Large Reasoning Models (LRMs) have shown excellent performance in reasoning tasks using long Chains of Thought (CoTs). However, this has also led to a significant increase of computational costs and the generation of verbose output, a phenomenon known as overthinking. The tendency to overthink is often exacerbated by Reinforcement Learning (RL) algorithms such as GRPO/DAPO. In this paper, we propose BFS-PO, an RL algorithm which alleviates this problem using a Best-First Search exploration strategy. Specifically, the reasoning chains generated at training time by BFS-PO are organized into a search tree, within which the shortest correct sequence is selected as the best and expanded using a backtracking mechanism based on maximum entropy nodes. In this way, we bias the exploration of the solution space towards the search for increasingly shorter solutions, training the LRM to generate progressively more concise answers. Using different benchmarks and base LRMs, we show that BFS-PO can simultaneously increase the LRM accuracy and shorten its reasoning chains.

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