While large language models perform well on a range of complex tasks (e.g., text generation, question answering, summarization), robust multi-step planning and reasoning remains a considerable challenge for them. In this paper we show that search-based planning can significantly improve LLMs' playing strength across several board games (Chess, Fischer Random / Chess960, Connect Four, and Hex). We introduce, compare and contrast two major approaches: In external search, the model guides Monte Carlo Tree Search (MCTS) rollouts and evaluations without calls to an external engine, and in internal search, the model directly generates in-context a linearized tree of potential futures and a resulting final choice. Both build on a language model pre-trained on relevant domain knowledge, capturing the transition and value functions across these games. We find that our pre-training method minimizes hallucinations, as our model is highly accurate regarding state prediction and legal moves. Additionally, both internal and external search indeed improve win-rates against state-of-the-art bots, even reaching Grandmaster-level performance in chess while operating on a similar move count search budget per decision as human Grandmasters. The way we combine search with domain knowledge is not specific to board games, suggesting direct extensions into more general language model inference and training techniques.

Progress in fields of machine learning and adversarial planning has benefited significantly from benchmark domains, from checkers and the classic UCI data sets to Go and Diplomacy. In sequential decision-making, agent evaluation has largely been restricted to few interactions against experts, with the aim to reach some desired level of performance (e.g. beating a human professional player). We propose a benchmark for multiagent learning based on repeated play of the simple game Rock, Paper, Scissors along with a population of forty-three tournament entries, some of which are intentionally sub-optimal. We describe metrics to measure the quality of agents based both on average returns and exploitability. We then show that several RL, online learning, and language model approaches can learn good counter-strategies and generalize well, but ultimately lose to the top-performing bots, creating an opportunity for research in multiagent learning.

Regret minimization has played a key role in online learning, equilibrium computation in games, and reinforcement learning (RL). In this paper, we describe a general model-free RL method for no-regret learning based on repeated reconsideration of past behavior. We propose a model-free RL algorithm, the AdvantageRegret-Matching Actor-Critic (ARMAC): rather than saving past state-action data, ARMAC saves a buffer of past policies, replaying through them to reconstruct hindsight assessments of past behavior. These retrospective value estimates are used to predict conditional advantages which, combined with regret matching, produces a new policy. In particular, ARMAC learns from sampled trajectories in a centralized training setting, without requiring the application of importance sampling commonly used in Monte Carlo counterfactual regret (CFR) minimization; hence, it does not suffer from excessive variance in large environments. In the single-agent setting, ARMAC shows an interesting form of exploration by keeping past policies intact. In the multiagent setting, ARMAC in self-play approaches Nash equilibria on some partially-observable zero-sum benchmarks. We provide exploitability estimates in the significantly larger game of betting-abstracted no-limit Texas Hold'em.