Decision Making Under Uncertainty - Bayesian Techniques

The Group David Beirne Explanation of terms Introduction to strike networks problem. Nag Benjum Introduction to Bayesian Networks. Examples of Bayesian Networks. Gordan Ingram Application of Bayesian Networks in strike networks problem. Pros and Cons of Baysian Networks.

Decision Making? Why does our AI need to make decisions? –One of the keys to human perception of intelligence is in the ability of an entity to react to external stimuli and to exhibit varying (and often unpredictable) behaviour. Real life decision making is often based on the outcome of past experience of similar situations or a learned response to a given situation (however errational), rather than a numerical reasoning based on known and quantifiable measurements or results.

Uncertainty? “The information necessary to assign numerical probabilities is not ordinarily available. Therefore a formalism that required numerical probabilities would be epistemologically inadequate.” (McCarthy and Hayes, MI 4, 1969) What is Uncertainty? –“Lack of sure knowledge or predictability because of randomness.”

Uncertainty In AI Games are played completely within the domain of a virtual world with restrictions enforced on the player by the computer. As such uncertainty may be artificially introduced in order to create more believable character responses. There are however areas in which uncertainty is implicit as in the need to pre-empt a players strategy or attempt to understand the motivation behind a players current course of action in order to predict their future actions. Believable AI, therefore should be able to respond in a way in which it can make mistakes. However the AI agent should also learn from those mistakes (and hopefully not repeat them too often).

Real Life Decision Making Under Uncertainty In real life when an unpredicted event occurs, we may not know the probability of the event taking place, but will (hopefully) be able to cope with the uncertainty that this possibility engenders. –You get to the train station. –Your train is cancelled. –How are you decide what to do next? Find an alternative train? Get a Taxi / Bus? Walk? Drive? Forget it?

Bayesian Networks A Bayesian network (or a belief network) is a probabilistic graphical model that represents a set of variables and their probabilistic independencies. Bayesian networks are directed acyclic graphs whose nodes represent variables, and whose edges encode conditional independencies between the variables. Nodes can represent any kind of variable, be it a measured parameter, a latent variable or a hypothesis. They are not restricted to representing random variables.

Example in Game AI Strike Networks Lets consider a simple of a fighting game - along the lines of Street Fighter, Virtua Fighter, DOA, or Tekken. How can we create a computer controlled character which can predict a players next move and act accordingly to defend itself? To keep things simple, let’s assume the player can perform three types of action: punch, kick, or throw. We’re going to keep track of three-action combinations. –For every action we're going to calculate a probability for that action given the previous two. –This will enable us to capture three-action combinations. –more are possible at the cost of memory / increased complexity of our network. Virtua Fighter 5 (SEGA-AM2) Street Fighter 2 Alpha (CAPCOM) Dead or Alive 4 (Team Ninja)

Strike Networks In this model, we call the first action in the combination event A, the second strike event B, and the third strike event C. We assume that the second action, event B, in any combination is dependent on the first action, event A. We also assume that the third action, event C, is dependant on both the first and second action, events A and B. Combinations can be anything—punch, punch, throw; or kick, punch, kick; and so on. To better understand this, lets take a closer look at how Bayesian Networks work. AB C