Next-Token Prediction and Regret Minimization

Abstract

We study the robustification of next-token prediction models in adversarial online decision-making environments. Suppose a next-token predictor is trained on a distribution over sequences of opponent actions, and a decision maker acts by approximately best responding to the model’s predictions. If this induced decision-making algorithm achieves low adversarial regret, we call such distributions low-regret distributions. For models with unbounded context, we show that every distribution is exponentially close in total variation distance to a low-regret distribution. Thus, sublinear regret can always be achieved while changing the original next-token prediction distribution by only a negligible amount. By contrast, for models with bounded context windows, as in standard transformer architectures, we prove an impossibility result: some distributions are $\Theta(1)$-far from every low-regret distribution. We complement these results with two positive findings. First, allowing a modest increase in context length restores robustification with near-optimal regret guarantees. Second, the unbounded-context robustification procedure can be implemented by adding a constant number of layers to a standard transformer architecture. Finally, we provide empirical evidence that small transformer models can be efficiently trained to represent these robustified low-regret distributions.