# Algorithms¶

Default algorithm is a random search based on the probability distribution given to a search parameter’s definition.

## Selecting and Configuring¶

In a Oríon configuration YAML, define:

```experiment:
algorithms:
learning_rate: 0.1
```

In this particular example, the name of the algorithm extension class to be imported and instantiated is `Gradient_Descent`, so the lower-case identifier corresponds to it.

All algorithms have default arguments that should work reasonably well in general. To tune the algorithm for a specific problem, you can set those arguments in the yaml file as shown above with `learning_rate`.

## Included Algorithms¶

### Hyperband¶

Hyperband extends the SuccessiveHalving algorithm by providing a way to exploit a fixed budget with different number of configurations for `SuccessiveHalving` algorithm to evaluate. Each run of `SuccessiveHalving` will be defined as a `bracket` in Hyperband. Hyperband requires two inputs (1) `R`, the maximum amount of resource that can be allocated to a single configuration, and (2) `eta`, an input that controls the proportion of configurations discarded in each round of SuccessiveHalving.

To use Hyperband in Oríon, you must specify one parameter with `fidelity(low, high, base)` as the prior, `low` will be ignored, `high` will be taken as the maximum resource `R` and `base` will be taken as the reduction factor `eta`.

Number of epochs usually can be used as the resource but the algorithm is generic and can be applied to any multi-fidelity setting. That is, you can use training time, specifying the fidelity with `--epochs~fidelity(low=1, high=81, base=3)` (assuming your script takes this argument in commandline), but you could also use other fidelity such as dataset size `--dataset-size~fidelity(low=500, high=50000)` (assuming your script takes this argument and adapt dataset size accordingly).

Note

Current implementation does not support more than one fidelity dimension.

#### Configuration¶

```experiment:
algorithms:
hyperband:
seed: null
repetitions: 1

strategy: StubParallelStrategy
```

Note

Notice the additional `strategy` in configuration which is not mandatory for most other algorithms. See StubParallelStrategy for more information.

class orion.algo.hyperband.Hyperband(space, seed=None, repetitions=inf)[source]

Hyperband formulates hyperparameter optimization as a pure-exploration non-stochastic infinite-armed bandit problem where a predefined resource like iterations, data samples, or features is allocated to randomly sampled configurations.`

Li, Lisha et al. “Hyperband: A Novel Bandit-Based Approach to Hyperparameter Optimization” Journal of Machine Learning Research, 18:1-52, 2018.

Parameters
space: `orion.algo.space.Space`

Optimisation space with priors for each dimension.

seed: None, int or sequence of int

Seed for the random number generator used to sample new trials. Default: `None`

repetitions: int

Number of executions for Hyperband. A single execution of Hyperband takes a finite budget of `(log(R)/log(eta) + 1) * (log(R)/log(eta) + 1) * R`, and `repetitions` allows you to run multiple executions of Hyperband. Default is `numpy.inf` which means to run Hyperband until no new trials can be suggested.

### ASHA¶

Asynchronous Successive Halving Algorithm, the asynchronous version of Hyperband, can be roughly interpreted as a sophisticated random search that leverages partial information of the trial execution to concentrate resources on the most promising ones.

The main idea of the algorithm is the following. Given a fidelity dimension, such as the number of epochs to train or the size of the dataset, ASHA samples trials with low-fidelity and promotes the most promising ones to the next fidelity level. This makes it possible to only execute one trial with full fidelity, leading to very optimal resource usage.

The most common way of using ASHA is to reduce the number of epochs, but the algorithm is generic and can be applied to any multi-fidelity setting. That is, you can use training time, specifying the fidelity with `--epochs~fidelity(low=1, high=100)` (assuming your script takes this argument in commandline), but you could also use other fidelity such as dataset size `--dataset-size~fidelity(low=500, high=50000)` (assuming your script takes this argument and adapt dataset size accordingly). The placeholder `fidelity(low, high)` is a special prior for multi-fidelity algorithms.

Note

Current implementation does not support more than one fidelity dimension.

#### Configuration¶

```experiment:
algorithms:
asha:
seed: null
num_rungs: null
num_brackets: 1
repetitions: 1

strategy: StubParallelStrategy
```

Note

Notice the additional `strategy` in configuration which is not mandatory for most other algorithms. See StubParallelStrategy for more information.

class orion.algo.asha.ASHA(space, seed=None, num_rungs=None, num_brackets=1, repetitions=inf)[source]

Asynchronous Successive Halving Algorithm

A simple and robust hyperparameter tuning algorithm with solid theoretical underpinnings that exploits parallelism and aggressive early-stopping.

