Contextual-Linear-Optimization-with-Bandit-Feedback

Replication code for the paper "Contextual Linear Optimization with Bandit Feedback".

Paper Link：https://arxiv.org/pdf/2405.16564

The Random_policy file corresponds to Tables 1 and 2 in the body of the paper, and Tables 3 and 4 in the appendix.

The X1_policy file corresponds to Tables 5 and 6 in the appendix.

The X1X2_policy file corresponds to Tables 7 and 8 in the appendix.

Details

File name interpretation

"No kernel" means that we do not use the kernel method. "Tree" means that we use the decision tree model to learn the policy in X1_policy and X1X2_policy settings. "Sample" means that we estimate probability of each path/decision given contexts from sample data. "Linear Wrong" means that we use the misspecified Nuisance model.

Table 1 and 3

● ETO

Random_policy/ETO/ETO.py --> Random_policy/ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> Random_policy/ETO/Regret_ETO.csv --> Random_policy/ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

Random_policy/SPO+DM_DR_PI_Lamdba_Clip/SPO+DM_DR_PI_Lamdba_Clip.py --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model.csv & regret_no_kernel_Sample_Double_Robust.csv & regret_no_kernel_Lambda_Sample_Double_Robust.csv & regret_no_kernel_Clip_Sample_Double_Robust.csv --> Result_processing_example_code.R --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_well_specified_result.csv --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_well_specified_result.xlsx

● SPO+ ISW

Random_policy/SPO+ISW/SPO+ISW.py --> Random_policy/SPO+ISW/regret_no_kernel_ISW_Sample.csv --> Result_processing_example_code.R --> Random_policy/SPO+ISW/SPO+ISW_result.csv --> Random_policy/SPO+ISW/SPO+ISW_result.xlsx

● Naive ETO

Random_policy/Naive_ETO/Naive_ETO.py --> Random_policy/Naive_ETO/regret_all_Correct_ETO.csv & regret_all_Wrong_ETO.csv --> Result_processing_example_code.R --> Random_policy/Naive_ETO/Regret_ETO.csv --> Random_policy/Naive_ETO/Regret_ETO.xlsx

● Naive SPO+ DM

Random_policy/Naive_SPO+DM/Naive_SPO+DM.py --> Random_policy/Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DM/Naive_SPO+DM_result.csv --> Random_policy/Naive_SPO+DM/Naive_SPO+DM_result.xlsx

● Naive SPO+ DR

Random_policy/Naive_SPO+DR/Naive_SPO+DR.py --> Random_policy/Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DR/Naive_SPO+DR_result.csv --> Random_policy/Naive_SPO+DR/Naive_SPO+DR_result.xlsx

● Naive SPO+ IPW

Random_policy/Naive_SPO+IPW/Naive_SPO+IPW.py --> Random_policy/Naive_SPO+IPW/regret_no_kernel_IPW.csv --> Result_processing_example_code.R --> Random_policy/Naive_SPO+IPW/Naive_SPO+IPW_result.csv --> Random_policy/Naive_SPO+IPW/Naive_SPO+IPW_result.xlsx

Table 2 and 4

● ETO (misspecified degree 2)

Random_policy/ETO_misspecified2/ETO_misspecified2.py --> Random_policy/ETO_misspecified2/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> Random_policy/ETO_misspecified2/Regret_ETO.csv --> Random_policy/ETO_misspecified2/Regret_ETO.xlsx

● ETO (misspecified degree 4)

Random_policy/ETO/ETO.py --> Random_policy/ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> Random_policy/ETO/Regret_ETO.csv --> Random_policy/ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 4

Random_policy/SPO+DM_DR_PI_Lamdba_Clip/SPO+DM_DR_PI_Lamdba_Clip.py --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model.csv & regret_no_kernel_Sample_Double_Robust.csv & regret_no_kernel_Lambda_Sample_Double_Robust.csv & regret_no_kernel_Clip_Sample_Double_Robust.csv --> Result_processing_example_code.R --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_well_specified_result.csv --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

