Game solving aims to find the optimal strategies for all players and determine the theoretical outcome of a game. However, due to the exponential growth of game trees, many games remain unsolved, even though methods like AlphaZero have demonstrated super-human level in game playing. The Relevance-Zone (RZ) is a local strategy reuse technique that restricts the search to only the regions relevant to the outcome, significantly reducing the search space. However, RZs are not unique. Different solutions may result in RZs of varying sizes. Smaller RZs are generally more favorable, as they increase the chance of reuse and improve pruning efficiency. To this end, we propose an iterative RZ reduction method that repeatedly solves the same position while gradually restricting the region involved, guiding the solver toward smaller RZs. We design three constraint generation strategies and integrate an RZ Pattern Table to fully leverage past solutions. In experiments on 7x7 Killall-Go, our method reduces the average RZ size to 85.95% of the original. Furthermore, the reduced RZs can be permanently stored as reusable knowledge for future solving tasks, especially for larger board sizes or different openings.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

The greedy algorithm is extensively studied in the field of combinatorial optimization for decades. In this paper, we address the online learning problem when the input to the greedy algorithm is stochastic with unknown parameters that have to be learned over time. We first propose the greedy regret and null -quasi greedy regret as learning metrics comparing with the performance of offline greedy algorithm. We then propose two online greedy learning algorithms with semi-bandit feedbacks, which use multi-armed bandit and pure exploration bandit policies at each level of greedy learning, one for each of the regret metrics respectively. Both algorithms achieve O (log T) problem-dependent regret bound ( T being the time horizon) for a general class of combinatorial structures and reward functions that allow greedy solutions. We further show that the bound is tight in T and other problem instance parameters.

We thank all the reviewers for the constructive comments. We address the major concerns below. Reproducibility: 1) learning to draft details; 2) feature details; 3) discussions on the computing resources used. The search tree is updated based on four steps of MCTS. The learning rate is set to 0.001 with Adam.

In this paper, we implement kSubS using a transformer-based subgoal module coupled with the classical best-first search framework.

Actor-Critic models are a class of model-free deep reinforcement learning (RL) algorithms that have demonstrated effectiveness across various robot learning tasks. While considerable research has focused on improving training stability and data sampling efficiency, most deployment strategies have remained relatively simplistic, typically relying on direct actor policy rollouts. In contrast, we propose \pachs{} (\textit{P}arallel \textit{A}ctor-\textit{C}ritic \textit{H}euristic \textit{S}earch), an efficient parallel best-first search algorithm for inference that leverages both components of the actor-critic architecture: the actor network generates actions, while the critic network provides cost-to-go estimates to guide the search. Two levels of parallelism are employed within the search -- actions and cost-to-go estimates are generated in batches by the actor and critic networks respectively, and graph expansion is distributed across multiple threads. We demonstrate the effectiveness of our approach in robotic manipulation tasks, including collision-free motion planning and contact-rich interactions such as non-prehensile pushing. Visit p-achs.github.io for demonstrations and examples.