Center for Analysis and Design of Intelligent Agents

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T-720-ATAI-2018

Lecture Notes, W3: Tasks & Environments

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 no 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.

What Kind of Task-Environments?

Environment	Large number of potentially relevant variables.
Task	Ditto.
	Medium number of Solutions.
	Instructions: possibly.

Characterizing a World

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, plus optional constraints on the Goal.
	“Goal” definition	<m>G subset S </m> attached to a Problem.

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 along with a Task by a Teacher.
Teacher	The Agent assigning a Task to another Agent (student).

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Table of Contents

T-720-ATAI-2018

Lecture Notes, W3: Tasks & Environments

What Kind of Worlds?

What Kind of Task-Environments?

Characterizing a World

Related Concepts