Artificial Intelligence: Foundations of Computational Agents,  3rd Edition

Chapter 12 Planning with Uncertainty

In retrospect… it is interesting to note that the original problem that started my research is still outstanding – namely the problem of planning or scheduling dynamically over time, particularly planning dynamically under uncertainty. If such a problem could be successfully solved it could eventually through better planning contribute to the well-being and stability of the world.

– George B. Dantzig (1991)

An agent that is not omniscient cannot just plan a fixed sequence of steps, as was assumed in Chapter 6. Planning must take into account the fact that an agent in the real world does not know what will actually happen when it acts, nor what it will observe in the future. An agent should plan to react to its environment.

What an agent should do at any time depends on what it will do in the future. For example, in a medical situation, sometimes tests hurt patients, but they are useful because they enable future actions. When an agent cannot precisely predict the effects of its actions, what it will do in the future depends on what it does now and what it will observe before it acts.

With uncertainty, an agent typically cannot guarantee to satisfy its goals, and even trying to maximize the probability of achieving a goal may not be sensible. For example, an agent whose goal is to minimize the probability of injury in a car accident would not get into a car or walk down a sidewalk or even go to the ground floor of a building, each of which increases the probability of being injured in a car accident, however slightly. An agent that does not guarantee to satisfy a goal can fail in many ways, some of which may be much worse than others.

This chapter is about how to take planning, reacting, observing, succeeding, and failing into account simultaneously. As George Dantzig, the inventor of linear programming, points out in the quote above, planning under uncertainty is essential for an intelligent agent.

An agent’s decision on what to do at any time (see Figure 2.10) depends on:

  • The agent’s ability. The agent has to select from the actions available to it.

  • What the agent believes and observes. An agent might like to condition its action on what is true in the world, but it only has access to the world via its sensors. When an agent has to decide what to do, it only has access to what it has remembered and what it observes. Sensing the world updates an agent’s beliefs. Beliefs and observations are the only information about the world available to an agent at any time.

  • The agent’s preferences. When an agent must reason with uncertainty, it has to consider not only what is most likely to happen but also what may happen. Some possible outcomes may have much worse consequences than others. The simple notion of a goal, considered in Chapter 6, is not adequate when reasoning under uncertainty because the designer of an agent has to trade off between different outcomes that may occur. For example, if an action results in a good outcome most of the time, but sometimes results in a disastrous outcome, it must be compared with performing an alternative action that results in the good outcome less often and the disastrous outcome less often and some mediocre outcome most of the time. Decision theory specifies how to trade off the desirability of outcomes with the probabilities of those outcomes.