A Bayesian Satisficing Model of Human Adaptive Planning

A Bayesian Satisficing Model of Human Adaptive Planning Wai-Tat Fu (wfu@andrew.cmu.edu) Department of Psychology, George Mason University 4400 University Drive, m/s 3f5 Virginia, VA 22030 USA Abstract This paper presents a Bayesian satisficing model of when a problem-solver stops planning and begins acting. Existing knowledge about the environment is incrementally updated by new observations, and performance improves as a consequence of better knowledge about the environment. The model aims at bridging the gap between machine learning and cognitive science by adopting the bounded rationality framework (Simon, 1956), which assumes that cognition tends to exploit the characteristics of the environment without engaging in psychologically implausible computations. Empirical studies were conducted when human subjects learned to find the fastest path in a simple map (only one was reported in this paper). The model fit the human learning and performance well and provided insights into the mechanisms behind learning and performance in problem solving. Introduction Problem-solving research shows that people seldom plan out complete sequences of actions before acting on the world (Hayes-Roth & Hayes-Roth, 1979; Roberson & Black, 1986). Instead, problem solvers construct partial plans, execute the actions, and plan on further as they act. Problem-solving behavior can therefore be cast somewhere along the planning continuum. At one extreme, a single action is decided and executed based purely on the current state of the problem. This results in highly reactive behavior that can respond quickly to the changing external world. However, this may lead to inefficient solutions to the problem. At the other extreme of the planning continuum, a complete sequence of actions is planned out before any action is executed. This results in highly efficient performance, as the best sequence of actions can be chosen and executed. However, the costs associated with planning often nullify the benefits of planning. Interleaving of planning and acting allows a balancing of problem- solving performance and planning cost involved in the search of actions. This paper focuses on a class of problems that can be solved relatively easily, but requires sufficient planning to find an efficient solution path. For example, finding a route from Pittsburgh to New York City is relatively easy (there are many possible routes to choose from), but finding the fastest route may require some planning ahead (to find out traffic conditions in different routes). A number of successful methods have been proposed to obtain the optimal level of planning given sufficient information about the problem-solving environment (Sun & Giles, 2001), but most of them adopt some variations of the dynamic programming approach that requires extensive backward search to find the optimal solution (e.g. Kopf, 1988). Although these methods are often able to lead to optimal solutions, the computations involved is clearly beyond the capacity of the human cognitive system. Psychological research, however, did find that people are able to change their level of planning in response to the characteristics of the environment to improve problem-solving performance (Kirsh & Maglio, Gunnzelman & Anderson, 2002). For example, Kirsh and Maglio found that expert players of the interactive video game Tetris outperformed novice players by better cost-benefit tradeoffs between mental planning and external planning (information-seeking actions). Gunzelmann and Anderson also found that their subjects increased the level of planning in the Tower-of-Hanoi task as they learned that it increased the efficiency of their solutions. In summary, the results suggest that (1) people are sensitive to the cost and benefit of planning, (2) people learn to perform better cost-benefit tradeoffs through experience, and (3) good cost-benefit tradeoffs are often critical to performance. The studies of how people perform cost-benefit tradeoffs have been of great interests to researchers in the domains of problem solving and decision-making (Christensen-Szalanski, J. J. J., 1980; Beach, L. R., & Mitchell, T. R., 1978; Payne, Bettman, & Johnson, 1993). Recently, a growing number of researchers have adopted the rational approach to explain cost-benefit tradeoffs in decision making behavior and strategy selection (Anderson, 1990; Lovett & Anderson, 1996; O'Hara & Payne, 1998; Fu & Gray, 2000). The major assumption of the rational approach is that people are well adapted to statistical characteristics of their environment, and computations in the human cognitive system perform in ways that are optimal in response to the demand of the environment. Under the rational framework, planning should stop as soon as the cost of further planning exceeds the benefit that further planning could bring. Since continued search of the problem space takes place at increasing cost, searching should stop and execution should begin once the expected benefit of further search drops below a certain level. At this point, the problem solver satisifices on