When Do We Need LLMs? A Diagnostic for Language-Driven Bandits

Contextual bandit algorithms suffer from high regret during cold-start, when the learner has insufficient data to distinguish good arms from bad. We propose augmenting Disjoint LinUCB with LLM pseudo-observations: after each round, a large language model predicts counterfactual rewards for the unplayed arms, and these predictions are injected into the learner as weighted pseudo-observations. The injection weight is controlled by a calibration-gated decay schedule that tracks the LLM's prediction accuracy on played arms via an exponential moving average; high calibration error suppresses the LLM's influence, while accurate predictions receive higher weight during the critical early rounds. We evaluate on two contextual bandit environments - UCI Mushroom (2-arm, asymmetric rewards) and MIND-small (5-arm news recommendation) - and find that when equipped with a task-specific prompt, LLM pseudo-observations reduce cumulative regret by 19% on MIND relative to pure LinUCB. However, generic counterfactual prompt framing increases regret on both environments, demonstrating that prompt design is the dominant factor, more important than the choice of decay schedule or calibration gating parameters. We analyze the failure modes of calibration gating on domains with small prediction errors and provide a theoretical motivation for the bias-variance trade-off governing pseudo-observation weight.

Large language models (LLMs) are increasingly deployed as decision-making agents in settings that require sophisticated environmental exploration. However, existing work has raised questions about how LLMs actually balance exploration and exploitation. Unlike classical agents, LLM agents engage with tasks through natural language, exposing them to semantic information with no formal counterpart in the task structure. We introduce the semantic bandit, an extension of the multi-armed bandit setting that explicitly considers the textual labels assigned to actions, and use it to study how semantic priors --- inductive biases arising from associations between language and expected reward learned during pre-training, shape LLM exploration behaviour. We find that semantically informative action labels reduce exploration in favour of exploitation, improving performance when aligned with the reward structure and severely degrading it when misaligned. We further find that negative rewards trigger substantially more exploration than equivalent positive rewards, consistent with an expected-scale bias induced by reward conventions common in pre-training data. Overall, we argue that the use of language to define the environment and rewards introduces unavoidable biases derived from the fact that the model is trained on word co-occurence, with implications for the reliability and robustness of LLM agents in real-world decision-making settings.

Inspired by the problem of identifying the best model from a collection of large language models (LLMs) with heterogeneous querying costs, we formulate and analyse a variant of the multi-armed bandit (MAB) with (i) dueling feedback, where pairwise comparisons between model responses provide robust preference signals, and (ii) heterogeneous sampling costs, reflecting the differing costs of querying different LLMs. Assuming the existence of a Condorcet winner, a condition we empirically validate across multiple real-world datasets, we propose a Track-and-Stop style algorithm for best-arm identification with prescribed confidence. We prove that the algorithm almost surely achieves the asymptotically optimal cost as the error tends to zero. Finally, we extensively evaluate our approach on both synthetic and real-world instances, demonstrating consistent improvements over classical cost-unaware algorithms and their cost-aware extensions.