Detailed Description

methods for bandit algorithms

Epsilon greedy

Epsilon greedy is a randomized algorithm for the multi-armed bandit problem.

In every iteration, it either selects an action uniformly at random with probability \( \varepsilon_t\) or it greedily exploits the best action seen so far with probability \( 1 - \varepsilon_t \). In this implementation, \( \varepsilon_t \) decreases over time (number of selections performed), controlled by the epsilon parameter.

Exp.3

Exp.3 is a randomized selection method for the multi-armed bandit problem

Exp3 maintains a probability distribution according to which an action is drawn in every iteration. The probability distribution is a mixture between a uniform distribution and a softmax distribution based on the cumulative rewards of the actions. The weight of the uniform distribution in the mixture is controlled by the parameter \( \gamma \), ie., setting \( \gamma = 1\) uses a uniform distribution in every selection step. The cumulative reward for the actions can be fine-tuned by adding a general bias for all actions. The bias is given by the parameter \( \beta \).

Upper Confidence Bounds (UCB)

UCB (Upper confidence bounds) is a deterministic selection algorithm for the multi-armed bandit problem. In every iteration, UCB selects the action that maximizes a tradeoff between its performance in the past and a variance term. The influence of the variance (confidence width) can be controlled by the parameter \( \alpha \).

Functions
SCIP_EXPORT SCIP_RETCODE	SCIPbanditSelect (SCIP_BANDIT bandit, int action)

SCIP_EXPORT SCIP_RETCODE	SCIPbanditUpdate (SCIP_BANDIT *bandit, int action, SCIP_Real score)

SCIP_EXPORT const char *	SCIPbanditvtableGetName (SCIP_BANDITVTABLE *banditvtable)

SCIP_EXPORT SCIP_RANDNUMGEN *	SCIPbanditGetRandnumgen (SCIP_BANDIT *bandit)

SCIP_EXPORT int	SCIPbanditGetNActions (SCIP_BANDIT *bandit)

SCIP_EXPORT SCIP_RETCODE	SCIPcreateBanditEpsgreedy (SCIP scip, SCIP_BANDIT epsgreedy, SCIP_Real priorities, SCIP_Real eps, SCIP_Bool preferrecent, SCIP_Real decayfactor, int avglim, int nactions, unsigned int initseed)

SCIP_EXPORT SCIP_Real *	SCIPgetWeightsEpsgreedy (SCIP_BANDIT *epsgreedy)

SCIP_EXPORT void	SCIPsetEpsilonEpsgreedy (SCIP_BANDIT *epsgreedy, SCIP_Real eps)

SCIP_EXPORT SCIP_RETCODE	SCIPcreateBanditExp3 (SCIP scip, SCIP_BANDIT exp3, SCIP_Real priorities, SCIP_Real gammaparam, SCIP_Real beta, int nactions, unsigned int initseed)

SCIP_EXPORT void	SCIPsetGammaExp3 (SCIP_BANDIT *exp3, SCIP_Real gammaparam)

SCIP_EXPORT void	SCIPsetBetaExp3 (SCIP_BANDIT *exp3, SCIP_Real beta)

SCIP_EXPORT SCIP_Real	SCIPgetProbabilityExp3 (SCIP_BANDIT *exp3, int action)

SCIP_EXPORT SCIP_RETCODE	SCIPcreateBanditUcb (SCIP scip, SCIP_BANDIT ucb, SCIP_Real priorities, SCIP_Real alpha, int nactions, unsigned int initseed)

SCIP_EXPORT SCIP_Real	SCIPgetConfidenceBoundUcb (SCIP_BANDIT *ucb, int action)

SCIP_EXPORT int *	SCIPgetStartPermutationUcb (SCIP_BANDIT *ucb)

SCIP_EXPORT SCIP_RETCODE	SCIPincludeBanditvtable (SCIP scip, SCIP_BANDITVTABLE banditvtable, const char name, SCIP_DECL_BANDITFREE((banditfree)), SCIP_DECL_BANDITSELECT((banditselect)), SCIP_DECL_BANDITUPDATE((banditupdate)), SCIP_DECL_BANDITRESET((banditreset)))

SCIP_EXPORT SCIP_BANDITVTABLE *	SCIPfindBanditvtable (SCIP scip, const char name)

SCIP_EXPORT SCIP_RETCODE	SCIPfreeBandit (SCIP scip, SCIP_BANDIT *bandit)

SCIP_EXPORT SCIP_RETCODE	SCIPresetBandit (SCIP scip, SCIP_BANDIT bandit, SCIP_Real *priorities, unsigned int seed)

Files
file	pub_bandit.h
	public methods for bandit algorithms

file	pub_bandit_epsgreedy.h
	public methods for the epsilon greedy bandit selector

file	pub_bandit_exp3.h
	public methods for Exp.3

file	pub_bandit_ucb.h
	public methods for UCB bandit selection

Function Documentation

◆ SCIPbanditSelect()

SCIP_EXPORT SCIP_RETCODE SCIPbanditSelect	(	SCIP_BANDIT *	bandit,
		int *	action
	)

select the next action

Parameters

bandit	bandit algorithm data structure
action	pointer to store the selected action

Definition at line 143 of file bandit.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPbanditGetNActions(), and SCIP_Bandit::vtable.

