We study the problem of representation learning in stochastic contextual linear bandits. While the primary concern in this domain is usually to find \textit{realizable} representations (i.e., those that allow predicting the reward function at any context-action pair exactly), it has been recently shown that representations with certain spectral properties (called \textit{HLS}) may be more effective for the exploration-exploitation task, enabling \textit{LinUCB} to achieve constant (i.e., horizon-independent) regret. In this paper, we propose \textsc{BanditSRL}, a representation learning algorithm that combines a novel constrained optimization problem to learn a realizable representation with good spectral properties with a generalized likelihood ratio test to exploit the recovered representation and avoid excessive exploration. We prove that \textsc{BanditSRL} can be paired with any no-regret algorithm and achieve constant regret whenever an \textit{HLS} representation is available. Furthermore, \textsc{BanditSRL} can be easily combined with deep neural networks and we show how regularizing towards \textit{HLS} representations is beneficial in standard benchmarks.

Large language models (LLMs) are primarily designed to understand unstructured text. When directly applied to structured formats such as tabular data, they may struggle to discern inherent relationships and overlook critical patterns. While tabular representation learning methods can address some of these limitations, existing efforts still face challenges with sparse high-cardinality fields, precise numerical reasoning, and column-heavy tables. Furthermore, leveraging these learned representations for downstream tasks through a language based interface is not apparent. In this paper, we present an innovative and scalable solution to these challenges. Concretely, our approach introduces a multi-tier partitioning mechanism that utilizes power-law dynamics to handle large vocabularies, an adaptive quantization mechanism to impose priors on numerical continuity, and a distinct treatment of core-columns and meta-information columns. To facilitate instruction tuning on LLMs, we propose a parameter efficient decoder that interleaves transaction and text modalities using a series of adapter layers, thereby exploiting rich cross-task knowledge.

We study the problem of representation learning in stochastic contextual linear bandits. While the primary concern in this domain is usually to find \textit{realizable} representations (i.e., those that allow predicting the reward function at any context-action pair exactly), it has been recently shown that representations with certain spectral properties (called \textit{HLS}) may be more effective for the exploration-exploitation task, enabling \textit{LinUCB} to achieve constant (i.e., horizon-independent) regret. In this paper, we propose \textsc{BanditSRL}, a representation learning algorithm that combines a novel constrained optimization problem to learn a realizable representation with good spectral properties with a generalized likelihood ratio test to exploit the recovered representation and avoid excessive exploration. We prove that \textsc{BanditSRL} can be paired with any no-regret algorithm and achieve constant regret whenever an \textit{HLS} representation is available. Furthermore, \textsc{BanditSRL} can be easily combined with deep neural networks and we show how regularizing towards \textit{HLS} representations is beneficial in standard benchmarks.