In off-policy reinforcement learning, a behaviour policy performs exploratory interactions with the environment to obtain state-action-reward samples which are then used to learn a target policy that optimises the expected return. This leads to a problem of off-policy evaluation, where one needs to evaluate the target policy from samples collected by the often unrelated behaviour policy. Importance sampling is a traditional statistical technique that is often applied to off-policy evaluation. While importance sampling estimators are unbiased, their variance increases exponentially with the horizon of the decision process due to computing the importance weight as a product of action probability ratios, yielding estimates with low accuracy for domains involving long-term planning. This paper proposes state-based importance sampling (SIS), which drops the action probability ratios of sub-trajectories with "neglible states" -- roughly speaking, those for which the chosen actions have no impact on the return estimate -- from the computation of the importance weight. Theoretical results show that this results in a reduction of the exponent in the variance upper bound as well as improving the mean squared error. An automated search algorithm based on covariance testing is proposed to identify a negligible state set which has minimal MSE when performing state-based importance sampling. Experiments are conducted on a lift domain, which include "lift states" where the action has no impact on the following state and reward. The results demonstrate that using the search algorithm, SIS yields reduced variance and improved accuracy compared to traditional importance sampling, per-decision importance sampling, and incremental importance sampling.
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The Shapley value (SV) has emerged as a promising method for data valuation. However, computing or estimating the SV is often computationally expensive. To overcome this challenge, Jia et al. (2019) propose an advanced SV estimation algorithm called ``Group Testing-based SV estimator'' which achieves favorable asymptotic sample complexity. In this technical note, we present several improvements in the analysis and design choices of this SV estimator. Moreover, we point out that the Group Testing-based SV estimator does not fully reuse the collected samples. Our analysis and insights contribute to a better understanding of the challenges in developing efficient SV estimation algorithms for data valuation.
Epilepsy is a chronic neurological disorder that affects a significant portion of the human population and imposes serious risks in the daily life of patients. Despite advances in machine learning and IoT, small, nonstigmatizing wearable devices for continuous monitoring and detection in outpatient environments are not yet available. Part of the reason is the complexity of epilepsy itself, including highly imbalanced data, multimodal nature, and very subject-specific signatures. However, another problem is the heterogeneity of methodological approaches in research, leading to slower progress, difficulty comparing results, and low reproducibility. Therefore, this article identifies a wide range of methodological decisions that must be made and reported when training and evaluating the performance of epilepsy detection systems. We characterize the influence of individual choices using a typical ensemble random-forest model and the publicly available CHB-MIT database, providing a broader picture of each decision and giving good-practice recommendations, based on our experience, where possible.
Evolution Strategy (ES) is a powerful black-box optimization technique based on the idea of natural evolution. In each of its iterations, a key step entails ranking candidate solutions based on some fitness score. For an ES method in Reinforcement Learning (RL), this ranking step requires evaluating multiple policies. This is presently done via on-policy approaches: each policy's score is estimated by interacting several times with the environment using that policy. This leads to a lot of wasteful interactions since, once the ranking is done, only the data associated with the top-ranked policies is used for subsequent learning. To improve sample efficiency, we propose a novel off-policy alternative for ranking, based on a local approximation for the fitness function. We demonstrate our idea in the context of a state-of-the-art ES method called the Augmented Random Search (ARS). Simulations in MuJoCo tasks show that, compared to the original ARS, our off-policy variant has similar running times for reaching reward thresholds but needs only around 70% as much data. It also outperforms the recent Trust Region ES. We believe our ideas should be extendable to other ES methods as well.
Vertical Federated Learning (VFL) enables multiple data owners, each holding a different subset of features about largely overlapping sets of data sample(s), to jointly train a useful global model. Feature selection (FS) is important to VFL. It is still an open research problem as existing FS works designed for VFL either assumes prior knowledge on the number of noisy features or prior knowledge on the post-training threshold of useful features to be selected, making them unsuitable for practical applications. To bridge this gap, we propose the Federated Stochastic Dual-Gate based Feature Selection (FedSDG-FS) approach. It consists of a Gaussian stochastic dual-gate to efficiently approximate the probability of a feature being selected, with privacy protection through Partially Homomorphic Encryption without a trusted third-party. To reduce overhead, we propose a feature importance initialization method based on Gini impurity, which can accomplish its goals with only two parameter transmissions between the server and the clients. Extensive experiments on both synthetic and real-world datasets show that FedSDG-FS significantly outperforms existing approaches in terms of achieving accurate selection of high-quality features as well as building global models with improved performance.