Referenced by selectNeighborhood().

◆ SCIPbanditUpdate()

SCIP_EXPORT SCIP_RETCODE SCIPbanditUpdate	(	SCIP_BANDIT *	bandit,
		int	action,
		SCIP_Real	score
	)

update the score of the selected action

Parameters

bandit	bandit algorithm data structure
action	index of action for which the score should be updated
score	observed gain of the i'th action

Definition at line 164 of file bandit.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPbanditGetNActions(), and SCIP_Bandit::vtable.

Referenced by updateBanditAlgorithm().

◆ SCIPbanditvtableGetName()

SCIP_EXPORT const char* SCIPbanditvtableGetName ( SCIP_BANDITVTABLE * banditvtable )

return the name of this bandit virtual function table

Parameters

banditvtable virtual table for bandit algorithm

Definition at line 272 of file bandit.c.

References SCIP_BanditVTable::name, and NULL.

Referenced by SCIPsetSortProps().

◆ SCIPbanditGetRandnumgen()

SCIP_EXPORT SCIP_RANDNUMGEN* SCIPbanditGetRandnumgen ( SCIP_BANDIT * bandit )

return the random number generator of a bandit algorithm

Parameters

bandit bandit algorithm data structure

Definition at line 283 of file bandit.c.

References NULL, and SCIP_Bandit::rng.

Referenced by alnsFixMoreVariables(), alnsUnfixVariables(), dataReset(), SCIP_DECL_BANDITRESET(), and SCIP_DECL_BANDITSELECT().

◆ SCIPbanditGetNActions()

SCIP_EXPORT int SCIPbanditGetNActions ( SCIP_BANDIT * bandit )

return number of actions of this bandit algorithm

Parameters

bandit bandit algorithm data structure

Definition at line 293 of file bandit.c.

References SCIP_Bandit::nactions, and NULL.

Referenced by SCIP_DECL_BANDITFREE(), SCIP_DECL_BANDITRESET(), SCIP_DECL_BANDITSELECT(), SCIP_DECL_BANDITUPDATE(), SCIP_DECL_HEURINITSOL(), SCIPbanditReset(), SCIPbanditSelect(), SCIPbanditUpdate(), SCIPgetConfidenceBoundUcb(), and SCIPgetProbabilityExp3().

◆ SCIPcreateBanditEpsgreedy()

SCIP_EXPORT SCIP_RETCODE SCIPcreateBanditEpsgreedy	(	SCIP *	scip,
		SCIP_BANDIT **	epsgreedy,
		SCIP_Real *	priorities,
		SCIP_Real	eps,
		SCIP_Bool	preferrecent,
		SCIP_Real	decayfactor,
		int	avglim,
		int	nactions,
		unsigned int	initseed
	)

create and resets an epsilon greedy bandit algorithm

Parameters

scip	SCIP data structure
epsgreedy	pointer to store the epsilon greedy bandit algorithm
priorities	nonnegative priorities for each action, or NULL if not needed
eps	parameter to increase probability for exploration between all actions
preferrecent	should the weights be updated in an exponentially decaying way?
decayfactor	the factor to reduce the weight of older observations if exponential decay is enabled
avglim	nonnegative limit on observation number before the exponential decay starts, only relevant if exponential decay is enabled
nactions	the positive number of possible actions
initseed	initial seed for random number generation

Definition at line 270 of file bandit_epsgreedy.c.

References BANDIT_NAME, NULL, SCIP_CALL, SCIP_INVALIDDATA, SCIP_OKAY, SCIPbanditCreateEpsgreedy(), SCIPblkmem(), SCIPbuffer(), SCIPerrorMessage, SCIPfindBanditvtable(), and SCIPinitializeRandomSeed().

Referenced by createBandit().

◆ SCIPgetWeightsEpsgreedy()

SCIP_EXPORT SCIP_Real* SCIPgetWeightsEpsgreedy ( SCIP_BANDIT * epsgreedy )

get weights array of epsilon greedy bandit algorithm

Parameters

epsgreedy epsilon greedy bandit algorithm

Definition at line 302 of file bandit_epsgreedy.c.

