Random Search
Random search replaces exhaustive enumeration with independent random
draws: each trial point is sampled from a declared distribution per parameter —
typically uniform over a continuous range [a_i, b_i] for each parameter i. [L]
The number of trials, n, is chosen directly as a budget, independent of the
number of parameters. [L]
Why a fixed budget beats a grid
A grid's cost is the product of its axes, so it explodes with
dimension. Random search fixes n up front: adding a parameter does not multiply
the cost — it only spreads the same n draws across one more axis. Two
consequences make it the stronger default in higher dimensions:
- Gridless coverage. Samples come from the continuous range, so the search is not confined to a pre-chosen lattice; with more draws the space simply becomes denser everywhere. [L]
- Coverage per important axis. Along any single parameter,
nrandom draws give up tondistinct values, whereas a grid of the same total size gives only a coarse per-axis resolution. When just a few parameters truly matter — but it is unknown which — this is decisive: Bergstra and Bengio showed that random search matches or beats grid search for hyperparameter optimization precisely because real problems tend to have low effective dimensionality. [C]
How many samples?
Coverage has an exact, dimension-independent form. If a target region occupies a
fraction v of the search volume, the probability that at least one of n
independent uniform draws lands in it is
P_{\text{hit}} = 1 - (1 - v)^{n}.
To hit the best fraction p of the space with confidence 1 - \varepsilon one
needs
n \ge \frac{\ln \varepsilon}{\ln(1 - p)}.
[L] For example, to be 95% confident of landing in the top 5% region
(p = 0.05, \varepsilon = 0.05) requires n \ge 59 draws — the same 59
regardless of how many parameters there are. [L] This is the quantitative core
of the random-over-grid argument.
Quasi-random (low-discrepancy) sampling
Pure pseudo-random draws clump: by chance they leave gaps and clusters. Low-discrepancy sequences (e.g. Sobol sequences, or Latin-hypercube designs) fill a space more evenly than pseudo-random points, so the proportion of points in any region tracks that region's volume more closely. [L] They are a drop-in improvement on uniform random with the same independence and budget properties, and reduce the sample count needed for a given coverage in quasi-Monte-Carlo settings. [C]
Properties
- Budget-driven and dimension-agnostic. You set
n; the cost isn. [L] - Independent evaluations. Draws do not depend on one another, so random search is embarrassingly parallel. [L]
- Reproducible when seeded. A fixed pseudo-random seed reproduces the exact draw sequence; without one, two runs differ. [L]
- A strong baseline. Cheap, simple, and parallel, random search is the standard yardstick an adaptive method must beat to justify its added machinery. [C]
When random search fits
Many parameters, continuous ranges, a fixed evaluation budget, or simply a trustworthy baseline before investing in adaptivity. [C]
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
- Bergstra, J. & Bengio, Y. (2012). Random Search for Hyper-Parameter Optimization. JMLR, 13, 281–305. https://jmlr.org/papers/v13/bergstra12a.html
- Hyperparameter optimization (Random search section). Wikipedia. https://en.wikipedia.org/wiki/Hyperparameter_optimization
- Low-discrepancy sequence. Wikipedia. https://en.wikipedia.org/wiki/Low-discrepancy_sequence
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