Deep Policy Gradient (PG) algorithms employ value networks to drive the learning of parameterized policies and reduce the variance of the gradient estimates. However, value function approximation gets stuck in local optima and struggles to fit the actual return, limiting the variance reduction efficacy and leading policies to sub-optimal performance. This paper focuses on improving value approximation and analyzing the effects on Deep PG primitives such as value prediction, variance reduction, and correlation of gradient estimates with the true gradient. To this end, we introduce a Value Function Search that employs a population of perturbed value networks to search for a better approximation. Our framework does not require additional environment interactions, gradient computations, or ensembles, providing a computationally inexpensive approach to enhance the supervised learning task on which value networks train. Crucially, we show that improving Deep PG primitives results in improved sample efficiency and policies with higher returns using common continuous control benchmark domains.
We consider the problem of evaluating the performance of a decision policy using past observational data. The outcome of a policy is measured in terms of a loss (aka. disutility or negative reward) and the main problem is making valid inferences about its out-of-sample loss when the past data was observed under a different and possibly unknown policy. Using a sample-splitting method, we show that it is possible to draw such inferences with finite-sample coverage guarantees about the entire loss distribution, rather than just its mean. Importantly, the method takes into account model misspecifications of the past policy -- including unmeasured confounding. The evaluation method can be used to certify the performance of a policy using observational data under a specified range of credible model assumptions.
With historic misses in the 2016 and 2020 US Presidential elections, interest in measuring polling errors has increased. The most common method for measuring directional errors and non-sampling excess variability during a postmortem for an election is by assessing the difference between the poll result and election result for polls conducted within a few days of the day of the election. Analyzing such polling error data is notoriously difficult with typical models being extremely sensitive to the time between the poll and the election. We leverage hidden Markov models traditionally used for election forecasting to flexibly capture time-varying preferences and treat the election result as a peak at the typically hidden Markovian process. Our results are much less sensitive to the choice of time window, avoid conflating shifting preferences with polling error, and are more interpretable despite a highly flexible model. We demonstrate these results with data on polls from the 2004 through 2020 US Presidential elections and 1992 through 2020 US Senate elections, concluding that previously reported estimates of bias in Presidential elections were too extreme by 10\%, estimated bias in Senatorial elections was too extreme by 25\%, and excess variability estimates were also too large.
Semiparametric inference on average causal effects from observational data is based on assumptions yielding identification of the effects. In practice, several distinct identifying assumptions may be plausible; an analyst has to make a delicate choice between these models. In this paper, we study three identifying assumptions based on the potential outcome framework: the back-door assumption, which uses pre-treatment covariates, the front-door assumption, which uses mediators, and the two-door assumption using pre-treatment covariates and mediators simultaneously. We provide the efficient influence functions and the corresponding semiparametric efficiency bounds that hold under these assumptions, and their combinations. We demonstrate that neither of the identification models provides uniformly the most efficient estimation and give conditions under which some bounds are lower than others. We show when semiparametric estimating equation estimators based on influence functions attain the bounds, and study the robustness of the estimators to misspecification of the nuisance models. The theory is complemented with simulation experiments on the finite sample behavior of the estimators. The results obtained are relevant for an analyst facing a choice between several plausible identifying assumptions and corresponding estimators. Our results show that this choice implies a trade-off between efficiency and robustness to misspecification of the nuisance models.
Reinforcement Learning has suffered from poor reward specification, and issues for reward hacking even in simple enough domains. Preference Based Reinforcement Learning attempts to solve the issue by utilizing binary feedbacks on queried trajectory pairs by a human in the loop indicating their preferences about the agent's behavior to learn a reward model. In this work, we present a state augmentation technique that allows the agent's reward model to be robust and follow an invariance consistency that significantly improved performance, i.e. the reward recovery and subsequent return computed using the learned policy over our baseline PEBBLE. We validate our method on three domains, Mountain Car, a locomotion task of Quadruped-Walk, and a robotic manipulation task of Sweep-Into, and find that using the proposed augmentation the agent not only benefits in the overall performance but does so, quite early in the agent's training phase.
Ensuring that analyses performed on a dataset are representative of the entire population is one of the central problems in statistics. Most classical techniques assume that the dataset is independent of the analyst's query and break down in the common setting where a dataset is reused for multiple, adaptively chosen, queries. This problem of \emph{adaptive data analysis} was formalized in the seminal works of Dwork et al. (STOC, 2015) and Hardt and Ullman (FOCS, 2014). We identify a remarkably simple set of assumptions under which the queries will continue to be representative even when chosen adaptively: The only requirements are that each query takes as input a random subsample and outputs few bits. This result shows that the noise inherent in subsampling is sufficient to guarantee that query responses generalize. The simplicity of this subsampling-based framework allows it to model a variety of real-world scenarios not covered by prior work. In addition to its simplicity, we demonstrate the utility of this framework by designing mechanisms for two foundational tasks, statistical queries and median finding. In particular, our mechanism for answering the broadly applicable class of statistical queries is both extremely simple and state of the art in many parameter regimes.
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