CSE    571  Homework    1

CSE    571 
Homework    1

Only    typed    answers    will    be accepted.    
Be    precise    and    concise    in    your    answers. You    may add    hand-drawn    figures    when    necessary.    
Exercise    1.1    (5pt)
Suppose that the performance measure is concerned with just the first T    time steps of the environment and
ignores everything thereafter. Show that a rational agent’s action may depend not just on the state of the
environment but also on the time step it has reached. Assume that the agent has access to time.
Exercise    1.2 (15pt)
For each of the following assertions, say whether it is true or false and support your answer with
examples or counterexamples where appropriate. Use our vacuum domain ONLY.
a. An agent that senses only partial information about the state cannot be perfectly rational.
b. There exist task environments in which no pure reflex agent can behave rationally.
c. There exists a task environment in which every agent is rational.
d. Suppose an agent selects its action uniformly at random from the set of possible actions. There exists a
deterministic task environment in which this agent is rational.
e. Every agent is rational in an unobservable environment.
Exercise    1.3 (15pt)
Consider a modified version of the vacuum environment in which the geography of the environment—its
extent, boundaries, and obstacles—is unknown, as is the initial dirt configuration. The agent can go Up    
and Down    as well as Left    and Right. The agent can sense its current location and whether there is dirt in
it. The performance metric is to clean the space.
a. Can a simple reflex agent be perfectly rational for this environment? Explain.
b. Can a simple reflex agent with a randomized agent function (i.e., the action may be a random choice
from a set) outperform a simple reflex agent? 
c. Can you design an environment in which your randomized agent will perform poorly, when movements
are penalized?
Exercise    1.4 (15pt)
You    are    to    design    an    agent    that    moves    from    a start    location    to    a    goal    location    with    obstacles    in    between.    
Assuming    that    your    agent    knows    about    the    start    and    goal    locations and    can    sense    its    current    location.    
However,    it    can    only    detect    an    obstacle    when    it    is    next to it    (i.e.,    tactile    sensing).    A    simple method    that    allows    
the    agent    to    solve    the    problem    is    to    follow    the    procedure:
1)    head    toward    goal
2)    follow    the    contour    of    an obstacle encountered (in    a    fixed    direction) until    you    can    head    toward    the    goal    
again
3)    continue
a. What    is    this    type    of    agent? Can    you    specify the    agent    function?
b. Can    this    agent    always    reach    the    goal location? If    your    answer    is    yes, explain    your    answer.    Otherwise, justify
your    answer by    giving    an    environment    where    it    won’t work.