Li, Liam, et al. “Massively parallel hyperparameter tuning.” arXiv preprint arXiv:1810.05934 (2018)

Parameters
space: `orion.algo.space.Space`

Optimisation space with priors for each dimension.

seed: None, int or sequence of int

Seed for the random number generator used to sample new trials. Default: `None`

num_rungs: int, optional

Number of rungs for the largest bracket. If not defined, it will be equal to `(base + 1)` of the fidelity dimension. In the original paper, `num_rungs == log(fidelity.high/fidelity.low) / log(fidelity.base) + 1`. Default: `log(fidelity.high/fidelity.low) / log(fidelity.base) + 1`

num_brackets: int

Using a grace period that is too small may bias ASHA too strongly towards fast converging trials that do not lead to best results at convergence (stagglers). To overcome this, you can increase the number of brackets, which increases the amount of resource required for optimisation but decreases the bias towards stragglers. Default: 1

repetitions: int

Number of execution of ASHA. Default is numpy.inf which means to run ASHA until no new trials can be suggested.

### TPE¶

Tree-structured Parzen Estimator (TPE) algorithm is one of Sequential Model-Based Global Optimization (SMBO) algorithms, which will build models to propose new points based on the historical observed trials.

Instead of modeling p(y|x) like other SMBO algorithms, TPE models p(x|y) and p(y), and p(x|y) is modeled by transforming that generative process, replacing the distributions of the configuration prior with non-parametric densities.

The TPE defines p(x|y) using two such densities l(x) and g(x) where l(x) is distribution of good points and g(x) is the distribution of bad points. Good and bad points are split from observed points so far with a parameter gamma which defines the ratio of good points. New point candidates will be sampled with l(x) and Expected Improvement (EI) optimization scheme will be used to find the most promising point among the candidates.

Note

Current implementation only supports uniform, loguniform, uniform discrete and choices as prior. As for choices prior, the probabilities if any given will be ignored.

#### Configuration¶

```experiment:
algorithms:
tpe:
seed: null
n_initial_points: 20
n_ei_candidates: 25
gamma: 0.25
equal_weight: False
prior_weight: 1.0
full_weight_num: 25
```
class orion.algo.tpe.TPE(space, seed=None, n_initial_points=20, n_ei_candidates=24, gamma=0.25, equal_weight=False, prior_weight=1.0, full_weight_num=25)[source]

Tree-structured Parzen Estimator (TPE) algorithm is one of Sequential Model-Based Global Optimization (SMBO) algorithms, which will build models to propose new points based on the historical observed trials.

Instead of modeling p(y|x) like other SMBO algorithms, TPE models p(x|y) and p(y), and p(x|y) is modeled by transforming that generative process, replacing the distributions of the configuration prior with non-parametric densities.

The TPE defines p(x|y) using two such densities l(x) and g(x) while l(x) is distribution of good points and g(x) is the distribution of bad points. New point candidates will be sampled with l(x) and Expected Improvement (EI) optimization scheme will be used to find the most promising point among the candidates.

Parameters
space: `orion.algo.space.Space`

Optimisation space with priors for each dimension.

seed: None, int or sequence of int

Seed to sample initial points and candidates points. Default: `None`

n_initial_points: int

Number of initial points randomly sampled. If new points are requested and less than n_initial_points are observed, the next points will also be sampled randomly instead of being sampled from the parzen estimators. Default: `20`

n_ei_candidates: int

Number of candidates points sampled for ei compute. Default: `24`

gamma: real

Ratio to split the observed trials into good and bad distributions. Default: `0.25`

equal_weight: bool

True to set equal weights for observed points. Default: `False`

prior_weight: int

The weight given to the prior point of the input space. Default: `1.0`

full_weight_num: int

The number of the most recent trials which get the full weight where the others will be applied with a linear ramp from 0 to 1.0. It will only take effect if equal_weight is False.

