Large Language Models (LLMs) have highlighted the necessity of effective unlearning mechanisms to comply with data regulations and ethical AI practices. LLM unlearning aims at removing undesired data influences and associated model capabilities without compromising utility beyond the scope of unlearning. While interest in studying LLM unlearning is growing, the impact of the optimizer choice for LLM unlearning remains unexplored. In this work, we shed light on the significance of optimizer selection in LLM unlearning for the first time, establishing a clear connection between second-order optimization and influence unlearning (a classical approach using influence functions to update the model for data influence removal). This insight propels us to develop a second-order optimization-based LLM unlearning framework, termed Second-Order UnLearning (SOUL), which extends the static, one-shot model update using influence unlearning to a dynamic, iterative unlearning process. Our extensive experiments show that SOUL consistently outperforms conventional first-order methods across various unlearning tasks, models, and metrics, indicating that second-order optimization offers an effective and broadly applicable solution for LLM unlearning.

Current logical reasoning evaluations of Large Language Models (LLMs) primarily focus on single-turn and static environments, such as arithmetic problems. The crucial problem of multi-turn, strategic reasoning is under-explored. In this work, we analyze the multi-turn strategic reasoning of LLMs through text-driven complete- and incomplete-information gaming, e.g., board games (Tic-Tac-Toe, Connect-4) and poker games (Texas Hold’em Poker). Specifically, we consider two distinct scenarios: 1) Online Racing, featuring multiple LLMs/agents to facilitate direct competition and comparison; 2) Offline Probing, constructing targeted questions with verified ground truth to evaluate LLMs’ strategic behaviors. Experimental results demonstrate that existing state-of-the-art LLMs and reasoning schemes are largely ineffective for strategic reasoning tasks. To mitigate these limitations, we propose a simple yet effective Recursively Thinking-Ahead (ReTA) agent, incorporating a recursive prompting mechanism that automatically analyzes the opponents’ future moves/actions and assigns reward signals for these situations, to strengthen the strategic reasoning of LLMs. We hope our work could spur further research and exploration in the multi-turn strategic reasoning of LLMs. The code is available at https://github.com/jinhaoduan/ReTA.