Theoretical Results on Reinforcement Learning with Temporally Abstract Options

We present new theoretical results on planning within the framework of temporally abstract reinforcement learning (Precup & Sutton, 1997; Sutton, 1995). Temporal abstraction is a key step in any decision making system that involves planning and prediction. In temporally abstract reinforcement learning, the agent is allowed to choose among "options", whole courses of action that may be temporally extended, stochastic, and contingent on previous events. Examples of options include closed-loop policies such as picking up an object, as well as primitive actions such as joint torques. Knowledge about the consequences of options is represented by special structures called multi-time models. In this paper we focus on the theory of planning with multi-time models. We define new Bellman equations that are satisfied for sets of multi-time models. As a consequence, multi-time models can be used interchangeably with models of primitive actions in a variety of well-known planning methods including value iteration, policy improvement and policy iteration.

[1]  Earl David Sacerdoti,et al.  A Structure for Plans and Behavior , 1977 .

[2]  R. Korf.  Learning to solve problems by searching for macro-operators , 1983 .

[3]  Dimitri P. Bertsekas,et al.  Dynamic Programming: Deterministic and Stochastic Models , 1987 .

[4]  Richard S. Sutton,et al.  Integrated Architectures for Learning, Planning, and Reacting Based on Approximating Dynamic Programming , 1990, ML.

[5]  Geoffrey E. Hinton,et al.  Feudal Reinforcement Learning , 1992, NIPS.

[6]  Satinder P. Singh,et al.  Scaling Reinforcement Learning Algorithms by Learning Variable Temporal Resolution Models , 1992, ML.

[7]  Sridhar Mahadevan,et al.  Automatic Programming of Behavior-Based Robots Using Reinforcement Learning , 1991, Artif. Intell..

[8]  C. Atkeson,et al.  Prioritized Sweeping: Reinforcement Learning with Less Data and Less Time , 1993, Machine Learning.

[9]  Peter Dayan,et al.  Improving Generalization for Temporal Difference Learning: The Successor Representation , 1993, Neural Computation.

[10]  J. Peng,et al.  Efficient Learning and Planning Within the Dyna Framework , 1993, IEEE International Conference on Neural Networks.

[11]  Leslie Pack Kaelbling,et al.  Hierarchical Learning in Stochastic Domains: Preliminary Results , 1993, ICML.

[12]  Martin L. Puterman,et al.  Markov Decision Processes: Discrete Stochastic Dynamic Programming , 1994 .

[13]  Richard S. Sutton,et al.  TD Models: Modeling the World at a Mixture of Time Scales , 1995, ICML.

[14]  Ben J. A. Kröse,et al.  Learning from delayed rewards , 1995, Robotics Auton. Syst..

[15]  Stuart J. Russell,et al.  Reinforcement Learning with Hierarchies of Machines , 1997, NIPS.

[16]  Richard S. Sutton,et al.  Roles of Macro-Actions in Accelerating Reinforcement Learning , 1998 .

[17]  Roderic A. Grupen,et al.  Learning to Coordinate Controllers - Reinforcement Learning on a Control Basis , 1997, IJCAI.

[18]  Doina Precup,et al.  Multi-time Models for Temporally Abstract Planning , 1997, NIPS.

[19]  Roderic A. Grupen,et al.  A feedback control structure for on-line learning tasks , 1997, Robotics Auton. Syst..

[20]  Andrew G. Barto,et al.  Reinforcement learning , 1998 .

[21]  Richard S. Sutton,et al.  Introduction to Reinforcement Learning , 1998 .

[22]  Thomas G. Dietterich.  Hierarchical Reinforcement Learning with the MAXQ Value Function Decomposition , 1999, J. Artif. Intell. Res..