osp.seq.batch.design: Adaptive Batching designs for optimal stopping

In mludkov/mlOSP: Machine Learning and Regression Monte Carlo Algorithms for Optimal Stopping

Adaptive Batching designs for optimal stopping

Description

Sequential experimental design for optimal stopping problems with several adaptive batching heuristics based on Lyu & Ludkovski (2020+)

Usage

osp.seq.batch.design(model, method = "km", t0 = 0.01, is.gbm = FALSE)

Arguments

model	a list containing all the model parameters.
method	A GP emulator to apply. Must be one of km, trainkm homgp, homtp or hetgp
t0	parameter t0 for the ABSUR heuristic [Default value is 0.01]
is.gbm	flag to indicate whether the underlying simulator is independent log-normals (used as part of density computation for integrated EI criteria) [Default FALSE]

Details

Implements the adaptive batching strategy defined in mode$batch.heuristic. Calls lhs from library tgp. Possible batch heuristics are:

• fb: [Default] fixed batch amounts (essentially same as osp.seq.design)

• mlb: Multi-level batching; relies on model$r.cand

• rb: Ratchet batching; relies on model$r.cand

• absur: Adaptive batching with Stepwise Uncertainty Reduction; relies on model$t0

• adsa: Adaptive Design with Sequential Allocation

• ddsa: Deterministic ADSA that alternates between adding a new input site and allocating to existing sites

All heuristics also require specifying the acquisition function for expected improvement criterion via model$ei.func, see osp.seq.design

Value

a list containing:

• fit a list of fitted response surfaces

• timeElapsed vector of time costs for each round

• nsims total number of 1-step model$sim.func calls

• empLoss vector of empirical losses

• ndesigns: number of unique designs k_T

• batches: matrix of replications r_i, indexed by time-steps and by sequential rounds

References

M. Ludkovski, X. Lyu (2020+) Adaptive Batching for Gaussian Process Surrogates with Application in Noisy Level Set Estimation, <http://arxiv.org/abs/2003.08579>

See Also

[mlOSP::osp.seq.design]

Examples

sob30 <- randtoolbox::sobol(55, d=2)  # construct a space-filling initial design
sob30 <- sob30[ which( sob30[,1] + sob30[,2] <= 1) ,]  
sob30 <- 25+30*sob30 
model2d <- list(x0 = rep(40,2),K=40,sigma=rep(0.2,2),r=0.06,
 div=0,T=1,dt=0.04,dim=2,sim.func=sim.gbm, 
 payoff.func=put.payoff, look.ahead=1, pilot.nsims=1000,
 cand.len=1000,max.lengthscale=c(40,40),min.lengthscale=c(3,3),
 seq.design.size=50,batch.nrep=25,total.budget=2000,init.size=30,
 init.grid=sob30, kernel.family="gauss",update.freq=5,
 r.cand=c(20, 30,40,50,60, 80, 120, 160))
set.seed(11)
require(tgp)
require(DiceKriging)
require(laGP)
require(ks)
model2d$batch.heuristic <- 'adsa'
model2d$ei.func <- 'amcu'
oos.obj.adsa <- osp.seq.batch.design(model2d,method="trainkm")
plt.2d.surf.with.batch(oos.obj.adsa$fit[[15]], 
                     oos.obj.adsa$batches[1:oos.obj.adsa$ndesigns[15] - 1, 15])

mludkov/mlOSP documentation built on April 29, 2023, 7:56 p.m.