Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization

Key points

• Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$.1
• We investigate the convergence rates of Gaussian process Thompson sampling (GP-TS) under noiseless observations, assuming a fixed objective function in a reproducing kernel Hilbert space (RKHS).1
• For Matérn kernels with smoothness parameter $ν$ in dimension $d$, we establish a worst-case expected simple-regret upper bound of $O(N^{-ν/d}\sqrt{\log N})$ for both discrete GP-TS on sufficiently fine grids and its continuous counterpart.1
• For the continuous implementation, we develop a nested-grid argument to control posterior sample paths over the entire domain.1

Sources (1)

• [1]Convergence Rates of Gaussian Process Thompson Sampling for Efficient Global Optimization
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 14, 10:15 AM

  Motivated by this limitation, we propose Gaussian Process Capped Thompson Sampling (GP-CTS), which caps posterior sample paths using a valid RKHS norm upper bound while preserving optimism.

  Efficient global optimization aims to identify a global optimum of an expensive black-box function within a limited evaluation budget $N$.

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