Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining (2310.08566v2)

Abstract: Large transformer models pretrained on offline reinforcement learning datasets have demonstrated remarkable in-context reinforcement learning (ICRL) capabilities, where they can make good decisions when prompted with interaction trajectories from unseen environments. However, when and how transformers can be trained to perform ICRL have not been theoretically well-understood. In particular, it is unclear which reinforcement-learning algorithms transformers can perform in context, and how distribution mismatch in offline training data affects the learned algorithms. This paper provides a theoretical framework that analyzes supervised pretraining for ICRL. This includes two recently proposed training methods -- algorithm distillation and decision-pretrained transformers. First, assuming model realizability, we prove the supervised-pretrained transformer will imitate the conditional expectation of the expert algorithm given the observed trajectory. The generalization error will scale with model capacity and a distribution divergence factor between the expert and offline algorithms. Second, we show transformers with ReLU attention can efficiently approximate near-optimal online reinforcement learning algorithms like LinUCB and Thompson sampling for stochastic linear bandits, and UCB-VI for tabular Markov decision processes. This provides the first quantitative analysis of the ICRL capabilities of transformers pretrained from offline trajectories.

Transformers as Decision Makers: Provable In-Context Reinforcement Learning via Supervised Pretraining

The paper focuses on leveraging transformer architectures for in-context reinforcement learning (ICRL), which involves using sequence-to-sequence models to make decisions based on historical interactions within unseen environments. While large transformer models have empirically demonstrated significant ICRL capabilities, this paper provides a crucial theoretical framework to understand when and how transformers can efficiently perform reinforcement learning tasks.

Theoretical Framework for ICRL

The paper introduces a comprehensive theoretical framework to analyze supervised pretraining in the context of ICRL, placing special emphasis on two training methodologies: algorithm distillation and decision-pretrained transformers. The authors explore the conditions under which transformers can imitate expert algorithms when trained with offline data. They prove that a transformer, when appropriately trained, can approximate the conditional expectations of expert algorithms. This finding is pivotal for understanding ICRL as it delineates the boundary within which transformers can function as RL algorithms.

Approximation of RL Algorithms

The authors demonstrate that transformers are capable of approximating several near-optimal online RL algorithms efficiently, such as LinUCB and Thompson sampling for stochastic linear bandits, and UCB-VI for tabular Markov decision processes. These approximations are achieved by constructing transformers that implement accelerated gradient descent and matrix square root algorithms. The ability of transformers to approximate these algorithms suggests that transformers can serve as effective in-context learning mechanisms across various RL scenarios.

Implications of Results

The paper thoroughly quantifies the generalization error of supervised-pretrained transformers, which scales with both the model capacity and a distribution divergence factor between expert and offline algorithms, termed the distribution ratio. This metric is crucial for understanding the sample efficiency of transformers in pretraining environments and highlights how distribution mismatch can impact learning efficacy.

Additionally, strong numerical results are showcased to validate the paper's claims, demonstrating that the pre-trained transformers achieve regret bounds comparable to state-of-the-art RL algorithms. This lays the groundwork for future experimentation with AI models capable of executing RL tasks within unseen environments without explicit retraining.

Practical and Theoretical Implications

Practically, the research provides critical insights for designing transformers adept at reinforcement learning, thus enabling more robust decision-making capabilities in AI models. The theoretical groundwork laid out by this paper also advances our understanding of ICRL, suggesting potential for further hybrid architectures combining traditional RL algorithms with sequence-model capabilities inherent in transformers.

Future Directions

With the theoretical basis established, future studies can explore optimizing the architecture of transformers for specific RL tasks or developing methodologies to mitigate the effects of distribution mismatch. Furthermore, exploration into cross-domain applications, where transformers learn efficient decision-making processes from varying data types, can be a promising avenue.

Overall, the paper offers a detailed theoretical and empirical examination of transformers as decision makers, contributing significantly to the domain of machine learning and artificial intelligence.