Random_policy/SPO+DM_DR_PI_Lamdba_Clip/SPO+DM_DR_PI_Lamdba_Clip.py --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Sample_Double_Robust.csv & regret_no_kernel_Lambda_Linear_Wrong_Sample_Double_Robust.csv & regret_no_kernel_Clip_Linear_Wrong_Sample_Double_Robust.csv --> Result_processing_example_code.R --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_misspecified_result.csv --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip/Nuisance_model_misspecified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 2

Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Direct_Model.csv & regret_no_kernel_Sample_Double_Robust.csv & regret_no_kernel_Lambda_Sample_Double_Robust.csv & regret_no_kernel_Clip_Sample_Double_Robust.csv --> Result_processing_example_code.R --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/Nuisance_model_well_specified_result.csv --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Sample_Double_Robust.csv & regret_no_kernel_Lambda_Linear_Wrong_Sample_Double_Robust.csv & regret_no_kernel_Clip_Linear_Wrong_Sample_Double_Robust.csv --> Result_processing_example_code.R --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/Nuisance_model_misspecified2_result.csv --> Random_policy/SPO+DM_DR_PI_Lamdba_Clip_misspecified2/Nuisance_model_misspecified2_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

Random_policy/Naive_SPO+DM/Naive_SPO+DM.py --> Random_policy/Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DM/Naive_SPO+DM_result.csv --> Random_policy/Naive_SPO+DM/Naive_SPO+DM_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

Random_policy/Naive_SPO+DM_misspecified2/Naive_SPO+DM_misspecified2.py --> Random_policy/Naive_SPO+DM_misspecified2/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DM_misspecified2/Naive_SPO+DM_misspecified2_result.csv --> Random_policy/Naive_SPO+DM_misspecified2/Naive_SPO+DM_misspecified2_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

Random_policy/Naive_SPO+DR/Naive_SPO+DR.py --> Random_policy/Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DR/Naive_SPO+DR_result.csv --> Random_policy/Naive_SPO+DR/Naive_SPO+DR_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

Random_policy/Naive_SPO+DR_misspecified2/Naive_SPO+DR_misspecified2.py --> Random_policy/Naive_SPO+DR_misspecified2/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> Random_policy/Naive_SPO+DR_misspecified2/Naive_SPO+DR_misspecified2_result.csv --> Random_policy/Naive_SPO+DR_misspecified2/Naive_SPO+DR_misspecified2_result.xlsx

Table 5

● ETO

X1_policy/X1_ETO/X1_ETO.py --> X1_policy/X1_ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1_policy/X1_ETO/Regret_ETO.csv --> X1_policy/X1_ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_SPO+DM_DR_PI_Lamdba_Clip.py --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_well_specified_result.csv --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_well_specified_result.xlsx

● SPO+ ISW

X1_policy/X1_SPO+ISW/X1_SPO+ISW.py --> X1_policy/X1_SPO+ISW/regret_no_kernel_ISW_Sample.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+ISW/X1_SPO+ISW_result.csv --> X1_policy/X1_SPO+ISW/X1_SPO+ISW_result.xlsx

● Naive ETO

X1_policy/X1_Naive_ETO/X1_Naive_ETO.py --> X1_policy/X1_Naive_ETO/regret_all_Correct_ETO.csv & regret_all_Wrong_ETO.csv --> Result_processing_example_code.R --> X1_policy/X1_Naive_ETO/Regret_ETO.csv --> X1_policy/X1_Naive_ETO/Regret_ETO.xlsx

● Naive SPO+ DM

X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM.py --> X1_policy/X1_Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM_result.csv --> X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM_result.xlsx

● Naive SPO+ DR

X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR.py --> X1_policy/X1_Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR_result.csv --> X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR_result.xlsx

● Naive SPO+ IPW

X1_policy/X1_Naive_SPO+IPW/X1_Naive_SPO+IPW.py --> X1_policy/X1_Naive_SPO+IPW/regret_no_kernel_IPW.csv --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+IPW/X1_Naive_SPO+IPW_result.csv --> X1_policy/X1_Naive_SPO+IPW/X1_Naive_SPO+IPW_result.xlsx

Table 6

● ETO (misspecified degree 2)

X1_policy/X1_ETO_misspecified2/X1_ETO_misspecified2.py --> X1_policy/X1_ETO_misspecified2/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1_policy/X1_ETO_misspecified2/Regret_ETO.csv --> X1_policy/X1_ETO_misspecified2/Regret_ETO.xlsx

