In this paper, we consider how to construct best-of-both-worlds linear bandit algorithms that achieve nearly optimal performance for both stochastic and adversarial environments. For this purpose, we show that a natural approach referred to as exploration by optimization [Lattimore and Szepesvári, 2020b] works well.

A key task in Bayesian machine learning is sampling from distributions that are only specified up to a partition function (i.e., constant of proportionality). One prevalent example of this is sampling posteriors in parametric distributions, such as latent-variable generative models. However sampling (even very approximately) can be #P-hard. Classical results (going back to Bakry and Emery) on sampling focus on log-concave distributions, and show a natural Markov chain called Langevin diffusion mix in polynomial time. However, all log-concave distributions are uni-modal, while in practice it is very common for the distribution of interest to have multiple modes.

Acommon modification, motivatedbyPACagnostic learning, assumes thatf isclosetoanatural distribution classC, and tries to find the distribution inC closest tof.

Neural Information Processing Systems http://nips.cc/

Neural Information Processing Systems http://nips.cc/

Interest in this problem derives from its applications to Bayesian inference and differential privacy.