We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

The word embedding space in neural models is skewed, and correcting this can improve task performance.

Large language models (LLMs), typically designed as a function of next-word prediction, have excelled across extensive NLP tasks. Despite the generality, next-word prediction is often not an efficient formulation for many of the tasks, demanding an extreme scale of model parameters (10s or 100s of billions) and sometimes yielding suboptimal performance. In practice, it is often desirable to build more efficient models--despite being less versatile, they still apply to a substantial subset of problems, delivering on par or even superior performance with much smaller model sizes.

Regularization is one of the most fundamental topics in optimization, statistics and machine learning.

Recently, large language models (LLMs) have achieved superior performance, empowering the development of large multimodal agents (LMAs).