  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.
