The John ellipsoid problem has far-reaching applications in numerous fields of computer science.

The field of learning-augmented online algorithms has gained rapid prominence in recent years.

Policy inference plays an essential role in the contextual bandit problem. In this paper, we use empirical likelihood to develop a Bayesian inference method for the joint analysis of multiple contextual bandit policies in finite sample regimes. The proposed inference method is robust to small sample sizes and is able to provide accurate uncertainty measurements for policy value evaluation. In addition, it allows for flexible inferences on policy comparison with full uncertainty quantification. We demonstrate the effectiveness of the proposed inference method using Monte Carlo simulations and its application to an adolescent body mass index data set.

Inparticular,standardmetricformulations as hierarchical k-center,k-means, andk-median received a lot of attention and the problems have been studied extensively in different models of computation.

In this paper, we study the role of machine-learned predictions inofflineNP-hard problems. For offline problems, an algorithm has no information disadvantage compared to an optimal solution: thedisadvantage iscomputational.

The hope is that these predictions allow the algorithm to circumvent worst case lower bounds when the predictions are good, and approximately match them otherwise. The precise definitions and guarantees vary with different settings, but there have been significant successes in applying this framework for many different algorithmic problems, ranging from general online problems to classical graph algorithms (see Section 1.2 for a more detailed discussion of related work, and [35] for a survey). In all of these settings it turns out to be possible to define a "prediction" where the "quality" of the algorithm (competitive ratio, running time, etc.) depends the "error" of the prediction.