Parti-game is a new algorithm for learning from delayed rewards in high dimensional real-valued state-spaces. In high dimensions it is essential that learning does not explore or plan over state space uniformly. Part i-game maintains a decision-tree partitioning of state-space and applies game-theory and computational geom(cid:173) etry techniques to efficiently and reactively concentrate high reso(cid:173) lution only on critical areas. Many simulated problems have been tested, ranging from 2-dimensional to 9-dimensional state-spaces, including mazes, path planning, non-linear dynamics, and uncurl(cid:173) ing snake robots in restricted spaces. In all cases, a good solution is found in less than twenty trials and a few minutes.

Parti-game (Moore 1994a; Moore 1994b; Moore and Atkeson 1995) is a reinforcement learning (RL) algorithm that has a lot of promise in over(cid:173) coming the curse of dimensionality that can plague RL algorithms when applied to high-dimensional problems. In this paper we introduce mod(cid:173) ifications to the algorithm that further improve its performance and ro(cid:173) bustness. In addition, while parti-game solutions can be improved locally by standard local path-improvement techniques, we introduce an add-on algorithm in the same spirit as parti-game that instead tries to improve solutions in a non-local manner.

In this paper, we introduce an efficient replanning algorithm for nonde- terministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic dis- cretization of continuous domains, resulting in an efficient implemen- tation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains.

In this paper, we introduce an efficient replanning algorithm for nondeterministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic discretization of continuous domains, resulting in an efficient implementation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains.

In this paper, we introduce an efficient replanning algorithm for nondeterministic domains, namely what we believe to be the first incremental heuristic minimax search algorithm. We apply it to the dynamic discretization of continuous domains, resulting in an efficient implementation of the parti-game reinforcement-learning algorithm for control in high-dimensional domains.

There also exist other ways of decreasing the amount of search performed by the parti-game algorithm.

Parti-game is a new algorithm for learning from delayed rewards in high dimensional real-valued state-spaces. In high dimensions it is essential that learning does not explore or plan over state space uniformly. Part i-game maintains a decision-tree partitioning of state-space and applies game-theory and computational geometry techniques to efficiently and reactively concentrate high resolution only on critical areas. Many simulated problems have been tested, ranging from 2-dimensional to 9-dimensional state-spaces, including mazes, path planning, nonlinear dynamics, and uncurling snake robots in restricted spaces. In all cases, a good solution is found in less than twenty trials and a few minutes. 1 REINFORCEMENT LEARNING Reinforcement learning [Samuel, 1959, Sutton, 1984, Watkins, 1989, Barto et al., 1991] is a promising method for control systems to program and improve themselves.

Parti-game is a new algorithm for learning from delayed rewards in high dimensional real-valued state-spaces. In high dimensions it is essential that learning does not explore or plan over state space uniformly. Part i-game maintains a decision-tree partitioning of state-space and applies game-theory and computational geometry techniques to efficiently and reactively concentrate high resolution only on critical areas. Many simulated problems have been tested, ranging from 2-dimensional to 9-dimensional state-spaces, including mazes, path planning, nonlinear dynamics, and uncurling snake robots in restricted spaces. In all cases, a good solution is found in less than twenty trials and a few minutes. 1 REINFORCEMENT LEARNING Reinforcement learning [Samuel, 1959, Sutton, 1984, Watkins, 1989, Barto et al., 1991] is a promising method for control systems to program and improve themselves.

Andrew W. Moore School of Computer Science Carnegie-Mellon University Pittsburgh, PA 15213 Abstract Parti-game is a new algorithm for learning from delayed rewards in high dimensional real-valued state-spaces. In high dimensions it is essential that learning does not explore or plan over state space uniformly. Parti-game maintains a decision-tree partitioning of state-space and applies game-theory and computational geometry techniquesto efficiently and reactively concentrate high resolution onlyon critical areas. Many simulated problems have been tested, ranging from 2-dimensional to 9-dimensional state-spaces, including mazes, path planning, nonlinear dynamics, and uncurling snakerobots in restricted spaces. In all cases, a good solution is found in less than twenty trials and a few minutes. 1 REINFORCEMENT LEARNING Reinforcement learning [Samuel, 1959, Sutton, 1984, Watkins, 1989, Barto et al., 1991] is a promising method for control systems to program and improve themselves.