are true. If so, the application manager terminates  3507 . Otherwise, in step  3508 , an updated belief distribution b′ is generated, as in step  2520  of  FIG. 25 . In step  3509 , a next action a′ is obtained from the policy, as in step  2522  in  FIG. 25 , and the application manager determines the action type, a_type, of the next action a′. The action type may be encoded within the action vector representing the action or may be otherwise obtained via a function call. In step  3510 , the application manager determines the probability pa of the next action being selected via a call to the probability-returning policy function π(b′, a′), discussed above with reference to  FIG. 15 . In step  3511 , the application manager determines a threshold probability value thresh by dividing pa by parameter h. In step  3512 , the application manager sets a temporary set variable B to the value of A. When the cardinality of the set of actions A is large, of course, methods are used to avoid actually copying the contents of the set variable A, but to provide for the equivalent of non-replacement selection of actions from A. In step  3513 , the application manager submits the next action a′ to the first filtering subsystem discussed above with reference to  FIG. 30A . When the first filtering subsystem returns a NULL output, the while-loop of steps  3514 - 3521  is executed by the application manager. Otherwise, when the first filtering subsystem returns a non-NULL output, control flows to step  3522 . In the while-loop of steps  3514 - 3521 , the next action a′ is removed from the set of actions A, in step  3515 , and, in step  3516 , the application manager determines whether or not the set of actions A is now an empty set. If so, then a NULL action or an indication of no action is returned to the managed environment via step  3518 . Otherwise, in step  3517 , a new next action a′, selection probability pa, and action type a_type are determined, as in steps  3509  and  3510 . If the probability of selection of the new action is less than the threshold probability thresh, as determined in step  3519 , a NULL action or an indication of no action is returned, via step  3518 , where a special action-value update function, U′ Q ( ), is called to update the action-value function for the case of a filtered-away action. Otherwise, in step  3520 , the application manager calls the first filtering subsystem to filter the new next action a′. When the first filtering subsystem outputs a NULL value, as determined in step  3521 , control returns to step  3515  for a next iteration of the while-loop of steps  3514 - 3521 . Otherwise, in step  3522 , the application manager calls a routine “predict observations” to generate a predicted observation vector o′, as discussed above with reference to  FIG. 31 . Then, in step  3523 , the application manager submits the new next action a′ and the predicted observation vector o′ to the second filtering subsystem. When the second filtering subsystem returns a NULL value, as determined in step  3524 , control flows back to the while-loop that begins with step  3514 . Otherwise, in step  3525 , the action-value function is updated, as in step  2524  in  FIG. 25 , the new belief distribution is accepted as the current belief distribution in step  3526 , as in step  2526  in  FIG. 25 , and, in step  3527 , the set A it is restored to the value that it had at step  3512 . In step  3528 , the new action a′ is returned to the managed environment. Thus, the application manager, in the described implementation, uses an exploratory policy, filters new actions, and when filtering produces no values, continues to try to generate new non-NULL actions, provided that the new actions have a selection probability greater than some threshold value. Otherwise, a NULL action or an indication of no action is returned to the managed environment. Of course, a NULL action means that no action is to be executed by the managed environment, as a result of which a reward of 0 is generally returned by the managed environment. 
     Although the present invention has been described in terms of particular embodiments, it is not intended that the invention be limited to these embodiments. Modification within the spirit of the invention will be apparent to those skilled in the art. For example, any of a variety of different implementations of the currently disclosed safe-operation-constrained reinforcement-learning application manager can be obtained by varying any of many different design and implementation parameters, including modular organization, programming language, underlying operating system, control structures, data structures, and other such design and implementation parameters. A wide variety of different types of filters can be employed to filter actions by the application manager in order to constrain expiration of state/action pairs to those that do not produce deleterious consequences for the managed environment. As discussed above, these filters can be encoded in different ways. Additional types of filters may be used, in alternative implementations, along with possibly additional types of filtering subsystems. In certain implementations, only a single filter stack is used to filter all possible action vectors. 
     It is appreciated that the previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.