Learning Hierarchical Skills from Problem Solutions Using Means-Ends Analysis

Learning Hierarchical Skills from Problem Solutions Using Means-Ends Analysis Nan Li (nan.li.3@asu.edu) David J. Stracuzzi (david.stracuzzi@asu.edu) Pat Langley (langley@asu.edu) School of Computing and Informatics, Arizona State University, Tempe, AZ 85281 USA Negin Nejati (negin@stanford.edu) Computational Learning Laboratory, CSLI, Stanford University, Stanford, CA 94305 USA Abstract The I CARUS Architecture Humans acquire skills in different ways, one of which involves learning from worked-out solutions to problems. In this paper, we present an extension to the I CARUS cognitive architecture that lets it acquire complex hierarchical skills in this manner. Unlike previous work on this topic, our approach relies on an existing architectural mechanism, means-ends analysis, to ex- plain steps in the problem solution and to learn new structures. We illustrate this method in the domains of multi-column sub- traction and football, after which we discuss related work and consider directions for future research in this area. In previous work, Langley and Choi (2006) have presented I CARUS , a cognitive architecture that shares many features with other frameworks like Soar (Laird, Rosenbloom, & Newell, 1986) and ACT-R (Anderson, 1993), including a distinction between short-term and long-term memories, re- liance on a recognize-act cycle, and a mixture of goal-driven with data-driven behavior. I CARUS also has distinctive fea- tures, such as separate memories for concepts and skills, in- dexing skills by the goals they achieve, and an architectural commitment to hierarchical structures. Before describing our approach to learning from problem solutions, we should re- view the framework’s basic assumptions. Introduction Research on cognitive architectures (Newell, 1990) attempts to explain the entire range of human cognition. In previous papers, we have described I CARUS (Langley & Choi, 2006), an architecture that, in addition to other capabilities, acquires hierarchical skills during problem solving. However, as Ohls- son (2008) has noted, humans learn skills from many different sources of input. Thus, an important research goal involves extending I CARUS to support the full range of human skill ac- quisition. In this paper, we report progress on modeling learn- ing from worked-out problem solutions, which often arise in educational settings. Our approach builds on previous work, LIGHT, a system that constructs hierarchical skills from expert solutions to problems developed by Nejati, Langley, and Konik (2006). Although LIGHT utilized I CARUS knowledge structures as input and output, it operated as a separate module that was not part of the unified architecture. At the same time, the system’s approach to explaining problem solutions bore a close resem- blance to I CARUS ’ existing mechanism for means-ends prob- lem solving. In response, we have adapted the latter mech- anism to support explanation of, and learning from, worked- out solutions to acquire complex cognitive skills, extending I CARUS ’ coverage of human cognition. In the sections that follow, we briefly review the I CARUS architecture, including its assumptions about representation, performance, and learning, along with Nejati et al.’s approach to learning from solution traces. After this, we describe our adaptation of the framework’s means-ends mechanism to ex- plain and learn from such traces, followed by an example in the domain of multi-column subtraction. We then report ex- periments that demonstrate the generality of our approach. In closing, we discuss related research and propose avenues for additional work on this topic. Beliefs, Concepts, and Inference Most cognitive architectures operate in discrete cycles that produce mental or physical action. However, before an agent takes action, it must first understand its situation. I CARUS accomplishes this by matching conceptual structures in long- term memory against dynamic percepts and beliefs that it up- dates on each cycle. This process begins when descriptions of the environment are deposited into a perceptual buffer. The architecture complements this with a belief memory that encodes higher-level inferences about the environment, typi- cally about relations among entities. I CARUS beliefs are instances of generalized concepts stated in a long-term, hierarchical conceptual memory. Ta- ble 1 shows some concepts for multi-column subtraction. Primitive concepts match directly against the perceptual buffer, whereas nonprimitive concepts match against in- stances of lower-level concepts. Each nonprimitive concept specifies subconcepts that must be present for it to match. For example, the all-processed concept in the table refers to pro- cessed and rightmost-column. An inference mechanism up- dates belief memory at the beginning of each cycle by match- ing the generalized concept definitions with percepts and ex- isting beliefs in a bottom-up manner, and stops when it infers all beliefs deductively implied by the concepts and percepts. Goals, Skills, and Execution After inferring a set of beliefs about its environment, I CARUS uses its available skills to take action there. The system stores these structures in a skill memory, which also has a hierarchi- cal organization. Skill clauses are indexed by the concepts