Coupon allocation drives customer purchases and boosts revenue. However, it presents a fundamental trade-off between exploiting the current optimal policy to maximize immediate revenue and exploring alternative policies to collect data for future policy improvement via off-policy evaluation (OPE). While online A/B testing can validate new policies, it risks compromising short-term revenue. Conversely, relying solely on an exploitative policy hinders the ability to reliably estimate and enhance future policies. To balance this trade-off, we propose a novel approach that combines a model-based revenue maximization policy and a randomized exploration policy for data collection. Our framework enables flexibly adjusting the mixture ratio between these two policies to optimize the balance between short-term revenue and future policy improvement. We formulate the problem of determining the optimal mixture ratio between a model-based revenue maximization policy and a randomized exploration policy for data collection. We empirically verified the effectiveness of the proposed mixed policy using both synthetic and real-world data. Our main contributions are: (1) Demonstrating a mixed policy combining deterministic and probabilistic policies, flexibly adjusting the data collection vs. revenue trade-off. (2) Formulating the optimal mixture ratio problem as multi-objective optimization, enabling quantitative evaluation of this trade-off. By optimizing the mixture ratio, businesses can maximize revenue while ensuring reliable future OPE and policy improvement. This framework is applicable in any context where the exploration-exploitation trade-off is relevant.

This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by a model. Typical AR methods provide a reasonable action by solving an optimization task of minimizing the required effort among executable actions. In practice, however, such actions do not always exist for models optimized only for predictive performance. To alleviate this issue, we formulate the task of learning an accurate classification tree under the constraint of ensuring the existence of reasonable actions for as many instances as possible. Then, we propose an efficient top-down greedy algorithm by leveraging the adversarial training techniques. We also show that our proposed algorithm can be applied to the random forest, which is known as a popular framework for learning tree ensembles. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

This paper introduces SCOPE-RL, a comprehensive open-source Python software designed for offline reinforcement learning (offline RL), off-policy evaluation (OPE), and selection (OPS). Unlike most existing libraries that focus solely on either policy learning or evaluation, SCOPE-RL seamlessly integrates these two key aspects, facilitating flexible and complete implementations of both offline RL and OPE processes. SCOPE-RL put particular emphasis on its OPE modules, offering a range of OPE estimators and robust evaluation-of-OPE protocols. This approach enables more in-depth and reliable OPE compared to other packages. For instance, SCOPE-RL enhances OPE by estimating the entire reward distribution under a policy rather than its mere point-wise expected value. Additionally, SCOPE-RL provides a more thorough evaluation-of-OPE by presenting the risk-return tradeoff in OPE results, extending beyond mere accuracy evaluations in existing OPE literature. SCOPE-RL is designed with user accessibility in mind. Its user-friendly APIs, comprehensive documentation, and a variety of easy-to-follow examples assist researchers and practitioners in efficiently implementing and experimenting with various offline RL methods and OPE estimators, tailored to their specific problem contexts. The documentation of SCOPE-RL is available at https://scope-rl.readthedocs.io/en/latest/.

Off-Policy Evaluation (OPE) aims to assess the effectiveness of counterfactual policies using only offline logged data and is often used to identify the top-k promising policies for deployment in online A/B tests. Existing evaluation metrics for OPE estimators primarily focus on the "accuracy" of OPE or that of downstream policy selection, neglecting risk-return tradeoff in the subsequent online policy deployment. To address this issue, we draw inspiration from portfolio evaluation in finance and develop a new metric, called SharpeRatio@k, which measures the risk-return tradeoff of policy portfolios formed by an OPE estimator under varying online evaluation budgets (k). We validate our metric in two example scenarios, demonstrating its ability to effectively distinguish between low-risk and high-risk estimators and to accurately identify the most efficient estimator. This efficient estimator is characterized by its capability to form the most advantageous policy portfolios, maximizing returns while minimizing risks during online deployment, a nuance that existing metrics typically overlook. These experiments offer several interesting directions and suggestions for future OPE research. Reinforcement Learning (RL) has achieved considerable success in a variety of applications requiring sequential decision-making. Nonetheless, its online learning approach is often seen as problematic due to the need for active interaction with the environment, which can be risky, time-consuming, and unethical (Fu et al., 2021; Matsushima et al., 2021). To mitigate these issues, learning new policies offline from existing historical data, known as Offline RL (Levine et al., 2020), is becoming increasingly popular for real-world applications (Qin et al., 2021). Typically, in the offline RL lifecycle, promising candidate policies are initially screened through Off-Policy Evaluation (OPE) (Fu et al., 2020), followed by the selection of the final production policy from the shortlisted candidates using more dependable online A/B tests (Kurenkov & Kolesnikov, 2022), as shown in Figure 1. When evaluating the efficacy of OPE methods, research has largely concentrated on "accuracy" metrics like mean-squared error (MSE) (Uehara et al., 2022; Voloshin et al., 2019), rank correlation (rankcorr) (Fu et al., 2021; Paine et al., 2020), and regret in subsequent policy selection (Doroudi et al., 2017; Tang & Wiens, 2021). However, these existing metrics do not adequately assess the balance between risk and return experienced by an estimator during the online deployment of selected policies. Crucially, MSE and rankcorr fall short in distinguishing whether an estimator is underevaluating nearoptimal policies or overevaluating poor-performing ones, which influence the risk-return dynamics in OPE and policy selection in different ways.