References NULL, and SCIPbanditGetData().

Referenced by printNeighborhoodStatistics().

◆ SCIPsetEpsilonEpsgreedy()

SCIP_EXPORT void SCIPsetEpsilonEpsgreedy	(	SCIP_BANDIT *	epsgreedy,
		SCIP_Real	eps
	)

set epsilon parameter of epsilon greedy bandit algorithm

Parameters

epsgreedy	epsilon greedy bandit algorithm
eps	parameter to increase probability for exploration between all actions

Definition at line 315 of file bandit_epsgreedy.c.

References eps, NULL, and SCIPbanditGetData().

◆ SCIPcreateBanditExp3()

SCIP_EXPORT SCIP_RETCODE SCIPcreateBanditExp3	(	SCIP *	scip,
		SCIP_BANDIT **	exp3,
		SCIP_Real *	priorities,
		SCIP_Real	gammaparam,
		SCIP_Real	beta,
		int	nactions,
		unsigned int	initseed
	)

creates and resets an Exp.3 bandit algorithm using scip pointer

Parameters

scip	SCIP data structure
exp3	pointer to store bandit algorithm
priorities	nonnegative priorities for each action, or NULL if not needed
gammaparam	weight between uniform (gamma ~ 1) and weight driven (gamma ~ 0) probability distribution
beta	gain offset between 0 and 1 at every observation
nactions	the positive number of actions for this bandit algorithm
initseed	initial seed for random number generation

Definition at line 301 of file bandit_exp3.c.

References BANDIT_NAME, NULL, SCIP_CALL, SCIP_INVALIDDATA, SCIP_OKAY, SCIPbanditCreateExp3(), SCIPblkmem(), SCIPbuffer(), SCIPerrorMessage, SCIPfindBanditvtable(), and SCIPinitializeRandomSeed().

Referenced by createBandit().

◆ SCIPsetGammaExp3()

SCIP_EXPORT void SCIPsetGammaExp3	(	SCIP_BANDIT *	exp3,
		SCIP_Real	gammaparam
	)

set gamma parameter of Exp.3 bandit algorithm to increase weight of uniform distribution

Parameters

exp3	bandit algorithm
gammaparam	weight between uniform (gamma ~ 1) and weight driven (gamma ~ 0) probability distribution

Definition at line 327 of file bandit_exp3.c.

References SCIPbanditGetData().

◆ SCIPsetBetaExp3()

SCIP_EXPORT void SCIPsetBetaExp3	(	SCIP_BANDIT *	exp3,
		SCIP_Real	beta
	)

set beta parameter of Exp.3 bandit algorithm to increase gain offset for actions that were not played

Parameters

exp3	bandit algorithm
beta	gain offset between 0 and 1 at every observation

Definition at line 340 of file bandit_exp3.c.

References SCIPbanditGetData().

◆ SCIPgetProbabilityExp3()

SCIP_EXPORT SCIP_Real SCIPgetProbabilityExp3	(	SCIP_BANDIT *	exp3,
		int	action
	)

returns probability to play an action

Parameters

exp3	bandit algorithm
action	index of the requested action

Definition at line 353 of file bandit_exp3.c.

References SCIP_Real, SCIPbanditGetData(), and SCIPbanditGetNActions().

Referenced by printNeighborhoodStatistics().

◆ SCIPcreateBanditUcb()

SCIP_EXPORT SCIP_RETCODE SCIPcreateBanditUcb	(	SCIP *	scip,
		SCIP_BANDIT **	ucb,
		SCIP_Real *	priorities,
		SCIP_Real	alpha,
		int	nactions,
		unsigned int	initseed
	)

create and reset UCB bandit algorithm

Parameters

scip	SCIP data structure
ucb	pointer to store bandit algorithm
priorities	nonnegative priorities for each action, or NULL if not needed
alpha	parameter to increase confidence width
nactions	the positive number of actions for this bandit algorithm
initseed	initial random number seed

Definition at line 329 of file bandit_ucb.c.

References BANDIT_NAME, NULL, SCIP_CALL, SCIP_INVALIDDATA, SCIP_OKAY, SCIPbanditCreateUcb(), SCIPblkmem(), SCIPbuffer(), SCIPerrorMessage, SCIPfindBanditvtable(), and SCIPinitializeRandomSeed().

Referenced by createBandit().

◆ SCIPgetConfidenceBoundUcb()

SCIP_EXPORT SCIP_Real SCIPgetConfidenceBoundUcb	(	SCIP_BANDIT *	ucb,
		int	action
	)

returns the upper confidence bound of a selected action

Parameters

ucb	UCB bandit algorithm
action	index of the queried action

Definition at line 254 of file bandit_ucb.c.

