Learning Optimal and Sample-Efficient Decision Policies with Guarantees

Daqian Shao

cs.LGFeb 20, 2026

Learning Optimal and Sample-Efficient Decision Policies with Guarantees

Authors: Daqian Shao

Organizations: Wolfson College University of Oxford

Abstract

The paradigm of decision-making has been revolutionised by reinforcement learning and deep learning. Although this has led to significant progress in domains such as robotics, healthcare, and finance, the use of RL in practice is challenging, particularly when learning decision policies in high-stakes applications that may require guarantees. Traditional RL algorithms rely on a large number of online interactions with the environment, which is problematic in scenarios where online interactions are costly, dangerous, or infeasible. However, learning from offline datasets is hindered by the presence of hidden confounders. Such confounders can cause spurious correlations in the dataset and can mislead the agent into taking suboptimal or adversarial actions. Firstly, we address the problem of learning from offline datasets in the presence of hidden confounders. We work with instrumental variables (IVs) to identify the causal effect, which is an instance of a conditional moment restrictions (CMR) problem. Inspired by double/debiased machine learning, we derive a sample-efficient algorithm for solving CMR problems with convergence and optimality guarantees, which outperforms state-of-the-art algorithms. Secondly, we relax the conditions on the hidden confounders in the setting of (offline) imitation learning, and adapt our CMR estimator to derive an algorithm that can learn effective imitator policies with convergence rate guarantees. Finally, we consider the problem of learning high-level objectives expressed in linear temporal logic (LTL) and develop a provably optimal learning algorithm that improves sample efficiency over existing methods. Through evaluation on reinforcement learning benchmarks and synthetic and semi-synthetic datasets, we demonstrate the usefulness of the methods developed in this thesis in real-world decision making.

Figures & tables

Figure 2.1 : An overview of the types of problems considered in policy learning, categorised by the learning objective and the data source from which the policy learns. Problems considered in this thesis are highlighted with the corresponding chapters.

Figure 2.2 : The causal graph of outcome $Y$ , treatment $A$ and hidden confounder $U$ .

Figure 2.3 : The causal graph of outcome $Y$ , treatment $A$ , hidden confounder $U$ and an instrumental variable $Z$ .

Figure 2.4 : The causal graph of outcome $Y$ , treatment $A$ , hidden confounder $U$ and proxies $V$ and $W$ .

Figure 4.1 : The causal graph of the contextual IV setting, where $R=f_{r}(C,A)+\epsilon$ and $Z$ is an instrumental variable that affects $R$ only through $A$ .

Panel of Figure 4 — Figure 4.2 : Results on the ticket demand dataset with low-dimensional context.

Figure 5.1 : A causal graph of MDPs with hidden confounders $u_{t}=(u^{o}_{t},u^{\epsilon}_{t})$ . The black dotted lines represent the causal effect of the expert-observable confounder $u^{o}_{t}$ , which directly affects the expert action $a_{t}$ . It also directly affects $s_{t+1}$ and $r_{t}$ . The red dotted lines represent the causal effect of the expert-unobservable $u^{\epsilon}_{t}$ , which acts as confounding noise and directly affects the states and actions. $u^{\epsilon}_{t}$ does not directly affect $r_{t}$ (following Swamy et al. (2022a) ) because the expert policy does not take $u^{\epsilon}_{t}$ into account, and letting $u^{\epsilon}_{t}$ directly affect $r_{t}$ would only add noise to the expected return.

Panel of Figure 5 — Figure 5.2 : Plane Ticket Environment ( Example 5.1 ): On the left, the MSE between the learnt policy and the expert. On the right, the average reward of our approach and baselines.

Panel of Figure 6 — Figure 6.1 : An LDBA for “ FG a & G !c” (left), and a probabilistic gate MDP (right) motivating the $K$ counter (see Example 6.5 ).

Figure 6.3 : Sensitivity analysis on key hyperparameters.

Appendix figures & tables15 assets

Supplementary material from the paper’s appendix.

Appendix

Figure A.1 : A graph of the nonlinear function $\psi(t)$ in the ticket demand dataset for IV regression.

Figure A.2 : An example of dSprites image, which is used as the treatment $A$ in PCL experiments. Its scale, rotation, $x$ position and $y$ position are randomly generated.

Table A.1 : Network architecture for DML-CMR and CE-DML-CMR for the ticket demand low-dimensional dataset for IV regression. For the input layer, we provide the input variables. For mixture of Gaussians output, we report the number of components. The dropout rate is given in the main text.

Layer Type	Configuration
Input	$28\times 28$
Conv + ReLU	$3\times 3\times 32$ , s:1, p:0
Max Pooling	$2\times 2$ , s:2
Dropout	-
Conv + ReLU	$3\times 3\times 64$ , s:1, p:0
Max Pooling	$2\times 2$ , s:2

Appendix

Table A.2 : Network architecture of the feature extractor used for the ticket demand dataset with MNIST for IV regression. For each convolution layer, we list the kernel size, input dimension and output dimension, where s stands for stride and p stands for padding. For max-pooling, we provide the size of the kernel. The dropout rate here is set to 0.3. We denote this feature extractor as ImageFeature .