### Evolution-ES¶

Evolution-ES, the evolution algorithm with early stop version. Here is an implementation of Evolution-ES. In the evolution algorithm, we follow the tournament selection algorithm as Large-Scale-Evolution. Tournament selection evolutionary hyper-parameter search is conducted by first defining a gene encoding that describes a hyper-parameter combination, and then creating the initial population by randomly sampling from the space of gene encodings to create individuals, which are trained and assigned fitnesses. The population is then repeatedly sampled from to produce groups, and the parent is selected by the individual with the highest fitness. Selected parents have their gene encodings mutated to produce child models. Individual in the group with the lowest fitness is killed, while the newly evaluated child model is added to the population, taking the killed individual’s place. This process is repeated and results in a population with high fitness individuals can represent the good hyper-parameter combination. Evolution-ES also formulated a method to dynamically allocate resources to more promising individual according to their fitness, which is referred to as Progressive Dynamic Hurdles (PDH), allows individuals that are consistently performing well to train for more steps. It can be roughly interpreted as a sophisticated random search that leverages partial information of the trial execution to concentrate resources on the most promising ones.

The implementation follows the process and use way of Hyperband. Additionally, The fidelity base in Evolution-ES can be extended to support `fidelity(low, high, base=1)`, which is the same as `linspace(low, high)`.

#### Configuration¶

```experiment:
algorithms:
EvolutionES:
seed: null
repetitions: 1
nums_population: 20
mutate:
function: orion.algo.mutate_functions.default_mutate
multiply_factor: 3.0

strategy: StubParallelStrategy
```
class orion.algo.evolution_es.EvolutionES(space, seed=None, repetitions=inf, nums_population=20, mutate=None, max_retries=1000)[source]

EvolutionES formulates hyperparameter optimization as an evolution.

For more information on the algorithm, see original paper at https://arxiv.org/pdf/1703.01041.pdf and https://arxiv.org/pdf/1901.11117.pdf

Real et al. “Large-Scale Evolution of Image Classifiers” So et all. “The Evolved Transformer”

Parameters
space: `orion.algo.space.Space`

Optimisation space with priors for each dimension.

seed: None, int or sequence of int

Seed for the random number generator used to sample new trials. Default: `None`

repetitions: int

Number of execution of Hyperband. Default is numpy.inf which means to run Hyperband until no new trials can be suggested.

nums_population: int

Number of population for EvolutionES. Larger number of population often gets better performance but causes more computation. So there is a trade-off according to the search space and required budget of your problems. Default: 20

mutate: str or None, optional

In the mutate part, one can define the customized mutate function with its mutate factors, such as multiply factor (times/divides by a multiply factor) and add factor (add/subtract by a multiply factor). The function must be defined by an importable string. If None, default mutate function is used: `orion.algo.mutate_functions.default_mutate`.

## Algorithm Plugins¶

Plugins documentation is hosted separately. See short documentations below to find links to full plugins documentation.

### Scikit-Optimize¶

This package is a plugin providing a wrapper for skopt optimizers.

### Robust Bayesian Optimization¶

This package is a plugin providing a wrapper for RoBO optimizers.

You will find in this plugin many models for Bayesian Optimization: Gaussian Process, Gaussian Process with MCMC, Random Forest, DNGO and BOHAMIANN.

## Parallel Strategies¶

A parallel strategy is a method to improve parallel optimization for sequential algorithms. Such algorithms can only observe trials that are completed and have a corresponding objective. To get around this, parallel strategies produces lies, noncompleted trials with fake objectives, which are then passed to a temporary copy of the algorithm that will suggest a new point. The temporary algorithm is then discarded. The original algorithm never obverses lies, and the temporary copy always observes lies that are based on most up-to-date data. The strategies will differ in how they assign objectives to the lies.

By default, the strategy used is MaxParallelStrategy

### NoParallelStrategy¶

Does not return any lie. This is useful to benchmark parallel strategies and measure how they can help compared to no strategy.

### StubParallelStrategy¶

Assign to lies an objective of `None` so that non-completed trials are observed and identifiable by algorithms that can leverage parallel optimization.

The value of the objective is customizable with `stub_value`.

```experiment:
strategy:
StubParallelStrategy:
stub_value: 'custom value'
```

### MaxParallelStrategy¶

Assigns to lies the best objective observed so far.

The default value assigned to objective when less than 1 trial is completed is configurable with `default_result`. It is `float('inf')` by default.

```experiment:
strategy:
MaxParallelStrategy:
default_result: 10000
```

### MeanParallelStrategy¶

Assigns to lies the mean of all objectives observed so far.

The default value assigned to objective when less than 2 trials are completed is configurable with `default_result`. It is `float('inf')` by default.

```experiment:
strategy:
MeanParallelStrategy:
default_result: 0.5
```