Stochastic Tasks: Difficulty and Levin Search
We establish a setting for asynchronous stochastic tasks that account for episodes, rewards and responses, and, most especially, the computational complexity of the algorithm behind an agent solving a task. This is used to determine the difficulty of a task as the (logarithm of the) number of computational steps required to acquire an acceptable policy for the task, which includes the exploration of policies and their verification. We also analyse instance difficulty, task compositions and decompositions.
KeywordsTask difficulty Task breadth Levin’s search Universal psychometrics
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- 1.Alpcan, T., Everitt, T., Hutter, M.: Can we measure the difficulty of an optimization problem? In: IEEE Information Theory Workshop (ITW) (2014)Google Scholar
- 3.Hernández-Orallo, J.: A computational definition of ‘consilience’. Philosophica 61, 901–920 (2000)Google Scholar
- 4.Hernández-Orallo, J.: Computational measures of information gain and reinforcement in inference processes. AI Communications 13(1), 49–50 (2000)Google Scholar
- 6.Hernández-Orallo, J.: On environment difficulty and discriminating power. Autonomous Agents and Multi-Agent Systems, 1–53 (2014). http://dx.doi.org/10.1007/s10458-014-9257-1
- 8.Hernández-Orallo, J., Dowe, D.L., Hernández-Lloreda, M.V.: Universal psychometrics: measuring cognitive abilities in the machine kingdom. Cognitive Systems Research 27, 50–74 (2014)Google Scholar
- 9.Hutter, M.: Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Springer (2005)Google Scholar
- 11.Li, M., Vitányi, P.: An introduction to Kolmogorov complexity and its applications, 3rd edn. Springer (2008)Google Scholar
- 13.Schmidhuber, J.: Gödel machines: fully self-referential optimal universal self-improvers. In: Artificial general intelligence, pp. 199–226. Springer (2007)Google Scholar