Estimation of the Average Treatment Effect (ATE) is a core problem in causal inference with strong connections to Off-Policy Evaluation in Reinforcement Learning. This paper considers the problem of adaptively selecting the treatment allocation probability in order to improve estimation of the ATE. The majority of prior work on adaptive ATE estimation focus on asymptotic guarantees, and in turn overlooks important practical considerations such as the difficulty of learning the optimal treatment allocation as well as hyper-parameter selection. Existing non-asymptotic methods are limited by poor empirical performance and exponential dependence on problem parameters. In order to address these gaps, we propose and analyze the Clipped Second Moment Tracking (ClipSMT) algorithm, a variant of an existing algorithm with strong asymptotic optimality guarantees, and provide finite sample bounds on its Neyman regret. Our analysis shows that, in the superpopulation setting, ClipSMT achieves exponential improvements in Neyman regret on two fronts: improving the dependence on $T$ from $O(\sqrt{T})$ to $O(\log T)$, as well as reducing the exponential dependence on problem parameters to a polynomial dependence—although the setting we consider is slightly less general. We conclude with simulations which show the marked improvement of ClipSMT over existing approaches.

Estimation and inference for the Average Treatment Effect (ATE) is a cornerstone of causal inference and often serves as the foundation for developing procedures for more complicated settings. Although traditionally analyzed in a batch setting, recent advances in martingale theory have paved the way for adaptive methods that can enhance the power of downstream inference. Despite these advances, progress in understanding and developing adaptive algorithms remains in its early stages. Existing work either focus on asymptotic analyses that overlook exploration-exploitation trade-offs relevant in finite-sample regimes or rely on simpler but suboptimal estimators. In this work, we address these limitations by studying adaptive sampling procedures that take advantage of the asymptotically optimal Augmented Inverse Probability Weighting (AIPW) estimator. Our analysis uncovers challenges obscured by asymptotic approaches and introduces a novel algorithmic design principle reminiscent of optimism in multi-armed bandits. This principled approach enables our algorithm to achieve significant theoretical and empirical gains compared to previous methods. Our findings mark a step forward in the advancement of adaptive causal inference methods in theory and practice.

Restricted Boltzmann Machines and Deep Belief Networks have been successfully used in probabilistic generative model applications such as image occlusion removal, pattern completion and motion synthesis. Generative inference in such algorithms can be performed very efficiently on hardware using a Markov Chain Monte Carlo procedure called Gibbs sampling, where stochastic samples are drawn from noisy integrate and fire neuron s implemented on neuromorphic substrates. Currently, no satisfactory metrics exist for evaluating the generative performance of such algorithms implemented on high-dimensional data for neuromorphic platforms. This paper demonstrates the application of nonparametric goodness-of-fit testing to both quantify the generative performance as well as provide decision-directed criteria for choosing the parameters of the neuromorphic Gibbs sampler and optimizing usage of hardware resources used during sampling.