References LOG1P, NULL, SCIP_Real, SCIPbanditGetData(), SCIPbanditGetNActions(), and sqrt().

Referenced by printNeighborhoodStatistics().

◆ SCIPgetStartPermutationUcb()

SCIP_EXPORT int* SCIPgetStartPermutationUcb ( SCIP_BANDIT * ucb )

return start permutation of the UCB bandit algorithm

Parameters

ucb	UCB bandit algorithm

Definition at line 283 of file bandit_ucb.c.

References NULL, and SCIPbanditGetData().

◆ SCIPincludeBanditvtable()

SCIP_EXPORT SCIP_RETCODE SCIPincludeBanditvtable	(	SCIP *	scip,
		SCIP_BANDITVTABLE **	banditvtable,
		const char *	name,
		SCIP_DECL_BANDITFREE((*banditfree))	,
		SCIP_DECL_BANDITSELECT((*banditselect))	,
		SCIP_DECL_BANDITUPDATE((*banditupdate))	,
		SCIP_DECL_BANDITRESET((*banditreset))
	)

includes a bandit algorithm virtual function table

Parameters

scip	SCIP data structure
banditvtable	bandit algorithm virtual function table
name	a name for the algorithm represented by this vtable

Definition at line 38 of file scip_bandit.c.

References NULL, SCIP_CALL, SCIP_INVALIDDATA, SCIP_OKAY, SCIPbanditvtableCreate(), SCIPerrorMessage, SCIPfindBanditvtable(), SCIPsetIncludeBanditvtable(), and Scip::set.

Referenced by SCIPincludeBanditvtableEpsgreedy(), SCIPincludeBanditvtableExp3(), and SCIPincludeBanditvtableUcb().

◆ SCIPfindBanditvtable()

SCIP_EXPORT SCIP_BANDITVTABLE* SCIPfindBanditvtable	(	SCIP *	scip,
		const char *	name
	)

returns the bandit virtual function table of the given name, or NULL if not existing

Parameters

scip	SCIP data structure
name	name of bandit algorithm virtual function table

Definition at line 70 of file scip_bandit.c.

References NULL, SCIPsetFindBanditvtable(), and Scip::set.

Referenced by SCIPcreateBanditEpsgreedy(), SCIPcreateBanditExp3(), SCIPcreateBanditUcb(), and SCIPincludeBanditvtable().

◆ SCIPfreeBandit()

SCIP_EXPORT SCIP_RETCODE SCIPfreeBandit	(	SCIP *	scip,
		SCIP_BANDIT **	bandit
	)

calls destructor and frees memory of bandit algorithm

Parameters

scip	SCIP data structure
bandit	pointer to bandit algorithm data structure

Definition at line 97 of file scip_bandit.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPbanditFree(), and SCIPblkmem().

Referenced by SCIP_DECL_HEURFREE(), and SCIP_DECL_HEURINITSOL().

◆ SCIPresetBandit()

SCIP_EXPORT SCIP_RETCODE SCIPresetBandit	(	SCIP *	scip,
		SCIP_BANDIT *	bandit,
		SCIP_Real *	priorities,
		unsigned int	seed
	)

reset the bandit algorithm

Parameters

scip	SCIP data structure
bandit	pointer to bandit algorithm data structure
priorities	priorities for every action, or NULL if not needed
seed	initial random seed for bandit selection

Definition at line 81 of file scip_bandit.c.

References NULL, SCIP_CALL, SCIP_OKAY, SCIPbanditReset(), SCIPbuffer(), and SCIPinitializeRandomSeed().

Referenced by SCIP_DECL_HEURINITSOL().

SCIP

Detailed Description

Epsilon greedy

Exp.3

Upper Confidence Bounds (UCB)

Functions

Files

Function Documentation

◆ SCIPbanditSelect()

◆ SCIPbanditUpdate()

◆ SCIPbanditvtableGetName()

◆ SCIPbanditGetRandnumgen()

◆ SCIPbanditGetNActions()

◆ SCIPcreateBanditEpsgreedy()

◆ SCIPgetWeightsEpsgreedy()

◆ SCIPsetEpsilonEpsgreedy()

◆ SCIPcreateBanditExp3()

◆ SCIPsetGammaExp3()

◆ SCIPsetBetaExp3()

◆ SCIPgetProbabilityExp3()

◆ SCIPcreateBanditUcb()

◆ SCIPgetConfidenceBoundUcb()

◆ SCIPgetStartPermutationUcb()

◆ SCIPincludeBanditvtable()

◆ SCIPfindBanditvtable()

◆ SCIPfreeBandit()

◆ SCIPresetBandit()