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=====T-720-ATAI-2018=====
====Lecture Notes, W3: Tasks & Environments====
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====Task-Environments: Key Concepts====

|  Task  | A Problem that can be assigned. Typically comes with Instructions (guide to Solutions).  |
|  Problem  | A Goal with (all) relevant constraints (≈ requirements).  |
|  Problem Family |  A set of problems that are similar in some (important) ways; a Problem plus variations of that Problem.  |
|  Goal  | A (future) State to be attained, plus optional constraints on the Goal.  |
|  State  | A set of values (with error bounds) for a set of variables relevant to a Goal.  |
|  Environment  | A set of constraints relevant to a Task but not counted as part of a Task proper.   |
|  World  | A set of constraints that a set of Environments have in common.  |
|  Constraint  | A set of factors that limit the flexibility of that which it constrains.  |
|  Solution  | The set of (atomic) actions that can achieve a Goal.  |
|  Action  | The changes an Agent can make to variables relevant to a Task-Environment.  |
|  Plan  | A partial way to accomplish a Task.   |
|  Instructions  | Partial Plan for accomplishing a Task, typically given to an Agent along with a Task by a Teacher.  |
|  Teacher  | The Agent assigning a Task to another Agent (student), optionally in charge of Instructions.  |

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====Task-Environment Constraints====

|  Solution Constraint  | Reduces the flexibility for producing a Solution.   |
|  Task Constraint  | Limits the allowed Solution Space for a Problem. Can help or hinder a Task to be achieved.   |
|  Solution Space  | The amount of variation allowed on a State while still counting as a Solution to a Problem.  |
|  Task Space  | The size of variations on a Task that would have be explored with no up-front knowledge or information about the Solution Space of a Problem.  |

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====Limited Time & Energy====

| Task | All tasks have a limited time & energy: No Task exists that can be performed with infinite energy, or for for which infinite time is available for achieving.  |
|  LTE  | Limited Time & Energy.  |

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====Problems in Task-Environments====

|  Closed Problem  | May be assigned as a Task with known Time & Energy for achieving a solution.  |
|  Example  | Doing the dishes.  |
|  Plans for Closed problems | Can be reliably produced for closed problems, e.g. in the form of Instructions.  |
|  Open Problem  | A Problem whose solution is unknown and cannot be obviously assumed from analogy with similar problems whose solution is known. Cannot be guaranteed a solution with LTE.  |
|  Example  | Any research problem for which no known solution exists.  |
|  Plans for Open problems | Cannot be reliably produced.   | 

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====What Kind of Worlds?====
|  Balance  | The Worlds we are interested in strike a balance between completely dynamic and completely static. \\ They also strike a balance between completely deterministic and completely random; some regularity must exist at a level that is observable initially by a learning agent.  |
|  Completely static  | No (or little) need for learning.   |
|  Completely random   | Learning is of no use.   |
|  Limited time  | No Task, no matter how small, takes zero time. \\ "Any task worth doing takes time." \\ All implemented intelligences will be subject to the laws of physics.   |
|  Limited energy  | "Any task worth doing takes energy." \\ All implemented intelligences will be subject to the laws of physics.   |
|  No task takes zero time or energy  | If <m>te</m> is a function that returns time and energy, an act of perception \\ <m>te(p in P) > 0</m> \\ a decision <m>d</m> in \\ <m>{te({d in D}) > 0}</m>, \\ and an action \\ <m>te(a in A) > 0</m>. \\ It follows deductively that since any Task requires at the very least one of each of these, in the minimum case to decide whether the Goal of a Task <m>T</m> is achieved, then \\ <m>te(T) > 0</m>. \\ Anything that takes zero time or zero energy is by definition not a Task.     |

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====What Kind of Task-Environments?====
|  Environment  | Large number of potentially relevant variables.  |
|  Task  | Ditto.    |
|  | Medium number of Solutions.  |
|  | Instructions: possibly.  |
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====How it Hangs Together: Worlds, Environments, Tasks, Goals====
|  World  | A set of variables with constraints and relationships. \\ <m>W = {lbrace V,F rbrace}</m> \\ where <m>V</m> is a set of variables and <m>F</m> is a set of transition functions / rules describing how the variables can change.  ||
|  :::    | Static World   | Changes State only through Agent Action. |
|  :::    | Dynamic World   | Changes State through Agent Action and through other means. |
|  :::   | Physical World  | In a physical world \\ <m>W = {lbrace}x_1, x_2, ... x_n, f_1, f_2, ... f_m {rbrace}</m> \\ <m>x</m> are real-valued variables, \\ <m>V_{t+delta} = F(V_{t})</m> \\ and \\ <m>{lbrace}{x}over{.}_1, {x}over{.}_2, ... {x}over{.}_n {rbrace}</m> \\ represent the first derivative of the variables during continuous change.    |
|  State  | A set of values (with constraints, e.g. error bounds) for a set of variables <m>x</m> relevant to a World. \\ For all practical purposes, in any complex World we will speak of "State" even for sub-states, as most useful States will be sub-states, since there will always be a vastly higher number of "don't care" variables than the variables listed for e.g. a Goal State.  ||
|     |   State definition | <m> S = V  </m> \\ where   \\ <m> {{lbrace}x_l , x_u{rbrace}} {|}  {{x_l <= x <= x_u}} </m> \\ \\ define lower and upper bounds on acceptable range for each <m>x</m> to count towards the State, respectively.    |
|  Environment  |<m>{E = {lbrace V_E, F_E rbrace} + C delim{|} V_E subset V & F_E subset F }</m> \\ \\ \\ where <m>C</m> are additional constraints on \\ <m>V, F</m> \\ and some values for <m>V</m> are fixed.   ||
|  Task  | A Problem that can be assigned in an Environment. Typically comes with Instructions (guide to Solutions, partial Solution or full Solution - at some level of maximum detail).  ||
|    | "Task" definition   | An assigned Problem.    |
|  Task-Environment  | An Environment in which one or more Tasks may be assigned.   ||
|  Problem  | A Goal with (all) relevant constraints imposed by a Task-Environment.  ||
|  Goal  | A (future) (sub-) State to be attained during period //t//, plus other //optional// constraints on the Goal.  ||
|     | "Goal" definition   | <m>G subset S  </m> \\ \\ attached to a Problem.   |

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===Related Concepts===
|  Family  | A set whose members share one or more common trait within some sensible (defined) allowed variability, defined as one or more of the types of variables, number of variables, the ranges of these variables.  ||
|    |  Problem Family   | A set of problems that are similar in important ways; a Problem and its variations.  |
|  Domain  | A Family of Environments.  ||
|  Constraint  | A set of factors that limit the flexibility of that which it constrains.  ||
|  Solution  | The set of (atomic) actions that can achieve a Goal in a Task-Environment.  ||
|  Action  | The changes an Agent can make to variables relevant to a Task-Environment.  ||
|  Plan  | A partial way to accomplish a Task.   ||
|  |  Instructions  | Partial Plan for accomplishing a Task typically given to an Agent by a Teacher, along with a Task.  |
|  Teacher  | The Agent assigning a Task to another Agent (student).  ||


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