Multiagent Systems

1. Multiagent Systems Course Overview and Introduction

2. Course Overview • Course Description: Multiagent systems has emerged as an important research area with applications in many fields of computer science, including artificial intelligence, e-commerce, sensor networks, distributed computing and information retrieval, information security, and robotics. In multiagent systems, multiple autonomous entities with their own objectives have to interact and make decisions. This course explores techniques for the modeling, design, decision making, and communication in these systems. While the course will focus on frameworks, methodologies, and algorithms, it will investigate (and illustrate) them in the context of a wide range of application areas, including multi-robot systems, distributed scheduling and resource allocation, sensor networks, distributed information extraction, and network security.

3. Course Overview • Course Topics: • Representations and modeling • Game theory: • Matrix and repeat games, stochastic and Bayesian games • Auction mechanisms • Sealed bid and Vickrey auctions, English and Dutch auctions, combinatorial auctions • Multiagent Communication • Multiagent Learning • Coalitional Game Theory

4. Course Overview • Prerequisites: Many of the techniques covered in this course are based on probabilities and random processes and a basic background in statistics is required for the course (CSE 5301 or equivalent). In addition, experience with Algorithms (CSE 5311), Artificial Intelligence (CSE 5360), and programming will be useful to perform assignments and projects

5. Course Overview • Course Page and Materials Textbook: Y. Shoham, K. Leyton-Brown, Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations, Cambridge Press, 2009. (Available at http://www.masfoundations.org/downloading.html ) Course web page: http://www-cse.uta.edu/~huber/cse6369_multi-agent. E-Mail: huber@cse.uta.edu Tentative Office Hours M 2:00-2:45, W 7:00-8:00, Th 2:00-3:00 ERB 128 or ERB 522

6. Course Overview • Course Work: • In-class presentation of a technical paper • Two homework assignments: • Two small projects • Final course project • Grading Policy:

7. Multiagent Systems and Distributed Decision Making • Multiagent Systems: A system consisting of multiple agents that interact (directly or indirectly through the environment) and reason and make decisions individually (generally with incomplete local information). • Centralized Systems: A central coordinator determines the actions that each agent in the system should take • Distributed Systems: Each agent has to determine the action to be taken (including the exchange of information) based on its local information

8. Collaborative and Competitive Systems • Collaborative Multiagent Systems: • Agents have the same desires • Well defined optimality • Issues: • Coordination between distributed agents • Communication and bandwidth • Competitive Multiagent Systems: • Different desires for different agents • Optimality only defined for individual agents • Issues: • Optimal decision making • Interpretation of communication (agents can lie)

9. Multiagent Decision Making • Agents and Rationality To make decisions, agents have to be able to determine what action is the best for them. • Rationality: • Rational agents make the decisions that result in the highest payoff for them (self-interest) • Rational agents do not take actions to harm others • Payoff is quantified in terms of utility • Multiagent Systems and Optimality • Maximizing an agent’s utility is not always rational • The Commons problem

10. Multiagent Decision Making • Multiagent Decisions: • In competitive systems (even deterministic ones) optimal decisions often have to be nondeterministic • An agent’s utility achieved depends not only on its own actions but also on the actions of the other agents • Decision Theory: • Combines probability, utility theory and rationality to allow an agent to determine the best action in a given situation

11. Multiagent Systems Background - Probability

12. Probability • Bayesian probabilities summarize the effects of uncertainty on the state of knowledge • Probabilities represent the values of statistics • P(o) = (# of times of outcome o) / (# of outcomes) • All types of uncertainty are incorporated into a single number P(H | E) • Probabilities follow a set of strict axioms

13. Probability • Random variables define the entities of probability theory • Propositional random variables: • E.g.: IsRed, Earthquake • Multivalued random variables: • E.g.: Color, Weather • Potentially Real-Valued • E.g.: Height, Weight

14. Axioms of Probability • Probability follows a fixed set of rules • Propositional random variables: • P(A)  [0..1] • P(T) = 1 , P(F) = 0 • P(AB) = P(A) + P(B) – P(AB) • P(AB) = P(A) P(B|A) • xValues(X) P(X=x) = 1

15. Probability Syntax • Unconditional or prior probabilities represent the state of knowledge before new observations or evidence • P(H) • A probability distribution gives values for all possible assignments to a random variable • A joint probability distribution gives values for all possible assignments to all random variables

16. Conditional Probability • Conditional probabilities represent the probability after certain observations or facts have been considered • P(H|E) is the posterior probability of H after evidence E is taken into account • Bayes rule allows to derive posterior probabilities from prior probabilities • P(H | E) = P(E | H) P(H)/P(E)

17. Conditional Probability • Probability calculations can be conditioned by conditioning all terms • Often it is easier to find conditional probabilities • Conditions can be removed by marginalization • P(H) = E P(H|E) P(E)

18. Joint Distributions • A joint distribution defines the probability values for all possible assignments to all random variables • Exponential in the number of random variables • Conditional probabilities can be computed from a joint probability distribution • P(A|B) = P(AB)/P(B)

19. Inference • Inference in probabilistic representation involves the computation of (conditional) probabilities from the available information • Most frequently the computation of a posterior probability P(H|E) form a prior probability P(H) and new evidence E