# What Algorithm to Choose?¶

The choice of the sampling/search strategy depends strongly on the problem tackled. Ultimately, their are 4 aspects of the problem to look at:

• the time required to evaluate a model,
• the number of variables,
• the type of variable (continuous or discrete),
• the conditionality of the search space.

Chocolate proposes 5 algorithms with their own advantages and disadvantages:

• Grid sampling applies when all variables are discrete and the number of possibilities is low. A grid search will perform the exhaustive combinatorial search over all possibilities making the search extremely long even for medium sized problems.
• Random sampling is an alternative to grid search when the number of discrete parameters to optimize and the time required for each evaluation is high. When all parameters are discrete, random search will perform sampling without replacement making it an algorithm of choice when combinatorial exploration is not possible. With continuous parameters, it is preferable to use quasi random sampling.
• QuasiRandom sampling ensures a much more uniform exploration of the search space than traditional pseudo random. Thus, quasi random sampling is preferable when not all variables are discrete, the number of dimensions is high and the time required to evaluate a solution is high.
• Bayes search models the search space using gaussian process regression, which allows to have an estimate of the loss function and the uncertainty on that estimate at every point of the search space. Modeling the search space suffers from the curse of dimensionality, which makes this method more suitable when the number of dimensions is low. Moreover, since it models both the expected loss and uncertainty, this search algorithm converges in few steps on superior configurations, making it a good choice when the time to complete the evaluation of a parameter configuration is high.
• CMAES search is one of the most powerful black-box optimization algorithm. However, it requires a significant number of model evaluation (in the order of 10 to 50 times the number of dimensions) to converge to an optimal solution. This search method is more suitable when the time required for a model evaluation is relatively low.
• MOCMAES search is a multi-objective algorithm optimizing multiple tradeoffs simultaneously. To do that, MOCMAES employs $$\mu$$ CMAES algorithms. Thus requiring even more evaluation to converge to the optimal solution (in the order of $$\mu$$ times 10 to 50, times the number of dimensions). This search method is more suitable when the time required for a model evaluation is relatively low.

In addition to the 5 previous algorithms Chocolate proposes a wrapper that transforms the conditional search space problem in a multi-armed bandit problem.

• ThompsonSampling is a wrapper around any of the sampling/search algorithms that will allocate more resources to the exploration of the most promising subspaces. This method will help any of the algorithm in finding a superior solution in conditional search spaces.

Here is a table that resumes when to use each algorithm.

Algorithm Time Dimensions Continuity Conditions Multi-objective
Grid Low Low Discrete Yes No
Random High High Discrete Yes No
QuasiRandom High High Mixed Yes No
Bayes High Medium Mixed Yes No
CMAES Low Low Mixed No No
MOCMAES Low Low Mixed No Yes
ThompsonSampling Yes