The workshop aims at bringing together researchers working on the theoretical foundations of learning, with an emphasis on methods at the intersection of statistics, probability and optimization.
Lecture blurb
Sampling algorithms are widely used in machine learning, and their success often depends on how well the algorithms are adapted to the problem at hand. This talk considers sampling methods that run several samplers in parallel and try to allocate more resources to the ones that produce better-quality samples. First, we show how multi-armed bandit algorithms can be used to choose sequentially from a set of unbiased Monte Carlo samplers so that the mean-squared error of the final combined estimate will be close to that of the best sampler in retrospect. Next, we generalize this approach to Markov-chain Monte Carlo (MCMC) samplers, which requires to overcome several challenges, for example how to measure sample quality properly or what to do with slowly mixing chains and multimodal target distributions. The resulting adaptive MCMC algorithm is asymptotically consistent and may lead to significant speedups, especially for multimodal target distributions, as demonstrated by our experiments.
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