Sobol sequence
A Sobol sequence is a low-discrepancy quasi-random sequence designed to distribute points evenly across a multidimensional domain.
Bayesian Optimization in Action
A Sobol sequence is a low-discrepancy numerical sequence that distributes points evenly across a multidimensional domain.
- How it is used
- Supports Thompson sampling and batch Bayesian optimization by populating a search space with evenly distributed candidate points.
- How deep it goes
- Defines the sequence, compares its coverage with uniform sampling, and demonstrates generation and scaling without deriving its construction.
- Examples
- Uses unit-square coverage plots, a one-dimensional PyTorch candidate set, hyperparameter tuning, and a four-dimensional airplane-design search.
- What you can do after
- Apply it via PyTorch and BoTorch to generate scaled candidates for sequential or batch optimization.
Read how Bayesian Optimization in Action explains Sobol sequence →
Optimization Algorithms: AI techniques for design, planning, and control problems
A quasi-random low-discrepancy sequence designed to distribute points evenly throughout a multidimensional sample space.
- How it is used
- Supports diverse initial populations for population-based metaheuristic search.
- How deep it goes
- Defines distribution and demonstrates Python usage, but does not derive the sequence’s internal construction.
- Examples
- Generates 2D samples with sobol_seq and compares plotted dispersion against four other sampling methods.
- What you can do after
- Apply it via sobol_seq to generate evenly distributed candidate points for search-space initialization.
Related concepts
- samplingalternative to · Sampling is a procedure for selecting or generating observations, values, or outcomes from a larger population, signal, or probability distribution according to a specified method.
- SobolEngineimplemented by · SobolEngine is a PyTorch quasi-random sampling class that generates Sobol-sequence points in a unit cube.
- max-value entropy searchused by · Max-value Entropy Search is a Bayesian optimization acquisition policy that selects evaluations expected to reduce uncertainty about the global maximum value of an objective.
- Thompson samplingused by · Thompson sampling is a Bayesian sequential decision method that samples from posterior beliefs about uncertain rewards or outcomes and selects an action according to the sampled values.
- search spaceuses · A search space is the set of possible states, choices, configurations, or candidate solutions that may be considered when exploring or solving a problem.
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