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Relational Equivalence-Based Planning

In this work, we propose a synthesis of logic and probability for solving stochastic sequential decision-making problems. We address two main questions: How we take advantage of logical structure to speed up planning in a principled way? And, how can probability inform the production of a more robust, yet still compact, policy? Consider a mobile robot acting in the world: it is faced with a varied amount of sensory data and uncertainty in its action outcomes. Or, consider a logistics planning system: it must manage to get a large number of objects to the right place at the right time. Many interesting sequential decision-making domains involve large state spaces, large stochastic action sets, and time pressure to act.

First, we show how structured representations of the environment's dynamics can constrain and speed up the planning process. We start with a problem domain described in a probabilistic logical description language. Our technique is based on, first, identifying the most parsimonious representation that permits solution of the described problem. Next, we take advantage of the structured problem description to dynamically partition the action space into a set of equivalence classes with respect to this minimal representation. The partitioned action space results in fewer distinct actions. This technique can yield significant gains in planning efficiency. Next, we develop an anytime technique to elaborate on this initial plan. Our approach uses the envelope MDP framework, which creates a Markov decision process out of a subset of the possible state space. This strategy lets an agent begin acting quickly within a restricted part of the full state space, as informed by the origin and the goal.