Gradient Descent (UDA)

class gd4cgp : public pagmo::not_population_based

Gradient descent for a Cartesian Genetic Program.

../../_images/gd.png

In a symbolic regression problem, models parameters are typically present in the form of ephemeral constants (i.e. extra input terminals). The actual values of the constants have a profound effect on the resulting loss and its an open question how to balance the learning of the model parameters (continuous optimization) with learning the model itself (integer optimization)

In this class we provide a simple gradient descent algorithm able to tackle :class:dcgp::symbolic_regression problems The gradient descent will only modify the continuous part of the chromosome, leaving the integer part (i.e. the actual model) unchanged.

Public Types

typedef std::tuple<unsigned, unsigned long long, unsigned long long, double, double, double> log_line_type

Single entry of the log (iter, fevals, gevals, gradient_magnitude, lr, best)

typedef std::vector<log_line_type> log_type

The log.

Public Functions

inline gd4cgp(unsigned max_iter = 1u, double lr = 1., double lr_min = 1e-3)

Constructor.

Constructs a stochastic gradient descent for use with a cgp::symbolic_regression UDP that has any strictly positive number of ephemeral constants

Parameters

  • max_iter – maximum number of iterations.

  • lr – initial learning rate.

  • lr_min – minimum learning rate.

Throws

std::invalid_argument – if lr_min is not in (0, lr)

inline pagmo::population evolve(pagmo::population pop) const

Algorithm evolve method.

Evolves the population for a maximum number of generations

Parameters

pop – population to be evolved

Throws

  • std::invalid_argument – if a dcgp::symbolic_regression cannot be extracted from the problem

  • std::invalid_argument – if no ephemeral constants are detected in the model.

  • std::invalid_argument – if the number of objectives is not 1.

Returns

evolved population

inline void set_verbosity(unsigned level)

Sets the algorithm verbosity.

Sets the verbosity level of the screen output and of the log returned by get_log(). level can be:

  • 0: no verbosity

  • >0: will print and log one line each level generations.

Example (verbosity 1): 

Iter:        Fevals:        Gevals:     grad norm:            lr:         Best:
    0              0              0              0              1        9349.95
    1              1              1        4180.21            1.5        7390.53
    2              2              2         308.04          0.375        7390.53
    3              3              3         308.04         0.5625        7386.77
    4              4              4        312.186       0.140625        7386.77
    5              5              5        312.186       0.210938        7353.28
    6              6              6        169.472       0.316406        7335.08
    7              7              7        186.938       0.474609        7320.24
    8              8              8        269.803       0.118652        7320.24
    9              9              9        269.803       0.177979        7295.06
   10             10             10        168.844       0.266968        7271.23
Gen is the generation number, Fevals the number of function evaluation used, Gevals the number of gradient evaluation used, lr is the current learning rate, or line search width and Best is the best fitness found.

Parameters

level – verbosity level

inline unsigned get_verbosity() const

Gets the verbosity level.

Returns

the verbosity level

inline std::string get_name() const

Algorithm name.

Returns

a string containing the algorithm name

inline std::string get_extra_info() const

Extra info.

Returns

a string containing extra info on the algorithm

inline const log_type &get_log() const

Get log.

A log containing relevant quantities monitoring the last call to evolve. Each element of the returned std::vector is a gd4cgp::log_line_type as described in gd4cgp::set_verbosity().

Returns

an std::vector of gd4cgp::log_line_type containing the logged values.

template<typename Archive>
inline void serialize(Archive &ar, unsigned)

Object serialization.

This method will save/load this into the archive ar.

Parameters

ar – target archive.

Throws

unspecified – any exception thrown by the serialization of the expression and of primitive types.