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Near-linear time Gaussian process optimization with adaptive batching and resparsification
Daniele Calandriello · Luigi Carratino · Alessandro Lazaric · Michal Valko · Lorenzo Rosasco

Tue Jul 14 11:00 AM -- 11:45 AM & Wed Jul 15 12:00 AM -- 12:45 AM (PDT) @ Virtual

Gaussian processes (GP) are one of the most successful frameworks to model uncertainty. However, GP optimization (e.g., GP-UCB) suffers from major scalability issues. Experimental time grows linearly with the number of evaluations, unless candidates are selected in batches (e.g., using GP-BUCB) and evaluated in parallel. Furthermore, computational cost is often prohibitive since algorithms such as GP-BUCB require a time at least quadratic in the number of dimensions and iterations to select each batch.

In this paper, we introduce BBKB (Batch Budgeted Kernel Bandits), the first no-regret GP optimization algorithm that provably runs in near-linear time and selects candidates in batches. This is obtained with a new guarantee for the tracking of the posterior variances that allows BBKB to choose increasingly larger batches, improving over GP-BUCB. Moreover, we show that the same bound can be used to adaptively delay costly updates to the sparse GP approximation used by BBKB, achieving a near-constant per-step amortized cost. These findings are then confirmed in several experiments, where BBKB is much faster than state-of-the-art methods.

Author Information

Daniele Calandriello (IIT/DeepMind)
Luigi Carratino (University of Genoa)
Alessandro Lazaric (Facebook AI Research)
Michal Valko (DeepMind)
Michal Valko

Michal is a machine learning scientist in DeepMind Paris, tenured researcher at Inria, and the lecturer of the master course Graphs in Machine Learning at l'ENS Paris-Saclay. Michal is primarily interested in designing algorithms that would require as little human supervision as possible. This means 1) reducing the “intelligence” that humans need to input into the system and 2) minimizing the data that humans need to spend inspecting, classifying, or “tuning” the algorithms. That is why he is working on methods and settings that are able to deal with minimal feedback, such as deep reinforcement learning, bandit algorithms, or self-supervised learning. Michal is actively working on represenation learning and building worlds models. He is also working on deep (reinforcement) learning algorithm that have some theoretical underpinning. He has also worked on sequential algorithms with structured decisions where exploiting the structure leads to provably faster learning. He received his Ph.D. in 2011 from the University of Pittsburgh under the supervision of Miloš Hauskrecht and after was a postdoc of Rémi Munos before taking a permanent position at Inria in 2012.

Lorenzo Rosasco (unige, mit, iit)

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