In modern recommendation systems, unbiased learning-to-rank (LTR) is crucial for prioritizing items from biased implicit user feedback, such as click data. Several techniques, such as Inverse Propensity Weighting (IPW), have been proposed for single-sided markets. However, less attention has been paid to two-sided markets, such as job platforms or dating services, where successful conversions require matching preferences from both users. This paper addresses the complex interaction of biases between users in two-sided markets and proposes a tailored LTR approach. We first present a formulation of feedback mechanisms in two-sided matching platforms and point out that their implicit feedback may include position bias from both user groups. On the basis of this observation, we extend the IPW estimator and propose a new estimator, named two-sided IPW, to address the position bases in two-sided markets. We prove that the proposed estimator satisfies the unbiasedness for the ground-truth ranking metric. We conducted numerical experiments on real-world two-sided platforms and demonstrated the effectiveness of our proposed method in terms of both precision and robustness. Our experiments showed that our method outperformed baselines especially when handling rare items, which are less frequently observed in the training data.

Counterfactual Explanation (CE) is a post-hoc explanation method that provides a perturbation for altering the prediction result of a classifier. Users can interpret the perturbation as an "action" to obtain their desired decision results. Existing CE methods require complete information on the features of an input instance. However, we often encounter missing values in a given instance, and the previous methods do not work in such a practical situation. In this paper, we first empirically and theoretically show the risk that missing value imputation methods affect the validity of an action, as well as the features that the action suggests changing. Then, we propose a new framework of CE, named Counterfactual Explanation by Pairs of Imputation and Action (CEPIA), that enables users to obtain valid actions even with missing values and clarifies how actions are affected by imputation of the missing values. Specifically, our CEPIA provides a representative set of pairs of an imputation candidate for a given incomplete instance and its optimal action. We formulate the problem of finding such a set as a submodular maximization problem, which can be solved by a simple greedy algorithm with an approximation guarantee. Experimental results demonstrated the efficacy of our CEPIA in comparison with the baselines in the presence of missing values.

B\'ezier simplex fitting algorithms have been recently proposed to approximate the Pareto set/front of multi-objective continuous optimization problems. These new methods have shown to be successful at approximating various shapes of Pareto sets/fronts when sample points exactly lie on the Pareto set/front. However, if the sample points scatter away from the Pareto set/front, those methods often likely suffer from over-fitting. To overcome this issue, in this paper, we extend the B\'ezier simplex model to a probabilistic one and propose a new learning algorithm of it, which falls into the framework of approximate Bayesian computation (ABC) based on the Wasserstein distance. We also study the convergence property of the Wasserstein ABC algorithm. An extensive experimental evaluation on publicly available problem instances shows that the new algorithm converges on a finite sample. Moreover, it outperforms the deterministic fitting methods on noisy instances.

This paper discusses the prediction of hierarchical time series, where each upper-level time series is calculated by summing appropriate lower-level time series. Forecasts for such hierarchical time series should be coherent, meaning that the forecast for an upper-level time series equals the sum of forecasts for corresponding lower-level time series. Previous methods for making coherent forecasts consist of two phases: first computing base (incoherent) forecasts and then reconciling those forecasts based on their inherent hierarchical structure. With the aim of improving time series predictions, we propose a structured regularization method for completing both phases simultaneously. The proposed method is based on a prediction model for bottom-level time series and uses a structured regularization term to incorporate upper-level forecasts into the prediction model. We also develop a backpropagation algorithm specialized for application of our method to artificial neural networks for time series prediction. Experimental results using synthetic and real-world datasets demonstrate the superiority of our method in terms of prediction accuracy and computational efficiency.

The Bezier simplex fitting is a novel data modeling technique which exploits geometric structures of data to approximate the Pareto front of multi-objective optimization problems. There are two fitting methods based on different sampling strategies. The inductive skeleton fitting employs a stratified subsampling from each skeleton of a simplex, whereas the all-at-once fitting uses a non-stratified sampling which treats a simplex as a whole. In this paper, we analyze the asymptotic risks of those B\'ezier simplex fitting methods and derive the optimal subsample ratio for the inductive skeleton fitting. It is shown that the inductive skeleton fitting with the optimal ratio has a smaller risk when the degree of a Bezier simplex is less than three. Those results are verified numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a Bezier simplex of degree two where the inductive skeleton fitting outperforms. The latter can be represented by a Bezier simplex of degree three where the all-at-once fitting gets an advantage.