● ETO (misspecified degree 4)

X1_policy/X1_ETO/X1_ETO.py --> X1_policy/X1_ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1_policy/X1_ETO/Regret_ETO.csv --> X1_policy/X1_ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 4

X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_SPO+DM_DR_PI_Lamdba_Clip.py --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model_tree.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_well_specified_result.csv --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_SPO+DM_DR_PI_Lamdba_Clip.py --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Lambda_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Clip_Linear_Wrong_Double_Robust_Tree_Sigma.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_misspecified_result.csv --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip/X1_Nuisance_model_misspecified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 2

X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Direct_Model_tree.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_Nuisance_model_well_specified_result.csv --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Lambda_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Clip_Linear_Wrong_Double_Robust_Tree_Sigma.csv --> Result_processing_example_code.R --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_Nuisance_model_misspecified2_result.csv --> X1_policy/X1_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1_Nuisance_model_misspecified2_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM.py --> X1_policy/X1_Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM_result.csv --> X1_policy/X1_Naive_SPO+DM/X1_Naive_SPO+DM_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1_policy/X1_Naive_SPO+DM_misspecified2/X1_Naive_SPO+DM_misspecified2.py --> X1_policy/X1_Naive_SPO+DM_misspecified2/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DM_misspecified2/X1_Naive_SPO+DM_misspecified2_result.csv --> X1_policy/X1_Naive_SPO+DM_misspecified2/X1_Naive_SPO+DM_misspecified2_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR.py --> X1_policy/X1_Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR_result.csv --> X1_policy/X1_Naive_SPO+DR/X1_Naive_SPO+DR_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1_policy/X1_Naive_SPO+DR_misspecified2/X1_Naive_SPO+DR_misspecified2.py --> X1_policy/X1_Naive_SPO+DR_misspecified2/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1_policy/X1_Naive_SPO+DR_misspecified2/X1_Naive_SPO+DR_misspecified2_result.csv --> X1_policy/X1_Naive_SPO+DR_misspecified2/X1_Naive_SPO+DR_misspecified2_result.xlsx

Table 7

● ETO

X1X2_policy/X1X2_ETO/X1X2_ETO.py --> X1X2_policy/X1X2_ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_ETO/Regret_ETO.csv --> X1X2_policy/X1X2_ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_SPO+DM_DR_PI_Lamdba_Clip.py --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_well_specified_result.csv --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_well_specified_result.xlsx

● SPO+ ISW

X1X2_policy/X1X2_SPO+ISW/X1X2_SPO+ISW.py --> X1X2_policy/X1X2_SPO+ISW/regret_no_kernel_ISW_Sample.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+ISW/X1X2_SPO+ISW_result.csv --> X1X2_policy/X1X2_SPO+ISW/X1X2_SPO+ISW_result.xlsx

● Naive ETO

X1X2_policy/X1X2_Naive_ETO/X1X2_Naive_ETO.py --> X1X2_policy/X1X2_Naive_ETO/regret_all_Correct_ETO.csv & regret_all_Wrong_ETO.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_ETO/Regret_ETO.csv --> X1X2_policy/X1X2_Naive_ETO/Regret_ETO.xlsx

● Naive SPO+ DM

X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM.py --> X1X2_policy/X1X2_Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM_result.csv --> X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM_result.xlsx

● Naive SPO+ DR

X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR.py --> X1X2_policy/X1X2_Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR_result.csv --> X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR_result.xlsx

● Naive SPO+ IPW

X1X2_policy/X1X2_Naive_SPO+IPW/X1X2_Naive_SPO+IPW.py --> X1X2_policy/X1X2_Naive_SPO+IPW/regret_no_kernel_IPW.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+IPW/X1X2_Naive_SPO+IPW_result.csv --> X1X2_policy/X1X2_Naive_SPO+IPW/X1X2_Naive_SPO+IPW_result.xlsx

Table 8

● ETO (misspecified degree 2)

X1X2_policy/X1X2_ETO_misspecified2/X1X2_ETO_misspecified2.py --> X1X2_policy/X1X2_ETO_misspecified2/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_ETO_misspecified2/Regret_ETO.csv --> X1X2_policy/X1X2_ETO_misspecified2/Regret_ETO.xlsx

