We propose Stable Yet Memory Bounded Open-Loop (SYMBOL) planning, a general memory bounded approach to partially observable open-loop planning. SYMBOL maintains an adaptive stack of Thompson Sampling bandits, whose size is bounded by the planning horizon and can be automatically adapted according to the underlying domain without any prior domain knowledge beyond a generative model. We empirically test SYMBOL in four large POMDP benchmark problems to demonstrate its effectiveness and robustness w.r.t. the choice of hyperparameters and evaluate its adaptive memory consumption. We also compare its performance with other open-loop planning algorithms and POMCP.
@cite_20: Monte Carlo Tree Search (MCTS) is an effective decision making algorithm that often works well without domain knowledge, finding an increasing application in commercial mobile and video games. A promising application of MCTS is creating AI opponents for board and card games, where Information Set MCTS (ISMCTS) can provide a challenging opponent and reduces the cost of creating game-specific AI opponents. Most research to date has aimed at improving the quality of decision making by (IS)MCTS, with respect to time usage. Memory usage is also an important constraint in commercial applications, particularly on mobile platforms or when there are many AI agents. This paper presents the first systematic study of memory bounding techniques for (IS)MCTS. (IS)MCTS is well known to be an anytime algorithm. We also introduce an anyspace version of (IS)MCTS which can make effective use of any pre-specified amount of memory. This algorithm has been implemented in a commercial version of the card game Spades downloaded more than 6 million times. We find that for games of imperfect information high quality decisions can be made with rather small memory footprints, making (IS)MCTS an even more attractive algorithm for commercial game implementations.
@cite_20 proposed a memory bounded version of MCTS with a fixed size state pool to add, discard, or reuse states depending on their visitation frequency. However, this approach cannot be easily adapted to tree-based open-loop approaches, because it requires (belief) states to be identifiable. SYMBOL does not require a pool to reuse states or nodes but maintains an of Thompson Sampling bandits. The bandits adapt according to the between actions, while the size of the bandit stack is bounded by the planning horizon and itself according to the underlying domain.