Grid Search
Grid search is the exhaustive evaluation of every combination drawn from a manually specified, discrete value set per parameter — the Cartesian product of those sets. [L] It is the most direct search: enumerate the lattice, evaluate every node, keep the best.
Cost: the product of the axes
For d parameters, where parameter i contributes k_i distinct values, the
grid has
N_{\text{grid}} = \prod_{i=1}^{d} k_i
points. [L] Because the count is a product, every added parameter multiplies the
work. In the simplest case of d binary parameters this is already 2^{d},
exponential in the number of parameters — an instance of the curse of
dimensionality. [L] Ten parameters at ten values each is ten billion
evaluations; the grid becomes unaffordable long before it is fine-grained enough.
Properties
- Complete within the lattice, but only the lattice. Grid search finds the best node it enumerates, but the resolution is chosen in advance; an optimum that falls between grid lines is unreachable. [L]
- Deterministic and reproducible. The same grid yields the same point set in the same order, with no randomness to seed. [L]
- Independent evaluations. No grid point depends on another's result, so the whole grid is embarrassingly parallel. [L]
- Wasteful in high dimensions. When only a few parameters affect the objective, grid search still spends its entire budget refining a coarse lattice along the parameters that do not matter. [C]
When grid search fits
Grid search is a reasonable default for few parameters (about three or fewer) over small, known discrete value sets, or when completeness over a specific lattice is itself the goal (e.g. a reproducible reference sweep). [C] Beyond a handful of dimensions, random search or an adaptive method covers the space far more economically.
Claim legend
- [L] law / exact — a definition, identity, or theorem that does not vary.
- [C] convention — a practitioner rule of thumb that varies by context.
References
- Hyperparameter optimization (Grid search section). Wikipedia. https://en.wikipedia.org/wiki/Hyperparameter_optimization
- Curse of dimensionality. Wikipedia. https://en.wikipedia.org/wiki/Curse_of_dimensionality
- Bergstra, J. & Bengio, Y. (2012). Random Search for Hyper-Parameter Optimization. JMLR, 13, 281–305. https://jmlr.org/papers/v13/bergstra12a.html
Backtesting Engine Architecture
- Architecture overview
- Event-Driven Backtesting
- Look-Ahead Bias & Causality
- Determinism & Reproducibility
- Reactive Streaming Dataflow
- Columnar Data Layout
- Signal, Exposure & Execution
- Graph Compilation & Optimization
- Authoring & Deployment Lifecycle
Strategy Analysis & Validation