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DA7. Decision Networks

Statement

Define “Decision Networks” in your own words in terms of variables and utility.

Then consider the following scenario:

A robot is dedicated to serving coffee for office employees. But it spills 20% of the time while pouring the coffee and on the way to the employee’s desk, making a mess. There are some decisions the robot can take for a better outcome. For example, improving its precision, or it can do nothing extra for a medium outcome. Complete the following:

  1. Draw a Decision Network based on chance nodes, decision nodes, and a utility node.
  2. Explain your Decision Network. For your response, you must design an approach for decision planning for the robot.
  3. Describe what optimization solution you would employ and why?

Answer

Define Decision Networks

Decision networks are belief networks that have been extended to include the utility of actions along with decision variables. Belief networks are directed acyclic graphs (DAGs) that include potential states and the probability (belief) that this state will occur along with the dependencies between these states. Decision networks draw chance nodes as ovals, decision nodes as rectangles, and utility nodes as diamonds (Poole & Mackworth, 2017).

The arcs coming into decision nodes represent the information that will be available when the decision is made. The arcs coming into chance nodes represent probabilistic dependence. The arcs coming into the utility node represent what the utility depends on. Decision networks are used to determine the best course of action based on the action that produces the greatest utility (Poole & Mackworth, 2017).

Decision Network for the Coffee Robot (1+2)

Let’s define the components of the decision network for the coffee robot:

  • Chance Nodes:
    • Spill: The probability of spilling coffee while pouring or en route. Domain: {Spill, NoSpill}
    • Mess: The probability of making a mess, a little spill does not make a mess. Domain: {Mess, NoMess}
  • Decision Nodes:
    • Pour: The decision to pour coffee. Domain: {Pour, NoPour}
    • Deliver: The decision to deliver coffee. Domain: {Deliver, NoDeliver}
    • Improve Precision: The decision to improve precision. Domain: {Improve, NoImprove}
  • Utility Node:
    • Utility: The utility of the outcome based on the decisions made. A number between 0 and 100 (higher is better).
    • Outcome: The final outcome of the decisions made. Domain: {Good, Medium, Bad}

Decision Network for Coffee Robot

  • This is an ordered sequence of decisions with the following sequence: Pour -> Improve Precision -> Deliver -> Improve Precision -> Outcome.
  • The 2 Improve Precision decisions are optional, that is, the robot can choose to improve its precision or do nothing extra (depending on the mess variable).
  • If the robot makes a Mess, it can invoke its Improve Precision process to keep the mess to a minimum.
  • The Mess variable is dependent on the Spill variable, as there are little spills that can be ignored.
  • The Outcome variable is an overall evaluation of the process, which is then used to calculate the Utility.
  • The table below shows the utility values for different combinations of decisions and outcomes.
Spill Mess Improve Precision Outcome Utility
Spill Mess Improve Bad 10
Spill Mess Improve Medium 50
Spill Mess Improve Good 60
Spill Mess Do Nothing Bad 20
Spill Mess Do Nothing Medium 40
Spill Mess Do Nothing Good 70
Spill No Mess Improve Bad 30
Spill No Mess Improve Medium 60
Spill No Mess Improve Good 80
Spill No Mess Do Nothing Bad 40
Spill No Mess Do Nothing Medium 70
Spill No Mess Do Nothing Good 90
No Spill Mess Improve Bad 20
No Spill Mess Improve Medium 50
No Spill Mess Improve Good 70
No Spill Mess Do Nothing Bad 30
No Spill Mess Do Nothing Medium 60
No Spill Mess Do Nothing Good 80
No Spill No Mess Improve Bad 40
No Spill No Mess Improve Medium 70
No Spill No Mess Improve Good 90
No Spill No Mess Do Nothing Bad 50
No Spill No Mess Do Nothing Medium 80
No Spill No Mess Do Nothing Good 100

Optimization Solution (3)

One possible improvement for the robot is to use variable elimination to eliminate the Mess variable and only consider the Spill variable. This requires the Spill to be quantified as opposed to being a binary; and this would simplify the decision-making process. The robot can then decide to improve precision based on the probability of spilling coffee and the utility of the outcome.

Another optimization is to utilize the expected utility of the outcomes to make decisions in a strategy such as Markov Decision Processes (MDP). MDPs are used to model decision-making processes where outcomes are uncertain and the utility of the outcomes is known. The robot can use history information to make educated guesses about future outcomes; for example, the utility is lower and the robot is more likely to spill if the order is for the room 10, which has a damaged floor that causes the robot to shake, so that the robot automatically improves precision for all orders to room 10.

Another optimization is to check the details of destination; for example, the destination has an expensive carpet. Or, to check the details of the coffee, as some liquids are more likely to spill than others. In both cases, the robot can automatically improve precision to prevent a mess.

References

  • Poole, D. L., & Mackworth, A. K. (2017). Artificial Intelligence: Foundations of computational agents. Cambridge University Press. https://artint.info/2e/html/ArtInt2e.html - Chapter 9 – Planning with Uncertainty.