● ETO (misspecified degree 4)

X1X2_policy/X1X2_ETO/X1X2_ETO.py --> X1X2_policy/X1X2_ETO/regret_all_Wrong_ETO.csv & regret_all_Correct_ETO.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_ETO/Regret_ETO.csv --> X1X2_policy/X1X2_ETO/Regret_ETO.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 4

X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_SPO+DM_DR_PI_Lamdba_Clip.py --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Direct_Model_tree.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_well_specified_result.csv --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_SPO+DM_DR_PI_Lamdba_Clip.py --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Lambda_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Clip_Linear_Wrong_Double_Robust_Tree_Sigma.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_misspecified_result.csv --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip/X1X2_Nuisance_model_misspecified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is well-specified and Policy-inducing model $F$ is misspecified degree 2

X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Direct_Model_tree.csv & regret_no_kernel_Sample_Double_Robust_tree.csv & regret_no_kernel_Lambda_Sample_Double_Robust_tree.csv & regret_no_kernel_Clip_Sample_Double_Robust_tree.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_Nuisance_model_well_specified_result.csv --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_Nuisance_model_well_specified_result.xlsx

● SPO+ DM & SPO+ DR PI & SPO+ DR Lambda & SPO+ DR Clip

1. Nuisance Model $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
2. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2.py --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/regret_no_kernel_Linear_Wrong_Direct_Model.csv & regret_no_kernel_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Lambda_Linear_Wrong_Double_Robust_Tree_Sigma.csv & regret_no_kernel_Clip_Linear_Wrong_Double_Robust_Tree_Sigma.csv --> Result_processing_example_code.R --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_Nuisance_model_misspecified2_result.csv --> X1X2_policy/X1X2_SPO+DM_DR_PI_Lamdba_Clip_misspecified2/X1X2_Nuisance_model_misspecified2_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM.py --> X1X2_policy/X1X2_Naive_SPO+DM/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM_result.csv --> X1X2_policy/X1X2_Naive_SPO+DM/X1X2_Naive_SPO+DM_result.xlsx

● Naive SPO+ DM

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1X2_policy/X1X2_Naive_SPO+DM_misspecified2/X1X2_Naive_SPO+DM_misspecified2.py --> X1X2_policy/X1X2_Naive_SPO+DM_misspecified2/regret_no_kernel_CDM & regret_no_kernel_Wrong_CDM --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DM_misspecified2/X1X2_Naive_SPO+DM_misspecified2_result.csv --> X1X2_policy/X1X2_Naive_SPO+DM_misspecified2/X1X2_Naive_SPO+DM_misspecified2_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 4
2. $F^{\text{N}}$ is misspecified degree 4, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 4

X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR.py --> X1X2_policy/X1X2_Naive_SPO+DR/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR_result.csv --> X1X2_policy/X1X2_Naive_SPO+DR/X1X2_Naive_SPO+DR_result.xlsx

● Naive SPO+ DR

1. Nuisance Model $F^{\text{N}}$ is well-specified, Policy-inducing model $F$ is misspecified degree 2
2. $F^{\text{N}}$ is misspecified degree 2, Policy-inducing model $F$ is well-specified
3. Nuisance Model $F^{\text{N}}$, Nuisance Model $F^{\text{N}}$ are both misspecified degree 2

X1X2_policy/X1X2_Naive_SPO+DR_misspecified2/X1X2_Naive_SPO+DR_misspecified2.py --> X1X2_policy/X1X2_Naive_SPO+DR_misspecified2/regret_no_kernel_CDR & regret_no_kernel_Wrong_CDR --> Result_processing_example_code.R --> X1X2_policy/X1X2_Naive_SPO+DR_misspecified2/X1X2_Naive_SPO+DR_misspecified2_result.csv --> X1X2_policy/X1X2_Naive_SPO+DR_misspecified2/X1X2_Naive_SPO+DR_misspecified2_result.xlsx

Dependencies

Python 3.8.8

● gurobipy 11.0.0

● joblib 1.0.1

● numpy 1.20.1

● scikit-learn 0.24.1

R 3.6.3

● tidyverse 1.3.1