Table A.3 : Network architecture for DML-CMR and CE-DML-CMR for the ticket demand dataset with MNIST for IV regression. For the input layer, we provide the input variables. For a mixture of Gaussians output, we report the number of components. The dropout rate is given in the main text.

Table A.4 : Network architecture for DML-CMR and CE-DML-CMR for the ticket demand dataset for PCL. For the input layer, we provide the input variables. For mixture of Gaussians output, we report the number of components. The dropout rate is given in the main text.

Layer Type	Configuration
Input	$64\times 64$
Conv + ReLU	$5\times 5\times 64$ , s:1, p:0
Max Pooling	$2\times 2$ , s:2
Dropout	-
Conv + ReLU	$5\times 5\times 128$ , s:1, p:0
Max Pooling	$2\times 2$ , s:2

Appendix

Table A.5 : Network architecture of the feature extractor used for the dSprites image dataset for PCL. For each convolution layer, we list the kernel size, input dimension and output dimension, where s stands for stride and p stands for padding. For max-pooling, we provide the size of the kernel. The dropout rate here is set to 0.2.

Figure A.5 : Comparing the average reward obtained by policies learnt using offline bandit algorithms that do not take IVs into account with a random policy on the ticket demand dataset with low-dimensional context.

IV Strength	1.0	0.8	0.6	0.4	0.2	0.01
DML-CMR	0.0676(0.0116)	0.0984(0.0161)	0.1295(0.0168)	0.1859(0.0376)	0.2899(0.0494)	0.4872(0.1295)
CE-DML-CMR	0.0765(0.0119)	0.1064(0.0120)	0.1514(0.0203)	0.2070(0.0329)	0.3194(0.0572)	0.5302(0.1625)
DeepIV	0.1213(0.0209)	0.2039(0.0269)	0.3051(0.0415)	0.4476(0.0656)	0.6891(0.1210)	0.9293(0.2382)
DFIV	0.1124(0.0481)	0.1586(0.0320)	0.3080(0.1907)	0.8117(0.2779)	0.9622(0.3892)	1.6503(0.6845)
DeepGMM	0.2699(0.0522)	0.3330(0.1171)	0.4762(0.1056)	0.8666(0.2248)	1.0056(0.4334)	2.0218(0.6555)
KIV	0.2312(0.0272)	0.3149(0.0218)	0.4275(0.0368)	0.6646(0.0538)	0.8099(0.0657)	1.226(0.1014)

Appendix

Table A.6 : Results for the low-dimensional ticket demand dataset when the IV is weakly correlated with the action.

IV Strength	Dataset Size	DNN (results in the paper)	Random Forests	Gradient Boosting
DML-CMR	2000	0.1308(0.0206)	0.1689(0.0172)	0.1301(0.0112)
CE-DML-CMR	2000	0.1410(0.0246)	0.1733(0.0198)	0.1329(0.0125)
DeepIV	2000	0.2388(0.0438)	0.2642(0.0261)	0.2052(0.0232)
DML-CMR	5000	0.0676(0.0129)	0.1067(0.0131)	0.0632(0.0107)
CE-DML-CMR	5000	0.0765(0.0119)	0.1154(0.0138)	0.0699(0.0069)
DeepIV	5000	0.1213(0.0209)	0.1626(0.0128)	0.1020(0.0091)

Appendix

Table A.7 : Results for the low-dimensional ticket demand dataset using tree-based estimators compared to DNN estimators.

Learning Rate	Weight Decay	Dropout	DNN Width	DML-CMR	CE-DML-CMR
0.0002	0.001	0.1	128	0.0676(0.0129)	0.0765(0.0119)
0.0005				0.0752(0.0122)	0.0897(0.0196)
0.0001				0.0703(0.0195)	0.0794(0.0201)
	0.0005			0.0794(0.0185)	0.0823(0.0149)
	0.005			0.0765(0.0135)	0.0809(0.0159)
	0.01			0.0820(0.0162)	0.0865(0.0174)

Appendix

Table A.8 : Results for the low-dimensional ticket demand dataset for a range of hyperparameter values. The default hyperparameters in this case are: learning rate=0.0002, weight decay=0.001, dropout=0.1 and DNN width 128. The bold results are the best performing hyperparameters.

Learning Rate	Weight Decay	Dropout	CNN Channels	DML-CMR	CE-DML-CMR
0.001	0.05	0.2	64	0.3513(0.0125)	0.3808(0.0150)
0.0005				0.4063(0.0129)	0.5008(0.0369)
0.002				0.3659(0.0219)	0.4133(0.0267)
0.005				0.3377(0.0218)	0.3555(0.0202)
	0.01			0.3935(0.0176)	0.4461(0.0478)
	0.02			0.3595(0.03013)	0.3851(0.0293)

Appendix

Table A.9 : Results for the high-dimensional ticket demand dataset for a range of hyperparameter values. The default hyperparameters in this case are: learning rate 0.001, weight decay=0.05, dropout=0.2 and 64 CNN channels. The bold results are the best performing hyperparameters.

Table B.1 : Network architecture for DML-IL. For the mixture of Gaussians output, we report the number of components. No dropout is used.

Figure C.0 : The optimal policy for the example probabilistic gate MDP task in Figure 6.1

Panel of Figure 33 — Figure C.1 : MDP environments used in the experiments.

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