The ability to solve problems creatively has been crucial for the adaptation and survival of humans throughout history. In many real–life situations, cognitive processes are not isolated. Humans are social, they communicate and form groups to solve daily problems and make decisions. Therefore, the final output of cognitive processes can come from multi–brains in groups rather than an individual one. This multi–brain output can be largely different from the output that an individual person produces in isolation. As a result, it is essential to include team–level processes in cognitive models to make a more accurate description of real– world cognitive processes in general and problem solving in particular. This research aims to answer the general question of how working in a team affects creative problem solving. For doing that, first, we propose a computational model for multi-agent creative problem solving. Then, we show how the model can be used to study the factors that are involved in creativity in teams and potentially will suggest answers to questions such as, ‘how team size is related to creativity’.

Operating and interacting in an environment requires the ability to manage uncertainty and to choose definite courses of action. In this thesis we look to Bayesian probability theory as the means to achieve the former, and find that through rigorous application of the rules it prescribes we can, in theory, solve problems of decision making under uncertainty. Unfortunately such methodology is intractable in realworld problems, and thus approximation of one form or another is inevitable. Many techniques make use of heuristic procedures for managing uncertainty. We note that such methods suffer unreliable performance and rely on the specification of ad-hoc variables. Performance is often judged according to long-term asymptotic performance measures which we also believe ignores the most complex and relevant parts of the problem domain. We therefore look to develop principled approximate methods that preserve the meaning of Bayesian theory but operate with the scalability of heuristics. We start doing this by looking at function approximation in continuous state and action spaces using Gaussian Processes. We develop a novel family of covariance functions which allow tractable inference methods to accommodate some of the uncertainty lost by not following full Bayesian inference. We also investigate the exploration versus exploitation tradeoff in the context of the Multi-Armed Bandit, and demonstrate that principled approximations behave close to optimal behaviour and perform significantly better than heuristics on a range of experimental test beds.